TY  - JOUR
AU  - Tomović, Aleksandar
AU  - Šalinić, Slaviša
AU  - Obradović, Aleksandar
AU  - Zorić, Nemanja
AU  - Mitrović, Zoran
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6872
AB  - Purpose This study aims to obtain and present the closed-form solution of coupled
axial-bending vibration problem for the general case of axially functionally graded
(AFG) beams, to create the frequency equation and to propose numerical method for
computing natural frequencies.
Methods The general model of a beam is introduced using two cylindrical springs, one
rotational spring, and a rigid body at each beam end. Mass centers of bodies are
placed eccentrically in axial and transverse direction with respect to end points of the
beam. The general boundary conditions are modelled by linearized Newton-Euler
differential equations and the general case of the in-plane axial-bending vibrations of
AFG beams is covered. It is assumed that the beam is made of a functionally graded
material whose material and cross-sectional characteristics change along its
longitudinal axis without any restrictions. The Euler-Bernoulli constitutive theory is
applied for modelling. Partial differential equations of motion are transformed into a
system of ordinary differential equations with variable coefficients, the form suitable for
the implementation of the symbolic-numeric methods of initial parameters. Natural
frequencies of the beam are computed as numerical solutions of the exact frequency
equation.
Results and conclusions The closed-form solution of coupled axial-bending vibrations
is derived for general case of AFG beams. Orthogonality conditions of mode shapes
are derived, and constants in time function. Also, the frequency equation is derived and
solved numerically in order to obtain natural frequencies. Obtained results of natural
frequencies and mode shapes are compared to those available in open literature.
PB  - Springer
T2  - Journal of Vibration Engineering & Technologies
T1  - Coupled bending and axial vibrations of axially functionally graded Euler-Bernoulli beams
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6872
ER  - 

@article{
author = "Tomović, Aleksandar and Šalinić, Slaviša and Obradović, Aleksandar and Zorić, Nemanja and Mitrović, Zoran",
year = "2023",
abstract = "Purpose This study aims to obtain and present the closed-form solution of coupled
axial-bending vibration problem for the general case of axially functionally graded
(AFG) beams, to create the frequency equation and to propose numerical method for
computing natural frequencies.
Methods The general model of a beam is introduced using two cylindrical springs, one
rotational spring, and a rigid body at each beam end. Mass centers of bodies are
placed eccentrically in axial and transverse direction with respect to end points of the
beam. The general boundary conditions are modelled by linearized Newton-Euler
differential equations and the general case of the in-plane axial-bending vibrations of
AFG beams is covered. It is assumed that the beam is made of a functionally graded
material whose material and cross-sectional characteristics change along its
longitudinal axis without any restrictions. The Euler-Bernoulli constitutive theory is
applied for modelling. Partial differential equations of motion are transformed into a
system of ordinary differential equations with variable coefficients, the form suitable for
the implementation of the symbolic-numeric methods of initial parameters. Natural
frequencies of the beam are computed as numerical solutions of the exact frequency
equation.
Results and conclusions The closed-form solution of coupled axial-bending vibrations
is derived for general case of AFG beams. Orthogonality conditions of mode shapes
are derived, and constants in time function. Also, the frequency equation is derived and
solved numerically in order to obtain natural frequencies. Obtained results of natural
frequencies and mode shapes are compared to those available in open literature.",
publisher = "Springer",
journal = "Journal of Vibration Engineering & Technologies",
title = "Coupled bending and axial vibrations of axially functionally graded Euler-Bernoulli beams",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6872"
}

Tomović, A., Šalinić, S., Obradović, A., Zorić, N.,& Mitrović, Z.. (2023). Coupled bending and axial vibrations of axially functionally graded Euler-Bernoulli beams. in Journal of Vibration Engineering & Technologies
Springer..
https://hdl.handle.net/21.15107/rcub_machinery_6872

Tomović A, Šalinić S, Obradović A, Zorić N, Mitrović Z. Coupled bending and axial vibrations of axially functionally graded Euler-Bernoulli beams. in Journal of Vibration Engineering & Technologies. 2023;.
https://hdl.handle.net/21.15107/rcub_machinery_6872 .

Tomović, Aleksandar, Šalinić, Slaviša, Obradović, Aleksandar, Zorić, Nemanja, Mitrović, Zoran, "Coupled bending and axial vibrations of axially functionally graded Euler-Bernoulli beams" in Journal of Vibration Engineering & Technologies (2023),
https://hdl.handle.net/21.15107/rcub_machinery_6872 .

TY  - CONF
AU  - Veg, Marko
AU  - Tomović, Aleksandar
AU  - Šiniković, Goran
AU  - Dikić, Stefan
AU  - Zorić, Nemanja
AU  - Šalinić, Slaviša
AU  - Obradović, Aleksandar
AU  - Mitrović, Zoran
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6909
AB  - This paper presents the continuation of the research by the authors on the topics of vibration analysis. Namely, a tapered cantilever beam has been studied in theoretical and experimental terms. The beam is 3D printed using the FDM technique of PLA material with two characteristics patterns, linear layered and the two-dimensional periodic structure. The former of the two is conducted to tensile test in order to determine elasticity modulus, so the computations of natural frequencies could be conducted. The experimental part of the research, in terms of natural frequency, is conducted on six specimens with various eccentricities. The angular frequencies of one representative sample, obtained by analytical computations and experimental measurement are compared.
C3  - 9th International Congress of the Serbian Society of Mechanics July 5-7, 2023, Vrnjačka Banja, Serbia
T1  - EXPERIMENTAL AND NUMERICAL APPROACH TO NATURAL FREQUENCY OF TAPERED 3D PRINTED CANTILEVER BEAM A TIP BODY
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6909
ER  - 

@conference{
author = "Veg, Marko and Tomović, Aleksandar and Šiniković, Goran and Dikić, Stefan and Zorić, Nemanja and Šalinić, Slaviša and Obradović, Aleksandar and Mitrović, Zoran",
year = "2023",
abstract = "This paper presents the continuation of the research by the authors on the topics of vibration analysis. Namely, a tapered cantilever beam has been studied in theoretical and experimental terms. The beam is 3D printed using the FDM technique of PLA material with two characteristics patterns, linear layered and the two-dimensional periodic structure. The former of the two is conducted to tensile test in order to determine elasticity modulus, so the computations of natural frequencies could be conducted. The experimental part of the research, in terms of natural frequency, is conducted on six specimens with various eccentricities. The angular frequencies of one representative sample, obtained by analytical computations and experimental measurement are compared.",
journal = "9th International Congress of the Serbian Society of Mechanics July 5-7, 2023, Vrnjačka Banja, Serbia",
title = "EXPERIMENTAL AND NUMERICAL APPROACH TO NATURAL FREQUENCY OF TAPERED 3D PRINTED CANTILEVER BEAM A TIP BODY",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6909"
}

Veg, M., Tomović, A., Šiniković, G., Dikić, S., Zorić, N., Šalinić, S., Obradović, A.,& Mitrović, Z.. (2023). EXPERIMENTAL AND NUMERICAL APPROACH TO NATURAL FREQUENCY OF TAPERED 3D PRINTED CANTILEVER BEAM A TIP BODY. in 9th International Congress of the Serbian Society of Mechanics July 5-7, 2023, Vrnjačka Banja, Serbia.
https://hdl.handle.net/21.15107/rcub_machinery_6909

Veg M, Tomović A, Šiniković G, Dikić S, Zorić N, Šalinić S, Obradović A, Mitrović Z. EXPERIMENTAL AND NUMERICAL APPROACH TO NATURAL FREQUENCY OF TAPERED 3D PRINTED CANTILEVER BEAM A TIP BODY. in 9th International Congress of the Serbian Society of Mechanics July 5-7, 2023, Vrnjačka Banja, Serbia. 2023;.
https://hdl.handle.net/21.15107/rcub_machinery_6909 .

Veg, Marko, Tomović, Aleksandar, Šiniković, Goran, Dikić, Stefan, Zorić, Nemanja, Šalinić, Slaviša, Obradović, Aleksandar, Mitrović, Zoran, "EXPERIMENTAL AND NUMERICAL APPROACH TO NATURAL FREQUENCY OF TAPERED 3D PRINTED CANTILEVER BEAM A TIP BODY" in 9th International Congress of the Serbian Society of Mechanics July 5-7, 2023, Vrnjačka Banja, Serbia (2023),
https://hdl.handle.net/21.15107/rcub_machinery_6909 .

TY  - JOUR
AU  - Šalinić, Slaviša
AU  - Obradović, Aleksandar
AU  - Tomović, Aleksandar
AU  - Trifković, Dragan
AU  - Grbović, Aleksandar
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6802
AB  - The coupled axial-bending vibration of an axially functionally graded Timoshenko cantilever beam
of non-uniform cross-section is considered. The coupling phenomenon appears due to the presence of the transverse eccentricity of the mass centre of a rigid body attached to the beam free end. To study the coupled phenomenon, an approach based on the symbolic-numeric method of initial parameters is proposed. The influence of the transverse eccentricity on the cantilever beam natural frequencies and mode shapes is examined. The approach has the potential to be also applied to vibration problems of the systems composed of rigid bodies interconnected by non-uniform non-homogeneous beams.
PB  - Springer
T2  - Meccanica
T1  - Coupled axial-bending vibration of axially functionally graded Timoshenko cantilever beams of non-uniform cross-section with an attached rigid body
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6802
ER  - 

@article{
author = "Šalinić, Slaviša and Obradović, Aleksandar and Tomović, Aleksandar and Trifković, Dragan and Grbović, Aleksandar",
year = "2023",
abstract = "The coupled axial-bending vibration of an axially functionally graded Timoshenko cantilever beam
of non-uniform cross-section is considered. The coupling phenomenon appears due to the presence of the transverse eccentricity of the mass centre of a rigid body attached to the beam free end. To study the coupled phenomenon, an approach based on the symbolic-numeric method of initial parameters is proposed. The influence of the transverse eccentricity on the cantilever beam natural frequencies and mode shapes is examined. The approach has the potential to be also applied to vibration problems of the systems composed of rigid bodies interconnected by non-uniform non-homogeneous beams.",
publisher = "Springer",
journal = "Meccanica",
title = "Coupled axial-bending vibration of axially functionally graded Timoshenko cantilever beams of non-uniform cross-section with an attached rigid body",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6802"
}

Šalinić, S., Obradović, A., Tomović, A., Trifković, D.,& Grbović, A.. (2023). Coupled axial-bending vibration of axially functionally graded Timoshenko cantilever beams of non-uniform cross-section with an attached rigid body. in Meccanica
Springer..
https://hdl.handle.net/21.15107/rcub_machinery_6802

Šalinić S, Obradović A, Tomović A, Trifković D, Grbović A. Coupled axial-bending vibration of axially functionally graded Timoshenko cantilever beams of non-uniform cross-section with an attached rigid body. in Meccanica. 2023;.
https://hdl.handle.net/21.15107/rcub_machinery_6802 .

Šalinić, Slaviša, Obradović, Aleksandar, Tomović, Aleksandar, Trifković, Dragan, Grbović, Aleksandar, "Coupled axial-bending vibration of axially functionally graded Timoshenko cantilever beams of non-uniform cross-section with an attached rigid body" in Meccanica (2023),
https://hdl.handle.net/21.15107/rcub_machinery_6802 .

