TY  - GEN
AU  - Obradović, Aleksandar
PY  - 2024
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7767
T1  - О брахистохронных движениях твердых тел с различными ограничениями реакции связи
UR  - https://hdl.handle.net/21.15107/rcub_machinery_7767
ER  - 

@misc{
author = "Obradović, Aleksandar",
year = "2024",
title = "О брахистохронных движениях твердых тел с различными ограничениями реакции связи",
url = "https://hdl.handle.net/21.15107/rcub_machinery_7767"
}

Obradović, A.. (2024). О брахистохронных движениях твердых тел с различными ограничениями реакции связи. .
https://hdl.handle.net/21.15107/rcub_machinery_7767

Obradović A. О брахистохронных движениях твердых тел с различными ограничениями реакции связи. 2024;.
https://hdl.handle.net/21.15107/rcub_machinery_7767 .

Obradović, Aleksandar, "О брахистохронных движениях твердых тел с различными ограничениями реакции связи" (2024),
https://hdl.handle.net/21.15107/rcub_machinery_7767 .

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  - JOUR
AU  - Karličić, Danilo
AU  - Cajić, Milan
AU  - Paunović, Stepa
AU  - Obradović, Aleksandar
AU  - Adtkihari, Sondipon
AU  - Christensen, Johan
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3972
AB  - Non-reciprocal wave propagation in acoustic and elastic media has received much atten- tion of researchers in recent years. This phenomenon can be achieved by breaking the reci- procity through space- and/or time-dependent constitutive material properties, which is an important step in overcoming the limitations of conventional acoustic- and phononic-like mechanical lattices. A special class of mechanical metamaterials with non-reciprocal wave transmission are latices with time-modulated mass and stiffness properties. Here, we in- vestigate the non-reciprocity in elastic locally resonant and phononic-like one-dimensional lattices with inerter elements where mass and stiffness properties are simultaneously modulated through inerters and springs as harmonic functions of time. By considering the Bloch theorem and Fourier expansions, the frequency-band structures are determined for each configuration while asymmetric band gaps are found by using the weighting and threshold method. The reduction in frequency due to introduced inerters was observed in both phononic and locally resonant metamaterials. Dynamic analysis of finite-length lat- tices by the finite difference method revealed a uni-directional wave propagation. Special attention is given to phononic-like lattice based on a discrete-continuous system of multi- ple coupled beams. Moreover, the existence of edge modes in the discrete phononic lattice is confirmed through the bulk-edge correspondence and their time evolution quantified by the topologically invariant Chern number. The proposed methodology used to inves- tigate non-reciprocal wave transmission in one-dimensional inerter-based lattices can be extended to study more complex two-dimensional lattices.
PB  - Elsevier
T2  - Applied Mathematical Modelling
T1  - Non-reciprocal wave propagation in time-modulated elastic lattices with inerters
EP  - 335
SP  - 316
VL  - 117
DO  - 10.1016/j.apm.2022.12.029
ER  - 

@article{
author = "Karličić, Danilo and Cajić, Milan and Paunović, Stepa and Obradović, Aleksandar and Adtkihari, Sondipon and Christensen, Johan",
year = "2023",
abstract = "Non-reciprocal wave propagation in acoustic and elastic media has received much atten- tion of researchers in recent years. This phenomenon can be achieved by breaking the reci- procity through space- and/or time-dependent constitutive material properties, which is an important step in overcoming the limitations of conventional acoustic- and phononic-like mechanical lattices. A special class of mechanical metamaterials with non-reciprocal wave transmission are latices with time-modulated mass and stiffness properties. Here, we in- vestigate the non-reciprocity in elastic locally resonant and phononic-like one-dimensional lattices with inerter elements where mass and stiffness properties are simultaneously modulated through inerters and springs as harmonic functions of time. By considering the Bloch theorem and Fourier expansions, the frequency-band structures are determined for each configuration while asymmetric band gaps are found by using the weighting and threshold method. The reduction in frequency due to introduced inerters was observed in both phononic and locally resonant metamaterials. Dynamic analysis of finite-length lat- tices by the finite difference method revealed a uni-directional wave propagation. Special attention is given to phononic-like lattice based on a discrete-continuous system of multi- ple coupled beams. Moreover, the existence of edge modes in the discrete phononic lattice is confirmed through the bulk-edge correspondence and their time evolution quantified by the topologically invariant Chern number. The proposed methodology used to inves- tigate non-reciprocal wave transmission in one-dimensional inerter-based lattices can be extended to study more complex two-dimensional lattices.",
publisher = "Elsevier",
journal = "Applied Mathematical Modelling",
title = "Non-reciprocal wave propagation in time-modulated elastic lattices with inerters",
pages = "335-316",
volume = "117",
doi = "10.1016/j.apm.2022.12.029"
}