TY  - CONF
AU  - Tomović, Aleksandar
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6208
AB  - Functionally graded materials can be designed to satisfy a specifc project conditions. Elastic beams made of functionally graded materials have been thoroughly analyzed in the last decades. The literature differs two types of beams of functionally graded materials, namely, sandwich beams and axially functionally graded (AFG) beams. The latter ones will be discussed in this presentation. AFG beams are designed in a manner that mass and/or material characteristics may change along the longitudinal axes of a beam, while the cross sectional area may be constant or may, also change along the axis. Modal analysis is of the utter importance in structural engineering in order to avoid critical behavior of a structure. The procedure for computation of natural frequencies using the Symbolic-Numeric method of initial parameters in differential form (SNMIP) is presented in [2] for the case of axial and transverse vibration of AFG beams. The idea is to discuss the topic of the dependence of natural frequencies to various boundary conditions in the case of an AFG cantilever beam. Governing equations [1] are written in a form suitable for the application of the SNMIP. The Euler-Bernoulli beam theory is implemented in modeling elastic behavior of the beam. Boundary conditions can cause coupling in mode shapes which will be discussed through the example of an AFG cantilever beam with a heavy rigid body eccentrically displaced at the free end of the beam. Even though the equations of axial and transverse vibrations are not coupled the coupling can occur due to boundary conditions as it is presented. For different values of eccentricities coupling of mode shapes will be discussed and the changes in natural frequencies of a cantilever beam presented.
PB  - University of Belgrade, Faculty of Mechanical Engineering
C3  - Abstract Book, Mathematics, Numerics and Applications, MNA 2022
T1  - Inluence of boundary conditions on natural frequencies of axially functionally graded Euler-Bernoulli cantilever beam with attached rigid body at the free end
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6208
ER  - 

@conference{
author = "Tomović, Aleksandar",
year = "2022",
abstract = "Functionally graded materials can be designed to satisfy a specifc project conditions. Elastic beams made of functionally graded materials have been thoroughly analyzed in the last decades. The literature differs two types of beams of functionally graded materials, namely, sandwich beams and axially functionally graded (AFG) beams. The latter ones will be discussed in this presentation. AFG beams are designed in a manner that mass and/or material characteristics may change along the longitudinal axes of a beam, while the cross sectional area may be constant or may, also change along the axis. Modal analysis is of the utter importance in structural engineering in order to avoid critical behavior of a structure. The procedure for computation of natural frequencies using the Symbolic-Numeric method of initial parameters in differential form (SNMIP) is presented in [2] for the case of axial and transverse vibration of AFG beams. The idea is to discuss the topic of the dependence of natural frequencies to various boundary conditions in the case of an AFG cantilever beam. Governing equations [1] are written in a form suitable for the application of the SNMIP. The Euler-Bernoulli beam theory is implemented in modeling elastic behavior of the beam. Boundary conditions can cause coupling in mode shapes which will be discussed through the example of an AFG cantilever beam with a heavy rigid body eccentrically displaced at the free end of the beam. Even though the equations of axial and transverse vibrations are not coupled the coupling can occur due to boundary conditions as it is presented. For different values of eccentricities coupling of mode shapes will be discussed and the changes in natural frequencies of a cantilever beam presented.",
publisher = "University of Belgrade, Faculty of Mechanical Engineering",
journal = "Abstract Book, Mathematics, Numerics and Applications, MNA 2022",
title = "Inluence of boundary conditions on natural frequencies of axially functionally graded Euler-Bernoulli cantilever beam with attached rigid body at the free end",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6208"
}

Tomović, A.. (2022). Inluence of boundary conditions on natural frequencies of axially functionally graded Euler-Bernoulli cantilever beam with attached rigid body at the free end. in Abstract Book, Mathematics, Numerics and Applications, MNA 2022
University of Belgrade, Faculty of Mechanical Engineering..
https://hdl.handle.net/21.15107/rcub_machinery_6208

Tomović A. Inluence of boundary conditions on natural frequencies of axially functionally graded Euler-Bernoulli cantilever beam with attached rigid body at the free end. in Abstract Book, Mathematics, Numerics and Applications, MNA 2022. 2022;.
https://hdl.handle.net/21.15107/rcub_machinery_6208 .

Tomović, Aleksandar, "Inluence of boundary conditions on natural frequencies of axially functionally graded Euler-Bernoulli cantilever beam with attached rigid body at the free end" in Abstract Book, Mathematics, Numerics and Applications, MNA 2022 (2022),
https://hdl.handle.net/21.15107/rcub_machinery_6208 .

TY  - CONF
AU  - Veg, Marko
AU  - Tomović, Aleksandar
AU  - Obradović, Aleksandar
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4065
AB  - In this paper, crossing and veering phenomena are discussed for a two-element frame consisted of beams of constant circular cross-sectional area, mass density and modulus elasticity, see Fig. 1. Depending on the mechanical characteristics of frames when two natural frequencies approach one another over the range of the diameter, their loci may cross or repel. Thus, phenomena of crossing and veering are introduced [1]. These phenomena have been thoroughly studied analytically using various discretization methods as in [2]and [3]. While experimental data on these topics are rather scarce, some experimental studies are given in [4]. An analytical solution for the presented problem is proposed in this paper.
PB  - Univerzitet u Beogradu, Mašinski fakultet
C3  - Book of abstracts: 1st International Conference on Mathematical Modelling in Mechanics and Engineering Mathematical Institute SANU, 08-10. September, 2022.
T1  - Analysis of Crossing and Veering Phenomena in Planar Frame Structures
EP  - 124
SP  - 124
UR  - https://hdl.handle.net/21.15107/rcub_machinery_4065
ER  - 

@conference{
author = "Veg, Marko and Tomović, Aleksandar and Obradović, Aleksandar",
year = "2022",
abstract = "In this paper, crossing and veering phenomena are discussed for a two-element frame consisted of beams of constant circular cross-sectional area, mass density and modulus elasticity, see Fig. 1. Depending on the mechanical characteristics of frames when two natural frequencies approach one another over the range of the diameter, their loci may cross or repel. Thus, phenomena of crossing and veering are introduced [1]. These phenomena have been thoroughly studied analytically using various discretization methods as in [2]and [3]. While experimental data on these topics are rather scarce, some experimental studies are given in [4]. An analytical solution for the presented problem is proposed in this paper.",
publisher = "Univerzitet u Beogradu, Mašinski fakultet",
journal = "Book of abstracts: 1st International Conference on Mathematical Modelling in Mechanics and Engineering Mathematical Institute SANU, 08-10. September, 2022.",
title = "Analysis of Crossing and Veering Phenomena in Planar Frame Structures",
pages = "124-124",
url = "https://hdl.handle.net/21.15107/rcub_machinery_4065"
}

Veg, M., Tomović, A.,& Obradović, A.. (2022). Analysis of Crossing and Veering Phenomena in Planar Frame Structures. in Book of abstracts: 1st International Conference on Mathematical Modelling in Mechanics and Engineering Mathematical Institute SANU, 08-10. September, 2022.
Univerzitet u Beogradu, Mašinski fakultet., 124-124.
https://hdl.handle.net/21.15107/rcub_machinery_4065

Veg M, Tomović A, Obradović A. Analysis of Crossing and Veering Phenomena in Planar Frame Structures. in Book of abstracts: 1st International Conference on Mathematical Modelling in Mechanics and Engineering Mathematical Institute SANU, 08-10. September, 2022.. 2022;:124-124.
https://hdl.handle.net/21.15107/rcub_machinery_4065 .

Veg, Marko, Tomović, Aleksandar, Obradović, Aleksandar, "Analysis of Crossing and Veering Phenomena in Planar Frame Structures" in Book of abstracts: 1st International Conference on Mathematical Modelling in Mechanics and Engineering Mathematical Institute SANU, 08-10. September, 2022. (2022):124-124,
https://hdl.handle.net/21.15107/rcub_machinery_4065 .

TY  - CONF
AU  - Obradović, Aleksandar
AU  - Tomović, Aleksandar
AU  - Šalinić, Slaviša
PY  - 2021
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4027
AB  - The problem of natural frequency computing of an axially functionally graded (AFG)
Timoshenko cantilever beam of a constant cross-sectional area is considered. The longitudinal
and transverse vibrations of the cantilever beam are coupled because of the boundary conditions
at its right end, where the eccentrically displaced rigid body is attached. Once the variables are
separated, the procedure of solving the system of partial differential equations is reduced to
solving the two-point boundary value problem of ordinary linear differential equations with
nonlinear coefficients and linear boundary conditions. In this case, it is possible to transfer
boundary conditions and to reduce the problem to the Cauchy problem of initial conditions. Also,
it is possible to analyze the influence of various parameters on the values of natural frequencies.
The impact of the cross-sectional area on natural frequency is analyzed and illustrated by a
numerical example.
PB  - Beograd : Srpsko društvo za mehaniku
C3  - Proceeding of 5th Serbian-Greek Symposium on Advanced Mechanics Kragujevac, Serbia, June 28-30, 2021
T1  - Free vibration of axially functionally graded Timoshenko cantilever beam with a large rigid body attached at its free end
EP  - 451
SP  - 444
UR  - https://hdl.handle.net/21.15107/rcub_machinery_4027
ER  - 

@conference{
author = "Obradović, Aleksandar and Tomović, Aleksandar and Šalinić, Slaviša",
year = "2021",
abstract = "The problem of natural frequency computing of an axially functionally graded (AFG)
Timoshenko cantilever beam of a constant cross-sectional area is considered. The longitudinal
and transverse vibrations of the cantilever beam are coupled because of the boundary conditions
at its right end, where the eccentrically displaced rigid body is attached. Once the variables are
separated, the procedure of solving the system of partial differential equations is reduced to
solving the two-point boundary value problem of ordinary linear differential equations with
nonlinear coefficients and linear boundary conditions. In this case, it is possible to transfer
boundary conditions and to reduce the problem to the Cauchy problem of initial conditions. Also,
it is possible to analyze the influence of various parameters on the values of natural frequencies.
The impact of the cross-sectional area on natural frequency is analyzed and illustrated by a
numerical example.",
publisher = "Beograd : Srpsko društvo za mehaniku",
journal = "Proceeding of 5th Serbian-Greek Symposium on Advanced Mechanics Kragujevac, Serbia, June 28-30, 2021",
title = "Free vibration of axially functionally graded Timoshenko cantilever beam with a large rigid body attached at its free end",
pages = "451-444",
url = "https://hdl.handle.net/21.15107/rcub_machinery_4027"
}

Obradović, A., Tomović, A.,& Šalinić, S.. (2021). Free vibration of axially functionally graded Timoshenko cantilever beam with a large rigid body attached at its free end. in Proceeding of 5th Serbian-Greek Symposium on Advanced Mechanics Kragujevac, Serbia, June 28-30, 2021
Beograd : Srpsko društvo za mehaniku., 444-451.
https://hdl.handle.net/21.15107/rcub_machinery_4027

Obradović A, Tomović A, Šalinić S. Free vibration of axially functionally graded Timoshenko cantilever beam with a large rigid body attached at its free end. in Proceeding of 5th Serbian-Greek Symposium on Advanced Mechanics Kragujevac, Serbia, June 28-30, 2021. 2021;:444-451.
https://hdl.handle.net/21.15107/rcub_machinery_4027 .

Obradović, Aleksandar, Tomović, Aleksandar, Šalinić, Slaviša, "Free vibration of axially functionally graded Timoshenko cantilever beam with a large rigid body attached at its free end" in Proceeding of 5th Serbian-Greek Symposium on Advanced Mechanics Kragujevac, Serbia, June 28-30, 2021 (2021):444-451,
https://hdl.handle.net/21.15107/rcub_machinery_4027 .

TY  - JOUR
AU  - Tomović, Aleksandar
AU  - Šalinić, Slaviša
AU  - Obradović, Aleksandar
AU  - Grbović, Aleksandar
AU  - Milovančević, Milorad
PY  - 2020
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3269
AB  - In this paper, the coupled axial-bending vibration of planar serial frame structures composed of rigid bodies and Euler-Bernoulli beam segments is considered. The corresponding mode orthogonality conditions for this kind of structures are derived. It is assumed that the mass centers of rigid bodies have both the transverse and the axial eccentricity with respect to beam neutral axes and that the mass centers are located in the plane in which the rigid bodies perform planar motion. The system responses to initial excitation in the case of distinct as well as repeated natural frequencies are considered. Theoretical considerations are accompanied by four numerical examples.
PB  - Elsevier Science Inc, New York
T2  - Applied Mathematical Modelling
T1  - Closed-form solution for the free axial-bending vibration problem of structures composed of rigid bodies and elastic beam segments
EP  - 1167
SP  - 1148
VL  - 77
DO  - 10.1016/j.apm.2019.09.008
ER  - 

@article{
author = "Tomović, Aleksandar and Šalinić, Slaviša and Obradović, Aleksandar and Grbović, Aleksandar and Milovančević, Milorad",
year = "2020",
abstract = "In this paper, the coupled axial-bending vibration of planar serial frame structures composed of rigid bodies and Euler-Bernoulli beam segments is considered. The corresponding mode orthogonality conditions for this kind of structures are derived. It is assumed that the mass centers of rigid bodies have both the transverse and the axial eccentricity with respect to beam neutral axes and that the mass centers are located in the plane in which the rigid bodies perform planar motion. The system responses to initial excitation in the case of distinct as well as repeated natural frequencies are considered. Theoretical considerations are accompanied by four numerical examples.",
publisher = "Elsevier Science Inc, New York",
journal = "Applied Mathematical Modelling",
title = "Closed-form solution for the free axial-bending vibration problem of structures composed of rigid bodies and elastic beam segments",
pages = "1167-1148",
volume = "77",
doi = "10.1016/j.apm.2019.09.008"
}

Tomović, A., Šalinić, S., Obradović, A., Grbović, A.,& Milovančević, M.. (2020). Closed-form solution for the free axial-bending vibration problem of structures composed of rigid bodies and elastic beam segments. in Applied Mathematical Modelling
Elsevier Science Inc, New York., 77, 1148-1167.
https://doi.org/10.1016/j.apm.2019.09.008

Tomović A, Šalinić S, Obradović A, Grbović A, Milovančević M. Closed-form solution for the free axial-bending vibration problem of structures composed of rigid bodies and elastic beam segments. in Applied Mathematical Modelling. 2020;77:1148-1167.
doi:10.1016/j.apm.2019.09.008 .

Tomović, Aleksandar, Šalinić, Slaviša, Obradović, Aleksandar, Grbović, Aleksandar, Milovančević, Milorad, "Closed-form solution for the free axial-bending vibration problem of structures composed of rigid bodies and elastic beam segments" in Applied Mathematical Modelling, 77 (2020):1148-1167,
https://doi.org/10.1016/j.apm.2019.09.008 . .

TY  - CONF
AU  - Zorić, Nemanja
AU  - Tomović, Aleksandar
AU  - Obradović, Aleksandar
AU  - Mitrović, Zoran
PY  - 2020
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4025
AB  - Smart structures are obtained by integration of actuators, sensors and controllers into conventional structures
and they play an important role in the field of active vibration control, especially in aerospace engineering.
Certain elements of a smart structure possess viscoelastic properties which can be modeled by using fractional
calculus. The fractional-order model of a smart structure implies the necessity of using fractional order
controllers instead of integer order controllers. This paper deals with design of the fractional-order proportionalderivative
(PD) controller with robust stability and disturbance rejection. The transfer function of the fractionalorder
PD controller is parameterized, and these parameters are found by using of the Particle swarm
optimization method minimizing a cost function related to the H����� norm. The fractional-order model of the smart
structure is found by experimental identification by using the frequency response method. In order to represent
the efficiency of the proposed controller, obtained results are compared with the corresponding results in the
case when an integer-order PD controller is applied.
C3  - International Conference of Experimental and Numerical Investigations and New Technologies (CNN TECH 2020)
T1  - Fractional-order PD control design for active vibration control of smart structures
EP  - 57
SP  - 57
UR  - https://hdl.handle.net/21.15107/rcub_machinery_4025
ER  - 

@conference{
author = "Zorić, Nemanja and Tomović, Aleksandar and Obradović, Aleksandar and Mitrović, Zoran",
year = "2020",
abstract = "Smart structures are obtained by integration of actuators, sensors and controllers into conventional structures
and they play an important role in the field of active vibration control, especially in aerospace engineering.
Certain elements of a smart structure possess viscoelastic properties which can be modeled by using fractional
calculus. The fractional-order model of a smart structure implies the necessity of using fractional order
controllers instead of integer order controllers. This paper deals with design of the fractional-order proportionalderivative
(PD) controller with robust stability and disturbance rejection. The transfer function of the fractionalorder
PD controller is parameterized, and these parameters are found by using of the Particle swarm
optimization method minimizing a cost function related to the H����� norm. The fractional-order model of the smart
structure is found by experimental identification by using the frequency response method. In order to represent
the efficiency of the proposed controller, obtained results are compared with the corresponding results in the
case when an integer-order PD controller is applied.",
journal = "International Conference of Experimental and Numerical Investigations and New Technologies (CNN TECH 2020)",
title = "Fractional-order PD control design for active vibration control of smart structures",
pages = "57-57",
url = "https://hdl.handle.net/21.15107/rcub_machinery_4025"
}

Zorić, N., Tomović, A., Obradović, A.,& Mitrović, Z.. (2020). Fractional-order PD control design for active vibration control of smart structures. in International Conference of Experimental and Numerical Investigations and New Technologies (CNN TECH 2020), 57-57.
https://hdl.handle.net/21.15107/rcub_machinery_4025

Zorić N, Tomović A, Obradović A, Mitrović Z. Fractional-order PD control design for active vibration control of smart structures. in International Conference of Experimental and Numerical Investigations and New Technologies (CNN TECH 2020). 2020;:57-57.
https://hdl.handle.net/21.15107/rcub_machinery_4025 .

Zorić, Nemanja, Tomović, Aleksandar, Obradović, Aleksandar, Mitrović, Zoran, "Fractional-order PD control design for active vibration control of smart structures" in International Conference of Experimental and Numerical Investigations and New Technologies (CNN TECH 2020) (2020):57-57,
https://hdl.handle.net/21.15107/rcub_machinery_4025 .

TY  - JOUR
AU  - Tomović, Aleksandar
AU  - Šalinić, Slaviša
AU  - Obradović, Aleksandar
AU  - Grbović, Aleksandar
AU  - Milovančević, Milorad
PY  - 2020
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4326
AB  - In this paper, the coupled axial-bending vibration of planar serial frame structures composed of rigid bodies and Euler-Bernoulli beam segments is considered. The corresponding mode orthogonality conditions for this kind of structures are derived. It is assumed that the mass centers of rigid bodies have both the transverse and the axial eccentricity with respect to beam neutral axes and that the mass centers are located in the plane in which the rigid bodies perform planar motion. The system responses to initial excitation in the case of distinct as well as repeated natural frequencies are considered. Theoretical considerations are accompanied by four numerical examples.
PB  - Elsevier Science Inc, New York
T2  - Applied Mathematical Modelling
T1  - Closed-form solution for the free axial-bending vibration problem of structures composed of rigid bodies and elastic beam segments
EP  - 1167
SP  - 1148
VL  - 77
DO  - 10.1016/j.apm.2019.09.008
ER  - 

@article{
author = "Tomović, Aleksandar and Šalinić, Slaviša and Obradović, Aleksandar and Grbović, Aleksandar and Milovančević, Milorad",
year = "2020",
abstract = "In this paper, the coupled axial-bending vibration of planar serial frame structures composed of rigid bodies and Euler-Bernoulli beam segments is considered. The corresponding mode orthogonality conditions for this kind of structures are derived. It is assumed that the mass centers of rigid bodies have both the transverse and the axial eccentricity with respect to beam neutral axes and that the mass centers are located in the plane in which the rigid bodies perform planar motion. The system responses to initial excitation in the case of distinct as well as repeated natural frequencies are considered. Theoretical considerations are accompanied by four numerical examples.",
publisher = "Elsevier Science Inc, New York",
journal = "Applied Mathematical Modelling",
title = "Closed-form solution for the free axial-bending vibration problem of structures composed of rigid bodies and elastic beam segments",
pages = "1167-1148",
volume = "77",
doi = "10.1016/j.apm.2019.09.008"
}

Tomović, A., Šalinić, S., Obradović, A., Grbović, A.,& Milovančević, M.. (2020). Closed-form solution for the free axial-bending vibration problem of structures composed of rigid bodies and elastic beam segments. in Applied Mathematical Modelling
Elsevier Science Inc, New York., 77, 1148-1167.
https://doi.org/10.1016/j.apm.2019.09.008

Tomović A, Šalinić S, Obradović A, Grbović A, Milovančević M. Closed-form solution for the free axial-bending vibration problem of structures composed of rigid bodies and elastic beam segments. in Applied Mathematical Modelling. 2020;77:1148-1167.
doi:10.1016/j.apm.2019.09.008 .

Tomović, Aleksandar, Šalinić, Slaviša, Obradović, Aleksandar, Grbović, Aleksandar, Milovančević, Milorad, "Closed-form solution for the free axial-bending vibration problem of structures composed of rigid bodies and elastic beam segments" in Applied Mathematical Modelling, 77 (2020):1148-1167,
https://doi.org/10.1016/j.apm.2019.09.008 . .

TY  - JOUR
AU  - Obradović, Aleksandar
AU  - Šalinić, Slaviša
AU  - Tomović, Aleksandar
PY  - 2020
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3463
AB  - This paper considers the problem of modal analysis and finding the closed-form solution to free vibrations of planar serial frame structures composed of Euler-Bernoulli beams of variable cross-sectional geometric characteristics in the case of axially functionally graded materials. Each of these beams is performing coupled axial and bending vibrations, where coupling occurs due to the boundary conditions at their joints. The numerical procedure for solving the system of partial differential equations, after the separation of variables, is reduced to solving the two-point boundary value problem of ordinary linear differential equations with nonlinear coefficients and linear boundary conditions. In this case, it is possible to transfer the boundary conditions and reduce the problem to the Cauchy initial value problem. Also, it is possible to analyze the influence of different parameters on the structure dynamic behavior. The method is applicable in the case of different boundary conditions at the right and left ends of such structures, as illustrated by an appropriate numerical example.
PB  - Srpsko društvo za mehaniku, Beograd
T2  - Theoretical and Applied Mechanics
T1  - Free vibrations of planar serial frame structures in the case of axially functionally graded materials
EP  - 239
IS  - 2
SP  - 221
VL  - 47
DO  - 10.2298/TAM2000017O
ER  - 

@article{
author = "Obradović, Aleksandar and Šalinić, Slaviša and Tomović, Aleksandar",
year = "2020",
abstract = "This paper considers the problem of modal analysis and finding the closed-form solution to free vibrations of planar serial frame structures composed of Euler-Bernoulli beams of variable cross-sectional geometric characteristics in the case of axially functionally graded materials. Each of these beams is performing coupled axial and bending vibrations, where coupling occurs due to the boundary conditions at their joints. The numerical procedure for solving the system of partial differential equations, after the separation of variables, is reduced to solving the two-point boundary value problem of ordinary linear differential equations with nonlinear coefficients and linear boundary conditions. In this case, it is possible to transfer the boundary conditions and reduce the problem to the Cauchy initial value problem. Also, it is possible to analyze the influence of different parameters on the structure dynamic behavior. The method is applicable in the case of different boundary conditions at the right and left ends of such structures, as illustrated by an appropriate numerical example.",
publisher = "Srpsko društvo za mehaniku, Beograd",
journal = "Theoretical and Applied Mechanics",
title = "Free vibrations of planar serial frame structures in the case of axially functionally graded materials",
pages = "239-221",
number = "2",
volume = "47",
doi = "10.2298/TAM2000017O"
}

Obradović, A., Šalinić, S.,& Tomović, A.. (2020). Free vibrations of planar serial frame structures in the case of axially functionally graded materials. in Theoretical and Applied Mechanics
Srpsko društvo za mehaniku, Beograd., 47(2), 221-239.
https://doi.org/10.2298/TAM2000017O

Obradović A, Šalinić S, Tomović A. Free vibrations of planar serial frame structures in the case of axially functionally graded materials. in Theoretical and Applied Mechanics. 2020;47(2):221-239.
doi:10.2298/TAM2000017O .