Karličić, D., Cajić, M., Paunović, S., Obradović, A., Adtkihari, S.,& Christensen, J.. (2023). Non-reciprocal wave propagation in time-modulated elastic lattices with inerters. in Applied Mathematical Modelling
Elsevier., 117, 316-335.
https://doi.org/10.1016/j.apm.2022.12.029

Karličić D, Cajić M, Paunović S, Obradović A, Adtkihari S, Christensen J. Non-reciprocal wave propagation in time-modulated elastic lattices with inerters. in Applied Mathematical Modelling. 2023;117:316-335.
doi:10.1016/j.apm.2022.12.029 .

Karličić, Danilo, Cajić, Milan, Paunović, Stepa, Obradović, Aleksandar, Adtkihari, Sondipon, Christensen, Johan, "Non-reciprocal wave propagation in time-modulated elastic lattices with inerters" in Applied Mathematical Modelling, 117 (2023):316-335,
https://doi.org/10.1016/j.apm.2022.12.029 . .

TY  - JOUR
AU  - Obradović, Aleksandar
AU  - Cherkasov, Oleg
AU  - Miličić, Luka
AU  - Šalinić, Slaviša
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7711
AB  - The paper considers the procedure for determining the brachistochronic motion of the Chaplygin sleigh in a vertical plane, where the blade
is such that it prevents the motion of the contact point in one direction only.
The position of the sleigh mass center and orientation at the final positions is
specified, as well as the initial value of mechanical energy. The simplest formulation of a corresponding optimal control problem is given and it is solved by
applying Pontryagin’s maximum principle. For some cases, analytical solutions
of differential equations of the two-point boundary value problem (TPBVP)
of the maximum principle were found. Numerical integration was carried out
for other cases using the shooting method, where the assessment of missing
terminal conditions was given and it was shown that the solution obtained
represents the global minimum time for the brachistochronic motion. The
method of the brachistochronic motion by means of a single holonomic and a
single unilateral nonholonomic mechanical constraint is presented.
PB  - Serbian Society of Mechanics and Mathematical Institute of the Serbian Academy of Sciences and Arts, Beograd
T1  - REALIZATION OF THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT
EP  - 183
IS  - 2
SP  - 171
VL  - 50
DO  - 10.2298/TAM231017011O
ER  - 

@article{
author = "Obradović, Aleksandar and Cherkasov, Oleg and Miličić, Luka and Šalinić, Slaviša",
year = "2023",
abstract = "The paper considers the procedure for determining the brachistochronic motion of the Chaplygin sleigh in a vertical plane, where the blade
is such that it prevents the motion of the contact point in one direction only.
The position of the sleigh mass center and orientation at the final positions is
specified, as well as the initial value of mechanical energy. The simplest formulation of a corresponding optimal control problem is given and it is solved by
applying Pontryagin’s maximum principle. For some cases, analytical solutions
of differential equations of the two-point boundary value problem (TPBVP)
of the maximum principle were found. Numerical integration was carried out
for other cases using the shooting method, where the assessment of missing
terminal conditions was given and it was shown that the solution obtained
represents the global minimum time for the brachistochronic motion. The
method of the brachistochronic motion by means of a single holonomic and a
single unilateral nonholonomic mechanical constraint is presented.",
publisher = "Serbian Society of Mechanics and Mathematical Institute of the Serbian Academy of Sciences and Arts, Beograd",
title = "REALIZATION OF THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT",
pages = "183-171",
number = "2",
volume = "50",
doi = "10.2298/TAM231017011O"
}