Obradović, Aleksandar, Šalinić, Slaviša, Tomović, Aleksandar, "Free vibrations of planar serial frame structures in the case of axially functionally graded materials" in Theoretical and Applied Mechanics, 47, no. 2 (2020):221-239,
https://doi.org/10.2298/TAM2000017O . .

TY  - THES
AU  - Tomović, Aleksandar
PY  - 2019
UR  - https://nardus.mpn.gov.rs/handle/123456789/11515
UR  - http://eteze.bg.ac.rs/application/showtheses?thesesId=6909
UR  - https://fedorabg.bg.ac.rs/fedora/get/o:20255/bdef:Content/download
UR  - http://vbs.rs/scripts/cobiss?command=DISPLAY&base=70036&RID=51652367
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/71
AB  - U disertaciji se analizira problem linearnih harmonijskih oscilacija elastičnih greda od funkcionalno gradijentnih materijala čije se karakteristike menjaju po uzdužnoj osi grede. S obzirom na mogućnosti modelovanja materijala tako da svojim karakteristikama, mogu da zadovolje strukturne i estetske zahteve, povećan je obim njihovog korišćenja u realnim konstrukcijama. Ovi materijali mogu se primenjivati u širokom spektru različitih inženjerskih oblasti, kao što su biomedicinsko inženjerstvo, energetika, vazduhoplovno inženjerstvo, građevinarstvo i mnoge druge. Analiza statičkih i dinamičkih karakteristika elastičnih greda, s obzirom na njihovu primenu u brojnim inženjerskim konstrukcijama je od posebnog značaja za savremenu tehniku. U disertaciji se analiziraju uzdužne i poprečne oscilacije, kao i spregnute poprečne i uzdužne oscilacije elastičnih greda, čiji se poprečni presek i karakteristike materijala menjaju po uzdužnoj osi grede. Sprezanje uzdužnih i poprečnih modova oscilovanja određeno je opštim načinom oslanjanja grede. S obzirom na prirodu funkcionalno gradijentnih materijala analizira se promena gustine i modula elastičnosti po uzdužnoj osi grede. Prilikom formiranja modela, greda se posmatra kao mehanički sistem sa beskonačno mnogo stepeni slobode. Ponašanje ovakvog sistema opisuje se parcijalnim diferencijalnim jednačinama sa promenljivim koeficijentima. Za izvedene jednačine određeni su analitički zapisi modela oslanjanja grede u opštem slučaju, koristeći sisteme opruga i krutih tela na krajevima grede. Na osnovu ovih zapisa analizira se sprezanje poprečnih i uzdužnih oscilacija. Razdvajanjem poromenljivih, dužine i vremena, kod harmonijskih oscilacija formiran je sistem običnih diferencijalnih jednačina kojima se jednačine svode na modalni oblik. Jednačine se svode na bezdimenzioni oblik koji je u određenim slučajevima pogodan za izvršavanje potrebnih izračunavanja. U postupku algebarskog svođenja krutosti opruga na bezdimenzioni oblik, njihove vrednosti svode se na jedinični interval, što predstavlja dodatno numeričko uprošćavanje. S obzirom na formirani sistem običnih diferencijalnih jednačina sa definisanim konturnim uslovima, problem izračunavanja sveden je na rešavanje dvotačkastog graničnog problema. Rešavanje problema vrši se simboličko-numeričkim metodom početnih parametara (SNMIP)...
AB  - he problem of linear harmonic vibration of elastic axially functionally graded (AFG) beams whose characteristics change along longitudinal axes is analyzed in the presented dissertation. The implementation of modern procedures in designing functionally gradient (FG) materials have caused the increased use of later materials in real-life engineering structures, due to the fact that they may satisfy specific structural and aesthetic demands. Thus, FG materials may be used to overcome a wide range of engineering problems in various areas, i.e., biomedical engineering, energy industry, airspace engineering, civil engineering, etc. and that is why the static and dynamic analysis is of special importance in modern engineering. In the dissertation the longitudinal and transverse vibration problems as well as coupled transverse and longitudinal vibration problems of AFG elastic beams are analyzed. The coupling of longitudinal and transverse mode shapes is achieved by the implementation of general boundary conditions. With respect to the nature of FG materials, the changes of mass density and elasticity modulus are analyzed along the beam longitudinal axes. An elastic beam is treated as a mechanical system with an infinite number of degrees of freedom and its behavior is described by partial differential equations with variable coefficients. For presented problems, the equations of motion are derived and boundary conditions are presented in a symbolic manner. Based on later writings, the coupling of mode shapes is analyzed. Using the method of separation of variables, namely longitude and time, the system of ordinary differential equations is formed and the equations are written in the modal form. The equations are written in the non-dimensional form, which may be suitable for practical calculations. In this process, stiffness coefficients are reduced to the unit interval that presents further numerical simplification. Based on the formed system of ordinary differential equations with defined boundary conditions, the computational problem is reduced to the two point boundary value problem. The presented problem is solved using the symbolic-numeric method of initial parameters (SNMIP)...
PB  - Univerzitet u Beogradu, Mašinski fakultet
T1  - Spregnute poprečne i uzdužne oscilacije Ojler-Bernulijevih i Timošenkovih greda od funkcionalno gradijentnih materijala
T1  - Coupled transverse and longitudinal vibrations of Euler-Bernoulli and Timoshenko beams of functionally graded materials
UR  - https://hdl.handle.net/21.15107/rcub_nardus_11515
ER  - 

@phdthesis{
author = "Tomović, Aleksandar",
year = "2019",
abstract = "U disertaciji se analizira problem linearnih harmonijskih oscilacija elastičnih greda od funkcionalno gradijentnih materijala čije se karakteristike menjaju po uzdužnoj osi grede. S obzirom na mogućnosti modelovanja materijala tako da svojim karakteristikama, mogu da zadovolje strukturne i estetske zahteve, povećan je obim njihovog korišćenja u realnim konstrukcijama. Ovi materijali mogu se primenjivati u širokom spektru različitih inženjerskih oblasti, kao što su biomedicinsko inženjerstvo, energetika, vazduhoplovno inženjerstvo, građevinarstvo i mnoge druge. Analiza statičkih i dinamičkih karakteristika elastičnih greda, s obzirom na njihovu primenu u brojnim inženjerskim konstrukcijama je od posebnog značaja za savremenu tehniku. U disertaciji se analiziraju uzdužne i poprečne oscilacije, kao i spregnute poprečne i uzdužne oscilacije elastičnih greda, čiji se poprečni presek i karakteristike materijala menjaju po uzdužnoj osi grede. Sprezanje uzdužnih i poprečnih modova oscilovanja određeno je opštim načinom oslanjanja grede. S obzirom na prirodu funkcionalno gradijentnih materijala analizira se promena gustine i modula elastičnosti po uzdužnoj osi grede. Prilikom formiranja modela, greda se posmatra kao mehanički sistem sa beskonačno mnogo stepeni slobode. Ponašanje ovakvog sistema opisuje se parcijalnim diferencijalnim jednačinama sa promenljivim koeficijentima. Za izvedene jednačine određeni su analitički zapisi modela oslanjanja grede u opštem slučaju, koristeći sisteme opruga i krutih tela na krajevima grede. Na osnovu ovih zapisa analizira se sprezanje poprečnih i uzdužnih oscilacija. Razdvajanjem poromenljivih, dužine i vremena, kod harmonijskih oscilacija formiran je sistem običnih diferencijalnih jednačina kojima se jednačine svode na modalni oblik. Jednačine se svode na bezdimenzioni oblik koji je u određenim slučajevima pogodan za izvršavanje potrebnih izračunavanja. U postupku algebarskog svođenja krutosti opruga na bezdimenzioni oblik, njihove vrednosti svode se na jedinični interval, što predstavlja dodatno numeričko uprošćavanje. S obzirom na formirani sistem običnih diferencijalnih jednačina sa definisanim konturnim uslovima, problem izračunavanja sveden je na rešavanje dvotačkastog graničnog problema. Rešavanje problema vrši se simboličko-numeričkim metodom početnih parametara (SNMIP)..., he problem of linear harmonic vibration of elastic axially functionally graded (AFG) beams whose characteristics change along longitudinal axes is analyzed in the presented dissertation. The implementation of modern procedures in designing functionally gradient (FG) materials have caused the increased use of later materials in real-life engineering structures, due to the fact that they may satisfy specific structural and aesthetic demands. Thus, FG materials may be used to overcome a wide range of engineering problems in various areas, i.e., biomedical engineering, energy industry, airspace engineering, civil engineering, etc. and that is why the static and dynamic analysis is of special importance in modern engineering. In the dissertation the longitudinal and transverse vibration problems as well as coupled transverse and longitudinal vibration problems of AFG elastic beams are analyzed. The coupling of longitudinal and transverse mode shapes is achieved by the implementation of general boundary conditions. With respect to the nature of FG materials, the changes of mass density and elasticity modulus are analyzed along the beam longitudinal axes. An elastic beam is treated as a mechanical system with an infinite number of degrees of freedom and its behavior is described by partial differential equations with variable coefficients. For presented problems, the equations of motion are derived and boundary conditions are presented in a symbolic manner. Based on later writings, the coupling of mode shapes is analyzed. Using the method of separation of variables, namely longitude and time, the system of ordinary differential equations is formed and the equations are written in the modal form. The equations are written in the non-dimensional form, which may be suitable for practical calculations. In this process, stiffness coefficients are reduced to the unit interval that presents further numerical simplification. Based on the formed system of ordinary differential equations with defined boundary conditions, the computational problem is reduced to the two point boundary value problem. The presented problem is solved using the symbolic-numeric method of initial parameters (SNMIP)...",
publisher = "Univerzitet u Beogradu, Mašinski fakultet",
title = "Spregnute poprečne i uzdužne oscilacije Ojler-Bernulijevih i Timošenkovih greda od funkcionalno gradijentnih materijala, Coupled transverse and longitudinal vibrations of Euler-Bernoulli and Timoshenko beams of functionally graded materials",
url = "https://hdl.handle.net/21.15107/rcub_nardus_11515"
}

Tomović, A.. (2019). Spregnute poprečne i uzdužne oscilacije Ojler-Bernulijevih i Timošenkovih greda od funkcionalno gradijentnih materijala. 
Univerzitet u Beogradu, Mašinski fakultet..
https://hdl.handle.net/21.15107/rcub_nardus_11515

Tomović A. Spregnute poprečne i uzdužne oscilacije Ojler-Bernulijevih i Timošenkovih greda od funkcionalno gradijentnih materijala. 2019;.
https://hdl.handle.net/21.15107/rcub_nardus_11515 .

Tomović, Aleksandar, "Spregnute poprečne i uzdužne oscilacije Ojler-Bernulijevih i Timošenkovih greda od funkcionalno gradijentnih materijala" (2019),
https://hdl.handle.net/21.15107/rcub_nardus_11515 .