Obradović, A., Cherkasov, O., Miličić, L.,& Šalinić, S.. (2023). REALIZATION OF THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT. 
Serbian Society of Mechanics and Mathematical Institute of the Serbian Academy of Sciences and Arts, Beograd., 50(2), 171-183.
https://doi.org/10.2298/TAM231017011O

Obradović A, Cherkasov O, Miličić L, Šalinić S. REALIZATION OF THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT. 2023;50(2):171-183.
doi:10.2298/TAM231017011O .

Obradović, Aleksandar, Cherkasov, Oleg, Miličić, Luka, Šalinić, Slaviša, "REALIZATION OF THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT", 50, no. 2 (2023):171-183,
https://doi.org/10.2298/TAM231017011O . .

TY  - GEN
AU  - Obradović, Aleksandar
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7770
T1  - К задаче о качении тяжелого однородного шара без проскальзывания по неподвижной поверхности вращения
UR  - https://hdl.handle.net/21.15107/rcub_machinery_7770
ER  - 

@misc{
author = "Obradović, Aleksandar",
year = "2023",
title = "К задаче о качении тяжелого однородного шара без проскальзывания по неподвижной поверхности вращения",
url = "https://hdl.handle.net/21.15107/rcub_machinery_7770"
}

Obradović, A.. (2023). К задаче о качении тяжелого однородного шара без проскальзывания по неподвижной поверхности вращения. .
https://hdl.handle.net/21.15107/rcub_machinery_7770

Obradović A. К задаче о качении тяжелого однородного шара без проскальзывания по неподвижной поверхности вращения. 2023;.
https://hdl.handle.net/21.15107/rcub_machinery_7770 .

Obradović, Aleksandar, "К задаче о качении тяжелого однородного шара без проскальзывания по неподвижной поверхности вращения" (2023),
https://hdl.handle.net/21.15107/rcub_machinery_7770 .

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  - CONF
AU  - Obradović, Aleksandar
AU  - Cherkasov, Oleg
AU  - Miličić, Luka
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6897
AB  - The paper considers the procedure for determining the brachistochronic motion of the Chaplygin sleigh in a vertical plane, where the blade is such that it prevents the motion of the contact point in one direction only. The position of the sleigh mass center and orientation at the final positions is specified, as well as the initial value of mechanical energy. The simplest formulation of a corresponding optimal control problem is given and it is solved by applying Pontryagin’s maximum principle. For some cases, analytical solutions of differential equations of the two-point boundary value problem (TPBVP) of the maximum principle, were found. Numerical integration was carried out for other cases using the shooting method, where the assessment of missing terminal conditions was given and it was shown that the solution obtained represents the global minimum time for the brachistochronic motion.
PB  - Belgrade : Serbian Society of Mechanics
C3  - 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023
T1  - THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT
SP  - T.4.3
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6897
ER  - 

@conference{
author = "Obradović, Aleksandar and Cherkasov, Oleg and Miličić, Luka",
year = "2023",
abstract = "The paper considers the procedure for determining the brachistochronic motion of the Chaplygin sleigh in a vertical plane, where the blade is such that it prevents the motion of the contact point in one direction only. The position of the sleigh mass center and orientation at the final positions is specified, as well as the initial value of mechanical energy. The simplest formulation of a corresponding optimal control problem is given and it is solved by applying Pontryagin’s maximum principle. For some cases, analytical solutions of differential equations of the two-point boundary value problem (TPBVP) of the maximum principle, were found. Numerical integration was carried out for other cases using the shooting method, where the assessment of missing terminal conditions was given and it was shown that the solution obtained represents the global minimum time for the brachistochronic motion.",
publisher = "Belgrade : Serbian Society of Mechanics",
journal = "9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023",
title = "THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT",
pages = "T.4.3",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6897"
}

Obradović, A., Cherkasov, O.,& Miličić, L.. (2023). THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT. in 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023
Belgrade : Serbian Society of Mechanics., T.4.3.
https://hdl.handle.net/21.15107/rcub_machinery_6897

Obradović A, Cherkasov O, Miličić L. THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT. in 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023. 2023;:T.4.3.
https://hdl.handle.net/21.15107/rcub_machinery_6897 .

Obradović, Aleksandar, Cherkasov, Oleg, Miličić, Luka, "THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT" in 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023 (2023):T.4.3,
https://hdl.handle.net/21.15107/rcub_machinery_6897 .

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  - JOUR
AU  - Grbović, Aleksandar
AU  - Kastratović, Gordana
AU  - Bozić, Željko
AU  - Božić, Ivan
AU  - Obradović, Aleksandar
AU  - Sedmak, Aleksandar
AU  - Sedmak, Simon
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3709
AB  - The aircraft industry is a leading industry in terms of the implementation of new materials and technologies. In the development of a light aircraft several different materials were considered for the engine cover design and the final decision was to select a composite material. Part of the research performed on the cover design is presented in this paper. The composite test specimens were produced and mechanical properties were investigated in the tensile and three-point flexural tests according to the required standards. The comparison of experimentally and numerically obtained mechanical properties showed good agreement, which led to the design, verification and manufacturing of the complex-shaped engine cover without costly and demanding tests. It was considered that numerical simulations of the engine cover performance under different loading conditions yielded realistic results, therefore experimental verification was excluded. The flight tests proved the predicted behavior, thus verifying the design methodology presented in this paper.
PB  - Pergamon-Elsevier Science Ltd, Oxford
T2  - Engineering Failure Analysis
T1  - Experimental and numerical evaluation of fracture characteristics of composite material used in the aircraft engine cover manufacturing
VL  - 137
DO  - 10.1016/j.engfailanal.2022.106286
ER  - 

@article{
author = "Grbović, Aleksandar and Kastratović, Gordana and Bozić, Željko and Božić, Ivan and Obradović, Aleksandar and Sedmak, Aleksandar and Sedmak, Simon",
year = "2022",
abstract = "The aircraft industry is a leading industry in terms of the implementation of new materials and technologies. In the development of a light aircraft several different materials were considered for the engine cover design and the final decision was to select a composite material. Part of the research performed on the cover design is presented in this paper. The composite test specimens were produced and mechanical properties were investigated in the tensile and three-point flexural tests according to the required standards. The comparison of experimentally and numerically obtained mechanical properties showed good agreement, which led to the design, verification and manufacturing of the complex-shaped engine cover without costly and demanding tests. It was considered that numerical simulations of the engine cover performance under different loading conditions yielded realistic results, therefore experimental verification was excluded. The flight tests proved the predicted behavior, thus verifying the design methodology presented in this paper.",
publisher = "Pergamon-Elsevier Science Ltd, Oxford",
journal = "Engineering Failure Analysis",
title = "Experimental and numerical evaluation of fracture characteristics of composite material used in the aircraft engine cover manufacturing",
volume = "137",
doi = "10.1016/j.engfailanal.2022.106286"
}

Grbović, A., Kastratović, G., Bozić, Ž., Božić, I., Obradović, A., Sedmak, A.,& Sedmak, S.. (2022). Experimental and numerical evaluation of fracture characteristics of composite material used in the aircraft engine cover manufacturing. in Engineering Failure Analysis
Pergamon-Elsevier Science Ltd, Oxford., 137.
https://doi.org/10.1016/j.engfailanal.2022.106286

Grbović A, Kastratović G, Bozić Ž, Božić I, Obradović A, Sedmak A, Sedmak S. Experimental and numerical evaluation of fracture characteristics of composite material used in the aircraft engine cover manufacturing. in Engineering Failure Analysis. 2022;137.
doi:10.1016/j.engfailanal.2022.106286 .