TY  - CONF
AU  - Tomović, Aleksandar
AU  - Šalinić, Slaviša
AU  - Obradović, Aleksandar
AU  - Lazarević, Mihailo
AU  - Mitrović, Zoran
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4028
AB  - In this paper we present the solution of exact equations of motion for coupled axial and
bending vibrations of a non-uniform axially functionally graded (AFG) cantilever beam with a
body of which mass center is eccentrically displaced in axial and transverse direction with respect
to the beam’s end. The Euler-Bernoulli beam theory is implemented to model behavior of the
beam under axial and transverse in-plane vibrations. Based on the paper [1], that is supported by
results publish in the paper [2] authors confirm the obtained results of natural frequencies of the
AFG cantilever beam, when boundary conditions define the vibration coupling. The modified
symbolic-numeric method of initial parameters presented in [3] is implemented in computing
natural frequencies of the beam. This method is expanded to solve axial-bending vibration
problems, with respect to the one presented in the literature [3] for the problem of the vibration of
a cantilever beam. Some minor deviations in the obtained results may be noticed with respect to
those obtained in [1], yet all within a tolerance domain due to the computational precision.
PB  - Beograd : Srpsko društvo za mehaniku
C3  - Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019
T1  - The exact natural frequency solution of a free axialbending vibration problem of a non-uniform AFG cantilever beam with a tip body
SP  - M4c
UR  - https://hdl.handle.net/21.15107/rcub_machinery_4028
ER  - 

@conference{
author = "Tomović, Aleksandar and Šalinić, Slaviša and Obradović, Aleksandar and Lazarević, Mihailo and Mitrović, Zoran",
year = "2019",
abstract = "In this paper we present the solution of exact equations of motion for coupled axial and
bending vibrations of a non-uniform axially functionally graded (AFG) cantilever beam with a
body of which mass center is eccentrically displaced in axial and transverse direction with respect
to the beam’s end. The Euler-Bernoulli beam theory is implemented to model behavior of the
beam under axial and transverse in-plane vibrations. Based on the paper [1], that is supported by
results publish in the paper [2] authors confirm the obtained results of natural frequencies of the
AFG cantilever beam, when boundary conditions define the vibration coupling. The modified
symbolic-numeric method of initial parameters presented in [3] is implemented in computing
natural frequencies of the beam. This method is expanded to solve axial-bending vibration
problems, with respect to the one presented in the literature [3] for the problem of the vibration of
a cantilever beam. Some minor deviations in the obtained results may be noticed with respect to
those obtained in [1], yet all within a tolerance domain due to the computational precision.",
publisher = "Beograd : Srpsko društvo za mehaniku",
journal = "Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019",
title = "The exact natural frequency solution of a free axialbending vibration problem of a non-uniform AFG cantilever beam with a tip body",
pages = "M4c",
url = "https://hdl.handle.net/21.15107/rcub_machinery_4028"
}

Tomović, A., Šalinić, S., Obradović, A., Lazarević, M.,& Mitrović, Z.. (2019). The exact natural frequency solution of a free axialbending vibration problem of a non-uniform AFG cantilever beam with a tip body. in Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019
Beograd : Srpsko društvo za mehaniku., M4c.
https://hdl.handle.net/21.15107/rcub_machinery_4028

Tomović A, Šalinić S, Obradović A, Lazarević M, Mitrović Z. The exact natural frequency solution of a free axialbending vibration problem of a non-uniform AFG cantilever beam with a tip body. in Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019. 2019;:M4c.
https://hdl.handle.net/21.15107/rcub_machinery_4028 .

Tomović, Aleksandar, Šalinić, Slaviša, Obradović, Aleksandar, Lazarević, Mihailo, Mitrović, Zoran, "The exact natural frequency solution of a free axialbending vibration problem of a non-uniform AFG cantilever beam with a tip body" in Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019 (2019):M4c,
https://hdl.handle.net/21.15107/rcub_machinery_4028 .

TY  - JOUR
AU  - Zorić, Nemanja
AU  - Tomović, Aleksandar
AU  - Obradović, Aleksandar
AU  - Radulović, Radoslav
AU  - Petrović, Goran R.
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4325
AB  - This paper deals with optimization of the sizing, location and orientation of the piezo-fiber reinforced composite (PFRC) actuators and active vibration control of the smart composite plates using particle-swarm optimized self-tuning fuzzy logic controller. The optimization criteria for optimal sizing, location and orientation of the PFRC actuators is based on the Gramian controllability matrix and the optimization process is performed by involving the limitation of the plates masses increase. Optimal configurations of five PFRC actuators for active vibration control of the first six modes of cantilever symmetric ((90 degrees/0 degrees/90 degrees/0 degrees)s), antisymmetric cross-ply ((90 degrees/0 degrees/90 degrees/0 degrees/90 degrees/0 degrees/90 degrees/0 degrees)) and antisymmetric angle-ply ((45 degrees/-45 degrees/45 degrees/-45 degrees/45 degrees/-45 degrees/45 degrees/-45 degrees)) composite plates are found using the particle swarm optimization. The detailed analysis of influences of the PFRC layer orientation and position (top or bottom side of composite plates), as well as bending-extension coupling of antisymmetric laminates on controllabilities is also performed. The experimental study is performed in order to validate this behavior on controllabilities of antisymmetric laminates. The particle swarm-optimized self-tuning fuzzy logic controller (FLC) adapted for the multiple-input multiple-output (MIMO) control is implemented for active vibration suppression of the plates. The membership functions as well as output matrices are optimized using the particle swarm optimization. The Mamdani and the zero-order Takagi-Sugeno-Kang fuzzy inference methods are employed and their performances are examined and compared. In order to represent the efficiency of the proposed controller, results obtained using the proposed particle swarm optimized self-tuning FLC are compared with the corresponding results in the case of the linear quadratic regulator (LQR) optimal control strategy.
PB  - Academic Press Ltd- Elsevier Science Ltd, London
T2  - Journal of Sound and Vibration
T1  - Active vibration control of smart composite plates using optimized self-tuning fuzzy logic controller with optimization of placement, sizing and orientation of PFRC actuators
EP  - 198
SP  - 173
VL  - 456
DO  - 10.1016/j.jsv.2019.05.035
ER  - 

@article{
author = "Zorić, Nemanja and Tomović, Aleksandar and Obradović, Aleksandar and Radulović, Radoslav and Petrović, Goran R.",
year = "2019",
abstract = "This paper deals with optimization of the sizing, location and orientation of the piezo-fiber reinforced composite (PFRC) actuators and active vibration control of the smart composite plates using particle-swarm optimized self-tuning fuzzy logic controller. The optimization criteria for optimal sizing, location and orientation of the PFRC actuators is based on the Gramian controllability matrix and the optimization process is performed by involving the limitation of the plates masses increase. Optimal configurations of five PFRC actuators for active vibration control of the first six modes of cantilever symmetric ((90 degrees/0 degrees/90 degrees/0 degrees)s), antisymmetric cross-ply ((90 degrees/0 degrees/90 degrees/0 degrees/90 degrees/0 degrees/90 degrees/0 degrees)) and antisymmetric angle-ply ((45 degrees/-45 degrees/45 degrees/-45 degrees/45 degrees/-45 degrees/45 degrees/-45 degrees)) composite plates are found using the particle swarm optimization. The detailed analysis of influences of the PFRC layer orientation and position (top or bottom side of composite plates), as well as bending-extension coupling of antisymmetric laminates on controllabilities is also performed. The experimental study is performed in order to validate this behavior on controllabilities of antisymmetric laminates. The particle swarm-optimized self-tuning fuzzy logic controller (FLC) adapted for the multiple-input multiple-output (MIMO) control is implemented for active vibration suppression of the plates. The membership functions as well as output matrices are optimized using the particle swarm optimization. The Mamdani and the zero-order Takagi-Sugeno-Kang fuzzy inference methods are employed and their performances are examined and compared. In order to represent the efficiency of the proposed controller, results obtained using the proposed particle swarm optimized self-tuning FLC are compared with the corresponding results in the case of the linear quadratic regulator (LQR) optimal control strategy.",
publisher = "Academic Press Ltd- Elsevier Science Ltd, London",
journal = "Journal of Sound and Vibration",
title = "Active vibration control of smart composite plates using optimized self-tuning fuzzy logic controller with optimization of placement, sizing and orientation of PFRC actuators",
pages = "198-173",
volume = "456",
doi = "10.1016/j.jsv.2019.05.035"
}

Zorić, N., Tomović, A., Obradović, A., Radulović, R.,& Petrović, G. R.. (2019). Active vibration control of smart composite plates using optimized self-tuning fuzzy logic controller with optimization of placement, sizing and orientation of PFRC actuators. in Journal of Sound and Vibration
Academic Press Ltd- Elsevier Science Ltd, London., 456, 173-198.
https://doi.org/10.1016/j.jsv.2019.05.035

Zorić N, Tomović A, Obradović A, Radulović R, Petrović GR. Active vibration control of smart composite plates using optimized self-tuning fuzzy logic controller with optimization of placement, sizing and orientation of PFRC actuators. in Journal of Sound and Vibration. 2019;456:173-198.
doi:10.1016/j.jsv.2019.05.035 .

Zorić, Nemanja, Tomović, Aleksandar, Obradović, Aleksandar, Radulović, Radoslav, Petrović, Goran R., "Active vibration control of smart composite plates using optimized self-tuning fuzzy logic controller with optimization of placement, sizing and orientation of PFRC actuators" in Journal of Sound and Vibration, 456 (2019):173-198,
https://doi.org/10.1016/j.jsv.2019.05.035 . .

TY  - JOUR
AU  - Zorić, Nemanja
AU  - Tomović, Aleksandar
AU  - Obradović, Aleksandar
AU  - Radulović, Radoslav
AU  - Petrović, Goran R.
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3026
AB  - This paper deals with optimization of the sizing, location and orientation of the piezo-fiber reinforced composite (PFRC) actuators and active vibration control of the smart composite plates using particle-swarm optimized self-tuning fuzzy logic controller. The optimization criteria for optimal sizing, location and orientation of the PFRC actuators is based on the Gramian controllability matrix and the optimization process is performed by involving the limitation of the plates masses increase. Optimal configurations of five PFRC actuators for active vibration control of the first six modes of cantilever symmetric ((90 degrees/0 degrees/90 degrees/0 degrees)s), antisymmetric cross-ply ((90 degrees/0 degrees/90 degrees/0 degrees/90 degrees/0 degrees/90 degrees/0 degrees)) and antisymmetric angle-ply ((45 degrees/-45 degrees/45 degrees/-45 degrees/45 degrees/-45 degrees/45 degrees/-45 degrees)) composite plates are found using the particle swarm optimization. The detailed analysis of influences of the PFRC layer orientation and position (top or bottom side of composite plates), as well as bending-extension coupling of antisymmetric laminates on controllabilities is also performed. The experimental study is performed in order to validate this behavior on controllabilities of antisymmetric laminates. The particle swarm-optimized self-tuning fuzzy logic controller (FLC) adapted for the multiple-input multiple-output (MIMO) control is implemented for active vibration suppression of the plates. The membership functions as well as output matrices are optimized using the particle swarm optimization. The Mamdani and the zero-order Takagi-Sugeno-Kang fuzzy inference methods are employed and their performances are examined and compared. In order to represent the efficiency of the proposed controller, results obtained using the proposed particle swarm optimized self-tuning FLC are compared with the corresponding results in the case of the linear quadratic regulator (LQR) optimal control strategy.
PB  - Academic Press Ltd- Elsevier Science Ltd, London
T2  - Journal of Sound and Vibration
T1  - Active vibration control of smart composite plates using optimized self-tuning fuzzy logic controller with optimization of placement, sizing and orientation of PFRC actuators
EP  - 198
SP  - 173
VL  - 456
DO  - 10.1016/j.jsv.2019.05.035
ER  - 

@article{
author = "Zorić, Nemanja and Tomović, Aleksandar and Obradović, Aleksandar and Radulović, Radoslav and Petrović, Goran R.",
year = "2019",
abstract = "This paper deals with optimization of the sizing, location and orientation of the piezo-fiber reinforced composite (PFRC) actuators and active vibration control of the smart composite plates using particle-swarm optimized self-tuning fuzzy logic controller. The optimization criteria for optimal sizing, location and orientation of the PFRC actuators is based on the Gramian controllability matrix and the optimization process is performed by involving the limitation of the plates masses increase. Optimal configurations of five PFRC actuators for active vibration control of the first six modes of cantilever symmetric ((90 degrees/0 degrees/90 degrees/0 degrees)s), antisymmetric cross-ply ((90 degrees/0 degrees/90 degrees/0 degrees/90 degrees/0 degrees/90 degrees/0 degrees)) and antisymmetric angle-ply ((45 degrees/-45 degrees/45 degrees/-45 degrees/45 degrees/-45 degrees/45 degrees/-45 degrees)) composite plates are found using the particle swarm optimization. The detailed analysis of influences of the PFRC layer orientation and position (top or bottom side of composite plates), as well as bending-extension coupling of antisymmetric laminates on controllabilities is also performed. The experimental study is performed in order to validate this behavior on controllabilities of antisymmetric laminates. The particle swarm-optimized self-tuning fuzzy logic controller (FLC) adapted for the multiple-input multiple-output (MIMO) control is implemented for active vibration suppression of the plates. The membership functions as well as output matrices are optimized using the particle swarm optimization. The Mamdani and the zero-order Takagi-Sugeno-Kang fuzzy inference methods are employed and their performances are examined and compared. In order to represent the efficiency of the proposed controller, results obtained using the proposed particle swarm optimized self-tuning FLC are compared with the corresponding results in the case of the linear quadratic regulator (LQR) optimal control strategy.",
publisher = "Academic Press Ltd- Elsevier Science Ltd, London",
journal = "Journal of Sound and Vibration",
title = "Active vibration control of smart composite plates using optimized self-tuning fuzzy logic controller with optimization of placement, sizing and orientation of PFRC actuators",
pages = "198-173",
volume = "456",
doi = "10.1016/j.jsv.2019.05.035"
}

Zorić, N., Tomović, A., Obradović, A., Radulović, R.,& Petrović, G. R.. (2019). Active vibration control of smart composite plates using optimized self-tuning fuzzy logic controller with optimization of placement, sizing and orientation of PFRC actuators. in Journal of Sound and Vibration
Academic Press Ltd- Elsevier Science Ltd, London., 456, 173-198.
https://doi.org/10.1016/j.jsv.2019.05.035

Zorić N, Tomović A, Obradović A, Radulović R, Petrović GR. Active vibration control of smart composite plates using optimized self-tuning fuzzy logic controller with optimization of placement, sizing and orientation of PFRC actuators. in Journal of Sound and Vibration. 2019;456:173-198.
doi:10.1016/j.jsv.2019.05.035 .

Zorić, Nemanja, Tomović, Aleksandar, Obradović, Aleksandar, Radulović, Radoslav, Petrović, Goran R., "Active vibration control of smart composite plates using optimized self-tuning fuzzy logic controller with optimization of placement, sizing and orientation of PFRC actuators" in Journal of Sound and Vibration, 456 (2019):173-198,
https://doi.org/10.1016/j.jsv.2019.05.035 . .

TY  - JOUR
AU  - Šalinić, Slaviša
AU  - Obradović, Aleksandar
AU  - Tomović, Aleksandar
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4329
AB  - In this paper a new non-iterative computational technique referred to as the symbolic-numeric method of initial parameters (SNMIP) is proposed. The SNMIP represents a modification of the iterative numeric method of initial parameters in differential form known in the literature. The SNMIP is applied to study free vibrations of Euler-Bernoulli axially functionally graded tapered, stepped, and continuously segmented rods and beams with elastically restrained end with attached masses. Both the longitudinal vibration of rods and transverse vibration of beams are considered. The influence of the attached masses and springs on the natural frequencies of vibration of axially functionally graded rods and beams is examined. The validity and accuracy of the method are proven through the comparison with the known results in the available literature.
PB  - Elsevier Sci Ltd, Oxford
T2  - Composites Part B-Engineering
T1  - Free vibration analysis of axially functionally graded tapered, stepped, and continuously segmented rods and beams
EP  - 143
SP  - 135
VL  - 150
DO  - 10.1016/j.compositesb.2018.05.060
ER  - 

@article{
author = "Šalinić, Slaviša and Obradović, Aleksandar and Tomović, Aleksandar",
year = "2018",
abstract = "In this paper a new non-iterative computational technique referred to as the symbolic-numeric method of initial parameters (SNMIP) is proposed. The SNMIP represents a modification of the iterative numeric method of initial parameters in differential form known in the literature. The SNMIP is applied to study free vibrations of Euler-Bernoulli axially functionally graded tapered, stepped, and continuously segmented rods and beams with elastically restrained end with attached masses. Both the longitudinal vibration of rods and transverse vibration of beams are considered. The influence of the attached masses and springs on the natural frequencies of vibration of axially functionally graded rods and beams is examined. The validity and accuracy of the method are proven through the comparison with the known results in the available literature.",
publisher = "Elsevier Sci Ltd, Oxford",
journal = "Composites Part B-Engineering",
title = "Free vibration analysis of axially functionally graded tapered, stepped, and continuously segmented rods and beams",
pages = "143-135",
volume = "150",
doi = "10.1016/j.compositesb.2018.05.060"
}

Šalinić, S., Obradović, A.,& Tomović, A.. (2018). Free vibration analysis of axially functionally graded tapered, stepped, and continuously segmented rods and beams. in Composites Part B-Engineering
Elsevier Sci Ltd, Oxford., 150, 135-143.
https://doi.org/10.1016/j.compositesb.2018.05.060

Šalinić S, Obradović A, Tomović A. Free vibration analysis of axially functionally graded tapered, stepped, and continuously segmented rods and beams. in Composites Part B-Engineering. 2018;150:135-143.
doi:10.1016/j.compositesb.2018.05.060 .

Šalinić, Slaviša, Obradović, Aleksandar, Tomović, Aleksandar, "Free vibration analysis of axially functionally graded tapered, stepped, and continuously segmented rods and beams" in Composites Part B-Engineering, 150 (2018):135-143,
https://doi.org/10.1016/j.compositesb.2018.05.060 . .

TY  - JOUR
AU  - Šalinić, Slaviša
AU  - Obradović, Aleksandar
AU  - Tomović, Aleksandar
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2873
AB  - In this paper a new non-iterative computational technique referred to as the symbolic-numeric method of initial parameters (SNMIP) is proposed. The SNMIP represents a modification of the iterative numeric method of initial parameters in differential form known in the literature. The SNMIP is applied to study free vibrations of Euler-Bernoulli axially functionally graded tapered, stepped, and continuously segmented rods and beams with elastically restrained end with attached masses. Both the longitudinal vibration of rods and transverse vibration of beams are considered. The influence of the attached masses and springs on the natural frequencies of vibration of axially functionally graded rods and beams is examined. The validity and accuracy of the method are proven through the comparison with the known results in the available literature.
PB  - Elsevier Sci Ltd, Oxford
T2  - Composites Part B-Engineering
T1  - Free vibration analysis of axially functionally graded tapered, stepped, and continuously segmented rods and beams
EP  - 143
SP  - 135
VL  - 150
DO  - 10.1016/j.compositesb.2018.05.060
ER  - 

@article{
author = "Šalinić, Slaviša and Obradović, Aleksandar and Tomović, Aleksandar",
year = "2018",
abstract = "In this paper a new non-iterative computational technique referred to as the symbolic-numeric method of initial parameters (SNMIP) is proposed. The SNMIP represents a modification of the iterative numeric method of initial parameters in differential form known in the literature. The SNMIP is applied to study free vibrations of Euler-Bernoulli axially functionally graded tapered, stepped, and continuously segmented rods and beams with elastically restrained end with attached masses. Both the longitudinal vibration of rods and transverse vibration of beams are considered. The influence of the attached masses and springs on the natural frequencies of vibration of axially functionally graded rods and beams is examined. The validity and accuracy of the method are proven through the comparison with the known results in the available literature.",
publisher = "Elsevier Sci Ltd, Oxford",
journal = "Composites Part B-Engineering",
title = "Free vibration analysis of axially functionally graded tapered, stepped, and continuously segmented rods and beams",
pages = "143-135",
volume = "150",
doi = "10.1016/j.compositesb.2018.05.060"
}

Šalinić, S., Obradović, A.,& Tomović, A.. (2018). Free vibration analysis of axially functionally graded tapered, stepped, and continuously segmented rods and beams. in Composites Part B-Engineering
Elsevier Sci Ltd, Oxford., 150, 135-143.
https://doi.org/10.1016/j.compositesb.2018.05.060

Šalinić S, Obradović A, Tomović A. Free vibration analysis of axially functionally graded tapered, stepped, and continuously segmented rods and beams. in Composites Part B-Engineering. 2018;150:135-143.
doi:10.1016/j.compositesb.2018.05.060 .

Šalinić, Slaviša, Obradović, Aleksandar, Tomović, Aleksandar, "Free vibration analysis of axially functionally graded tapered, stepped, and continuously segmented rods and beams" in Composites Part B-Engineering, 150 (2018):135-143,
https://doi.org/10.1016/j.compositesb.2018.05.060 . .

TY  - JOUR
AU  - Radovanović, Nikola V.
AU  - Zorić, Nemanja
AU  - Trišović, Nataša
AU  - Tomović, Aleksandar
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2591
AB  - Ovaj rad predstavlja analizu slobodnih vibracija struktura sastavljenih od krutih tela međusobno spojenih sa elastičnim gredama. Pretpostavlja se da se centri masa krutih tela ne nalaze na neutralnoj osi nedeformisanog elastičnog grednog segmenta kao i da kruta tela vrše ravno kretanje u istoj ravni i da se njihovi centri masa nalaze u toj istoj ravni. Za određivanje frekvencija sistema, modifikacija klasične 'CTMM' metode je upotrebljena. Elastični gredni segmenti se tretiraju kao Ojler-Bernulijeve grede. Prikazan je numerički primer.
AB  - This article presents free vibration analysis of structures composed of rigid bodies connected with elastic beam segments. It is assumed that the mass centers of rigid bodies are not located on the neutral axes of undeformed elastic beam segments as well as rigid bodies perform planar motion in the same plane and their mass centers are located in that plane. For determination of natural frequencies of the system, modification of the conventional continuous-mass transfer matrix method has been performed. The elastic beam segments are treated as Euler-Bernoulli beams. Numerical example is presented.
PB  - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2  - FME Transactions
T1  - Analiza slobodnih ravanskih oscilacija struktura sastavljenih od krutih tela i elastičnih grednih segmenata
T1  - Free planar vibration of structures composed of rigid bodies and elastic beam segments
EP  - 102
IS  - 1
SP  - 97
VL  - 45
DO  - 10.5937/fmet1701097R
ER  - 

@article{
author = "Radovanović, Nikola V. and Zorić, Nemanja and Trišović, Nataša and Tomović, Aleksandar",
year = "2017",
abstract = "Ovaj rad predstavlja analizu slobodnih vibracija struktura sastavljenih od krutih tela međusobno spojenih sa elastičnim gredama. Pretpostavlja se da se centri masa krutih tela ne nalaze na neutralnoj osi nedeformisanog elastičnog grednog segmenta kao i da kruta tela vrše ravno kretanje u istoj ravni i da se njihovi centri masa nalaze u toj istoj ravni. Za određivanje frekvencija sistema, modifikacija klasične 'CTMM' metode je upotrebljena. Elastični gredni segmenti se tretiraju kao Ojler-Bernulijeve grede. Prikazan je numerički primer., This article presents free vibration analysis of structures composed of rigid bodies connected with elastic beam segments. It is assumed that the mass centers of rigid bodies are not located on the neutral axes of undeformed elastic beam segments as well as rigid bodies perform planar motion in the same plane and their mass centers are located in that plane. For determination of natural frequencies of the system, modification of the conventional continuous-mass transfer matrix method has been performed. The elastic beam segments are treated as Euler-Bernoulli beams. Numerical example is presented.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "Analiza slobodnih ravanskih oscilacija struktura sastavljenih od krutih tela i elastičnih grednih segmenata, Free planar vibration of structures composed of rigid bodies and elastic beam segments",
pages = "102-97",
number = "1",
volume = "45",
doi = "10.5937/fmet1701097R"
}

Radovanović, N. V., Zorić, N., Trišović, N.,& Tomović, A.. (2017). Analiza slobodnih ravanskih oscilacija struktura sastavljenih od krutih tela i elastičnih grednih segmenata. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 45(1), 97-102.
https://doi.org/10.5937/fmet1701097R

Radovanović NV, Zorić N, Trišović N, Tomović A. Analiza slobodnih ravanskih oscilacija struktura sastavljenih od krutih tela i elastičnih grednih segmenata. in FME Transactions. 2017;45(1):97-102.
doi:10.5937/fmet1701097R .

Radovanović, Nikola V., Zorić, Nemanja, Trišović, Nataša, Tomović, Aleksandar, "Analiza slobodnih ravanskih oscilacija struktura sastavljenih od krutih tela i elastičnih grednih segmenata" in FME Transactions, 45, no. 1 (2017):97-102,
https://doi.org/10.5937/fmet1701097R . .

TY  - CONF
AU  - Zorić, Nemanja
AU  - Tomović, Aleksandar
AU  - Jovanović, Miroslav
AU  - Lukić, Nebojša
AU  - Stokić, Zoran
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4074
AB  - Piezoelectric materials have a wide range of application on the active vibration control of
flexible structures as actuators and sensors due to its inverse and direct piezoelectric effect. In
order to increase performance of active vibration control, piezoelectric fibers are stacked into
single layer composite, making piezoelectric fiber-reinforced composite (PFRC) actuator and
sensor. These actuators and sensors are used for active vibration control of a thin-walled
structures, placing them at the surface of the structure. Since that, control performances depend
on sizes, positions and orientations of PFRC actuators and sensors. The aim of this paper is to
investigate the effect of PFRC actuator orientation and position (top or bottom) on controllability
of cross-ply and angle-ply antisymmetric composite plates for active vibration control. Depending
on layers' orientation, composite laminates possess coupling behavior (bending-stretching,
bending-shear coupling). Since antisymmetric laminates possess bending-stretching coupling
behavior, the effect of this behavior on controllability will be also discussed.
PB  - Serbian Society of Mechanics
C3  - 6th International Congress of Serbian Society of Mechanics, Tara, Serbia, 2017
T1  - Effect of piezoelectric fiber-reinforced composite (PFRC) actuator orientation on controllability of antisymmetric composite plates for active vibration control
IS  - C1a
UR  - https://hdl.handle.net/21.15107/rcub_machinery_4074
ER  - 

@conference{
author = "Zorić, Nemanja and Tomović, Aleksandar and Jovanović, Miroslav and Lukić, Nebojša and Stokić, Zoran",
year = "2017",
abstract = "Piezoelectric materials have a wide range of application on the active vibration control of
flexible structures as actuators and sensors due to its inverse and direct piezoelectric effect. In
order to increase performance of active vibration control, piezoelectric fibers are stacked into
single layer composite, making piezoelectric fiber-reinforced composite (PFRC) actuator and
sensor. These actuators and sensors are used for active vibration control of a thin-walled
structures, placing them at the surface of the structure. Since that, control performances depend
on sizes, positions and orientations of PFRC actuators and sensors. The aim of this paper is to
investigate the effect of PFRC actuator orientation and position (top or bottom) on controllability
of cross-ply and angle-ply antisymmetric composite plates for active vibration control. Depending
on layers' orientation, composite laminates possess coupling behavior (bending-stretching,
bending-shear coupling). Since antisymmetric laminates possess bending-stretching coupling
behavior, the effect of this behavior on controllability will be also discussed.",
publisher = "Serbian Society of Mechanics",
journal = "6th International Congress of Serbian Society of Mechanics, Tara, Serbia, 2017",
title = "Effect of piezoelectric fiber-reinforced composite (PFRC) actuator orientation on controllability of antisymmetric composite plates for active vibration control",
number = "C1a",
url = "https://hdl.handle.net/21.15107/rcub_machinery_4074"
}

Zorić, N., Tomović, A., Jovanović, M., Lukić, N.,& Stokić, Z.. (2017). Effect of piezoelectric fiber-reinforced composite (PFRC) actuator orientation on controllability of antisymmetric composite plates for active vibration control. in 6th International Congress of Serbian Society of Mechanics, Tara, Serbia, 2017
Serbian Society of Mechanics.(C1a).
https://hdl.handle.net/21.15107/rcub_machinery_4074

Zorić N, Tomović A, Jovanović M, Lukić N, Stokić Z. Effect of piezoelectric fiber-reinforced composite (PFRC) actuator orientation on controllability of antisymmetric composite plates for active vibration control. in 6th International Congress of Serbian Society of Mechanics, Tara, Serbia, 2017. 2017;(C1a).
https://hdl.handle.net/21.15107/rcub_machinery_4074 .

Zorić, Nemanja, Tomović, Aleksandar, Jovanović, Miroslav, Lukić, Nebojša, Stokić, Zoran, "Effect of piezoelectric fiber-reinforced composite (PFRC) actuator orientation on controllability of antisymmetric composite plates for active vibration control" in 6th International Congress of Serbian Society of Mechanics, Tara, Serbia, 2017, no. C1a (2017),
https://hdl.handle.net/21.15107/rcub_machinery_4074 .

TY  - JOUR
AU  - Šalinić, Slaviša
AU  - Vranić, Aleksandar
AU  - Nešić, Nikola D.
AU  - Tomović, Aleksandar
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2624
AB  - Proučavana je kinemtika i dinamika Kardan-Hukovog zgloba. Kinematička analiza se bazira na teoriji složenog kretanja krutog tela. Dinamička analiza Kardan-Hukovog zgloba je izvršena na bazi Lagranževih jednačina druge vrste. Kardan-Hukov zglob je analiziran u uslovima promenljive ugaone brzine pogonskog (ulaznog) vratila zgloba. Razmatrane su dve varijante zgloba: (1) ravan pogonske viljuške se poklapa sa ravni vratila; (2) ravan pogonske viljuške je normalna na ravan vratila. Izveden je izraz kojim se opisuje prenos obrtnog momenta Kardan-Hukovim zglobom. Izvedeni izraz sadrži članove koji potiču od inercije ulaznog i izlaznog vratila kao i od inercije krsta Kardan-Hukovog zgloba. Teorijska razmatranja su propraćena numeričkim primerom.
AB  - Kinematics and dynamics of a Cardan-Hooke joint are investigated. Kinematic analysis is based on the kinematic chain rule for angular velocity vectors. Dynamics of the Cardan-Hooke joint is analyzed by means of the Lagrange equations of the second kind. The Cardan-Hooke joint is analysed under varying operating conditions, that is, it is assumed that the input shaft has variable angular velocity. Two cases are considered: (1) the driving yoke plane coincides with the plane of the shafts; (2) the driving yoke plane is normal to the plane of the shafts. An expression for torque transmission in a Cardan-Hooke joint in varying operating conditions was developed. The expression contains terms representing inertia of the shafts and the cross of the Cardan-Hooke joint. Theoretical considerations are accompanied by a numerical example.
PB  - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2  - FME Transactions
T1  - O prenosu obrtnog momenta Kardan-Hukovim zglobom
T1  - On the torque transmission by a Cardan-Hooke joint
EP  - 121
IS  - 1
SP  - 117
VL  - 45
DO  - 10.5937/fmet1701117S
ER  - 

@article{
author = "Šalinić, Slaviša and Vranić, Aleksandar and Nešić, Nikola D. and Tomović, Aleksandar",
year = "2017",
abstract = "Proučavana je kinemtika i dinamika Kardan-Hukovog zgloba. Kinematička analiza se bazira na teoriji složenog kretanja krutog tela. Dinamička analiza Kardan-Hukovog zgloba je izvršena na bazi Lagranževih jednačina druge vrste. Kardan-Hukov zglob je analiziran u uslovima promenljive ugaone brzine pogonskog (ulaznog) vratila zgloba. Razmatrane su dve varijante zgloba: (1) ravan pogonske viljuške se poklapa sa ravni vratila; (2) ravan pogonske viljuške je normalna na ravan vratila. Izveden je izraz kojim se opisuje prenos obrtnog momenta Kardan-Hukovim zglobom. Izvedeni izraz sadrži članove koji potiču od inercije ulaznog i izlaznog vratila kao i od inercije krsta Kardan-Hukovog zgloba. Teorijska razmatranja su propraćena numeričkim primerom., Kinematics and dynamics of a Cardan-Hooke joint are investigated. Kinematic analysis is based on the kinematic chain rule for angular velocity vectors. Dynamics of the Cardan-Hooke joint is analyzed by means of the Lagrange equations of the second kind. The Cardan-Hooke joint is analysed under varying operating conditions, that is, it is assumed that the input shaft has variable angular velocity. Two cases are considered: (1) the driving yoke plane coincides with the plane of the shafts; (2) the driving yoke plane is normal to the plane of the shafts. An expression for torque transmission in a Cardan-Hooke joint in varying operating conditions was developed. The expression contains terms representing inertia of the shafts and the cross of the Cardan-Hooke joint. Theoretical considerations are accompanied by a numerical example.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "O prenosu obrtnog momenta Kardan-Hukovim zglobom, On the torque transmission by a Cardan-Hooke joint",
pages = "121-117",
number = "1",
volume = "45",
doi = "10.5937/fmet1701117S"
}

Šalinić, S., Vranić, A., Nešić, N. D.,& Tomović, A.. (2017). O prenosu obrtnog momenta Kardan-Hukovim zglobom. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 45(1), 117-121.
https://doi.org/10.5937/fmet1701117S

Šalinić S, Vranić A, Nešić ND, Tomović A. O prenosu obrtnog momenta Kardan-Hukovim zglobom. in FME Transactions. 2017;45(1):117-121.
doi:10.5937/fmet1701117S .

Šalinić, Slaviša, Vranić, Aleksandar, Nešić, Nikola D., Tomović, Aleksandar, "O prenosu obrtnog momenta Kardan-Hukovim zglobom" in FME Transactions, 45, no. 1 (2017):117-121,
https://doi.org/10.5937/fmet1701117S . .

TY  - CONF
AU  - Tomović, Aleksandar
PY  - 2016
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6213
AB  - In this paper, the synchronous axial and bending vibration problem of elastic beams with
variable cross-sectional profile and inhomogeneous material and conjugated boundary conditions
is considered. The orthogonality conditions of mode shapes are derived for the case with no
repeated natural frequencies, along with the constants for the corresponding time function. In that
manner the response of the beam to initial excitations is covered in the theoretical aspect. The
numerical background for solving the problem is explained based on the theory of numerical
“shooting” method and boundary conditions of a considered mechanical case. The case of beams
with no attached end masses and rigid bodies is considered in this paper. Also, one numerical
example is presented to accompany theoretical considerations. The numerical procedure which is
introduced in this paper can also be applied to more complex systems of elastic and rigid bodies,
for instance, those considered in references [11, 15].
PB  - Serbian Society of Mechanics
PB  - Faculty of Mechanical Engineering
C3  - Proceedings, The 6th International Congress of Serbian Society of Mechanics
T1  - A NOVEL APPROACH TO THE FREE AXIAL-BENDING VIBRATION PROBLEM OF INHOMOGENEOUS ELASTIC BEAMS WITH VARIABLE CROSS-SECTIONAL PROFILES
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6213
ER  - 

@conference{
author = "Tomović, Aleksandar",
year = "2016",
abstract = "In this paper, the synchronous axial and bending vibration problem of elastic beams with
variable cross-sectional profile and inhomogeneous material and conjugated boundary conditions
is considered. The orthogonality conditions of mode shapes are derived for the case with no
repeated natural frequencies, along with the constants for the corresponding time function. In that
manner the response of the beam to initial excitations is covered in the theoretical aspect. The
numerical background for solving the problem is explained based on the theory of numerical
“shooting” method and boundary conditions of a considered mechanical case. The case of beams
with no attached end masses and rigid bodies is considered in this paper. Also, one numerical
example is presented to accompany theoretical considerations. The numerical procedure which is
introduced in this paper can also be applied to more complex systems of elastic and rigid bodies,
for instance, those considered in references [11, 15].",
publisher = "Serbian Society of Mechanics, Faculty of Mechanical Engineering",
journal = "Proceedings, The 6th International Congress of Serbian Society of Mechanics",
title = "A NOVEL APPROACH TO THE FREE AXIAL-BENDING VIBRATION PROBLEM OF INHOMOGENEOUS ELASTIC BEAMS WITH VARIABLE CROSS-SECTIONAL PROFILES",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6213"
}

Tomović, A.. (2016). A NOVEL APPROACH TO THE FREE AXIAL-BENDING VIBRATION PROBLEM OF INHOMOGENEOUS ELASTIC BEAMS WITH VARIABLE CROSS-SECTIONAL PROFILES. in Proceedings, The 6th International Congress of Serbian Society of Mechanics
Serbian Society of Mechanics..
https://hdl.handle.net/21.15107/rcub_machinery_6213

Tomović A. A NOVEL APPROACH TO THE FREE AXIAL-BENDING VIBRATION PROBLEM OF INHOMOGENEOUS ELASTIC BEAMS WITH VARIABLE CROSS-SECTIONAL PROFILES. in Proceedings, The 6th International Congress of Serbian Society of Mechanics. 2016;.
https://hdl.handle.net/21.15107/rcub_machinery_6213 .

Tomović, Aleksandar, "A NOVEL APPROACH TO THE FREE AXIAL-BENDING VIBRATION PROBLEM OF INHOMOGENEOUS ELASTIC BEAMS WITH VARIABLE CROSS-SECTIONAL PROFILES" in Proceedings, The 6th International Congress of Serbian Society of Mechanics (2016),
https://hdl.handle.net/21.15107/rcub_machinery_6213 .

TY  - CONF
AU  - Zorić, Nemanja
AU  - Tomović, Aleksandar
AU  - Mitrović, Zoran
AU  - Lazarević, Mihailo
AU  - Pavišić, Mirko
PY  - 2015
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4076
AB  - Position of piezoelectric actuators and sensors on a smart structure directly affects the
control performances of a smart structure. In order to improve efficiency of active vibration
control of a smart structure, optimization of piezoelectric actuators and sensors placement has
been performed. There are various optimization criteria for optimal placement of piezoelectric
actuator. The ‘state-of-the-art’ of optimization criteria is presented in [1]. The aim of this paper is
to compare control effectiveness of smart composite cantilever beam, where optimal
configurations of actuator-sensor pairs were found by using four optimization criteria (LQR based
optimization, grammian matrices, performance index and fuzzy optimization strategy). The
problem is formulated as multi-input-multi-output (MIMO) model. The beam is discretized by
using the finite element method (FEM). The particle swarm optimization (PSO) method is used to
find optimal configurations for each configuration.
PB  - Serbian Society of Mechanics
C3  - 5th International Congress of Serbian Society of Mechanics, Aranđelovac, 2015
T1  - Comparison of various optimization criteria for actuator placement for active vibration control of smart composite beam
IS  - C2b
UR  - https://hdl.handle.net/21.15107/rcub_machinery_4076
ER  - 

@conference{
author = "Zorić, Nemanja and Tomović, Aleksandar and Mitrović, Zoran and Lazarević, Mihailo and Pavišić, Mirko",
year = "2015",
abstract = "Position of piezoelectric actuators and sensors on a smart structure directly affects the
control performances of a smart structure. In order to improve efficiency of active vibration
control of a smart structure, optimization of piezoelectric actuators and sensors placement has
been performed. There are various optimization criteria for optimal placement of piezoelectric
actuator. The ‘state-of-the-art’ of optimization criteria is presented in [1]. The aim of this paper is
to compare control effectiveness of smart composite cantilever beam, where optimal
configurations of actuator-sensor pairs were found by using four optimization criteria (LQR based
optimization, grammian matrices, performance index and fuzzy optimization strategy). The
problem is formulated as multi-input-multi-output (MIMO) model. The beam is discretized by
using the finite element method (FEM). The particle swarm optimization (PSO) method is used to
find optimal configurations for each configuration.",
publisher = "Serbian Society of Mechanics",
journal = "5th International Congress of Serbian Society of Mechanics, Aranđelovac, 2015",
title = "Comparison of various optimization criteria for actuator placement for active vibration control of smart composite beam",
number = "C2b",
url = "https://hdl.handle.net/21.15107/rcub_machinery_4076"
}

Zorić, N., Tomović, A., Mitrović, Z., Lazarević, M.,& Pavišić, M.. (2015). Comparison of various optimization criteria for actuator placement for active vibration control of smart composite beam. in 5th International Congress of Serbian Society of Mechanics, Aranđelovac, 2015
Serbian Society of Mechanics.(C2b).
https://hdl.handle.net/21.15107/rcub_machinery_4076

Zorić N, Tomović A, Mitrović Z, Lazarević M, Pavišić M. Comparison of various optimization criteria for actuator placement for active vibration control of smart composite beam. in 5th International Congress of Serbian Society of Mechanics, Aranđelovac, 2015. 2015;(C2b).
https://hdl.handle.net/21.15107/rcub_machinery_4076 .

Zorić, Nemanja, Tomović, Aleksandar, Mitrović, Zoran, Lazarević, Mihailo, Pavišić, Mirko, "Comparison of various optimization criteria for actuator placement for active vibration control of smart composite beam" in 5th International Congress of Serbian Society of Mechanics, Aranđelovac, 2015, no. C2b (2015),
https://hdl.handle.net/21.15107/rcub_machinery_4076 .

TY  - CONF
AU  - Tomović, Aleksandar
AU  - Stanojević, Miroslav
AU  - Jovović, Aleksandar
AU  - Karličić, Nikola
PY  - 2014
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4683
AB  - Proces proizvodnje cementa je energetski izuzetno zahtevan. Naime, preko 30 % od ukupnih
proizvodnih troškova odlazi upravo na energetske troškove. U cilju smanjenja ovih troškova počelo
se sa korišćenjem alternativnih goriva poreklom iz otpadnih materijala pre skoro pola veka.
Prednosti korišćenja otpadnih materijala u rotacionim pećima su višestruke, a ogledaju se kroz
smanjenje proizvodnih troškova cementa, redukovanje količine otpadnih materija koje bi bile
deponovane, smanjenje emisije CO2 u atmosferu, kao i očuvanje neobnovljivih sirovina i fosilnih
goriva. Sam proizvodni proces u rotacionim pećima pogodan je za sagorevanje otpadnih materijala
zbog visoke radne temperature koja omogućava uništavanje oslobođenih polutanata, dugog perioda zadržavanja gorivih materijala u peći i alkalne radne sredine. Predmet ovog rada jeste korišćenje čvrstog goriva dobijenog iz otpada (SRF-a) kao dodatnog goriva u procesu proizvodnje cementa. Dat je prikaz potencijala Srbije u proizvodnji SRF-a i kontinuitetu obezbeđivanja goriva. Za određeni sastav ovog alternativnog goriva izračunat je sastav produkata sagorevanja.
AB  - The process of cement production has great energy demands. Namely, over 30 % of total
production costs are energy consumption costs. In order to decrease these costs the exploitation of alternative fuels that originate from waste materials started almost half a century ago. Advantages of waste material utilization in the rotary kilns are numerous and they can be observed through the decrease of cement production costs, landfill reduction, CO2 emmission reduction and preservation of natural sources and fossil fuels as well. The production process in rotary kilns, itself enables destruction of produced polutants, long period of passing material through a kiln and alkaline environment as well. The subject of this paper is the utilization of Solid Recoverd Fuel (SRF) as the alternative fuel in cement industry. Serbia’s potentials in production and continuity are presented. For a particular structure of this alternative fuel the composition of combustion products has been calculated.
PB  - Beograd : Savez mašinskih i elektrotehničkih inženjera i tehničara Srbije (SMEITS)
C3  - Zbornik Međunarodnog kongresa o procesnoj industriji – Procesing, 22-24. septembra 2014.
T1  - Upotreba otpadnih gorivih materijala u cementnoj industriji
T1  - The use of waste combustible materials in the cement industry
IS  - 1
VL  - 27
UR  - https://hdl.handle.net/21.15107/rcub_machinery_4683
ER  - 

@conference{
author = "Tomović, Aleksandar and Stanojević, Miroslav and Jovović, Aleksandar and Karličić, Nikola",
year = "2014",
abstract = "Proces proizvodnje cementa je energetski izuzetno zahtevan. Naime, preko 30 % od ukupnih
proizvodnih troškova odlazi upravo na energetske troškove. U cilju smanjenja ovih troškova počelo
se sa korišćenjem alternativnih goriva poreklom iz otpadnih materijala pre skoro pola veka.
Prednosti korišćenja otpadnih materijala u rotacionim pećima su višestruke, a ogledaju se kroz
smanjenje proizvodnih troškova cementa, redukovanje količine otpadnih materija koje bi bile
deponovane, smanjenje emisije CO2 u atmosferu, kao i očuvanje neobnovljivih sirovina i fosilnih
goriva. Sam proizvodni proces u rotacionim pećima pogodan je za sagorevanje otpadnih materijala
zbog visoke radne temperature koja omogućava uništavanje oslobođenih polutanata, dugog perioda zadržavanja gorivih materijala u peći i alkalne radne sredine. Predmet ovog rada jeste korišćenje čvrstog goriva dobijenog iz otpada (SRF-a) kao dodatnog goriva u procesu proizvodnje cementa. Dat je prikaz potencijala Srbije u proizvodnji SRF-a i kontinuitetu obezbeđivanja goriva. Za određeni sastav ovog alternativnog goriva izračunat je sastav produkata sagorevanja., The process of cement production has great energy demands. Namely, over 30 % of total
production costs are energy consumption costs. In order to decrease these costs the exploitation of alternative fuels that originate from waste materials started almost half a century ago. Advantages of waste material utilization in the rotary kilns are numerous and they can be observed through the decrease of cement production costs, landfill reduction, CO2 emmission reduction and preservation of natural sources and fossil fuels as well. The production process in rotary kilns, itself enables destruction of produced polutants, long period of passing material through a kiln and alkaline environment as well. The subject of this paper is the utilization of Solid Recoverd Fuel (SRF) as the alternative fuel in cement industry. Serbia’s potentials in production and continuity are presented. For a particular structure of this alternative fuel the composition of combustion products has been calculated.",
publisher = "Beograd : Savez mašinskih i elektrotehničkih inženjera i tehničara Srbije (SMEITS)",
journal = "Zbornik Međunarodnog kongresa o procesnoj industriji – Procesing, 22-24. septembra 2014.",
title = "Upotreba otpadnih gorivih materijala u cementnoj industriji, The use of waste combustible materials in the cement industry",
number = "1",
volume = "27",
url = "https://hdl.handle.net/21.15107/rcub_machinery_4683"
}

Tomović, A., Stanojević, M., Jovović, A.,& Karličić, N.. (2014). Upotreba otpadnih gorivih materijala u cementnoj industriji. in Zbornik Međunarodnog kongresa o procesnoj industriji – Procesing, 22-24. septembra 2014.
Beograd : Savez mašinskih i elektrotehničkih inženjera i tehničara Srbije (SMEITS)., 27(1).
https://hdl.handle.net/21.15107/rcub_machinery_4683

Tomović A, Stanojević M, Jovović A, Karličić N. Upotreba otpadnih gorivih materijala u cementnoj industriji. in Zbornik Međunarodnog kongresa o procesnoj industriji – Procesing, 22-24. septembra 2014.. 2014;27(1).
https://hdl.handle.net/21.15107/rcub_machinery_4683 .

Tomović, Aleksandar, Stanojević, Miroslav, Jovović, Aleksandar, Karličić, Nikola, "Upotreba otpadnih gorivih materijala u cementnoj industriji" in Zbornik Međunarodnog kongresa o procesnoj industriji – Procesing, 22-24. septembra 2014., 27, no. 1 (2014),
https://hdl.handle.net/21.15107/rcub_machinery_4683 .