Grbović, Aleksandar, Kastratović, Gordana, Bozić, Željko, Božić, Ivan, Obradović, Aleksandar, Sedmak, Aleksandar, Sedmak, Simon, "Experimental and numerical evaluation of fracture characteristics of composite material used in the aircraft engine cover manufacturing" in Engineering Failure Analysis, 137 (2022),
https://doi.org/10.1016/j.engfailanal.2022.106286 . .

TY  - JOUR
AU  - Obradović, Aleksandar
AU  - Mitrović, Zoran
AU  - Šalinić, Slaviša
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3691
AB  - The paper considers a heavy homogeneous ball rolling without slipping on the outside of a real rough fixed surface of revolution, which is generated by rotating a plane curve around a vertical axis. By applying the Coulomb sliding friction law, the position is established at which slipping occurs during rolling down the surface, and thereafter this mechanical system ceases to be holonomic. Dynamic differential equations of motion are obtained using general theorems of mechanics. The paper presents the procedure of determining the tangential and normal component of the reaction of constraint depending on the height of the contact point between the ball and the surface. On the basis of the initial total mechanical energy of the system and the value of Coulomb friction coefficient, the condition is determined to prevent the ball from slipping, as well as the height interval in which the considered system behaves as a nonholonomic system. The procedure is illustrated by examples of surfaces generated by rotating segments of the circular arc, line and parabola. In the last example there is not a closed-form solution, so that numerical integration of a corresponding Cauchy problem is performed.
PB  - Elsevier Science Inc, New York
T2  - Applied Mathematics and Computation
T1  - On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution
VL  - 420
DO  - 10.1016/j.amc.2021.126906
ER  - 

@article{
author = "Obradović, Aleksandar and Mitrović, Zoran and Šalinić, Slaviša",
year = "2022",
abstract = "The paper considers a heavy homogeneous ball rolling without slipping on the outside of a real rough fixed surface of revolution, which is generated by rotating a plane curve around a vertical axis. By applying the Coulomb sliding friction law, the position is established at which slipping occurs during rolling down the surface, and thereafter this mechanical system ceases to be holonomic. Dynamic differential equations of motion are obtained using general theorems of mechanics. The paper presents the procedure of determining the tangential and normal component of the reaction of constraint depending on the height of the contact point between the ball and the surface. On the basis of the initial total mechanical energy of the system and the value of Coulomb friction coefficient, the condition is determined to prevent the ball from slipping, as well as the height interval in which the considered system behaves as a nonholonomic system. The procedure is illustrated by examples of surfaces generated by rotating segments of the circular arc, line and parabola. In the last example there is not a closed-form solution, so that numerical integration of a corresponding Cauchy problem is performed.",
publisher = "Elsevier Science Inc, New York",
journal = "Applied Mathematics and Computation",
title = "On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution",
volume = "420",
doi = "10.1016/j.amc.2021.126906"
}

Obradović, A., Mitrović, Z.,& Šalinić, S.. (2022). On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution. in Applied Mathematics and Computation
Elsevier Science Inc, New York., 420.
https://doi.org/10.1016/j.amc.2021.126906

Obradović A, Mitrović Z, Šalinić S. On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution. in Applied Mathematics and Computation. 2022;420.
doi:10.1016/j.amc.2021.126906 .

Obradović, Aleksandar, Mitrović, Zoran, Šalinić, Slaviša, "On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution" in Applied Mathematics and Computation, 420 (2022),
https://doi.org/10.1016/j.amc.2021.126906 . .

TY  - JOUR
AU  - Nešić, Nikola
AU  - Cajić, Milan
AU  - Karličić, Danilo
AU  - Obradović, Aleksandar
AU  - Simonović, Julijana
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3789
AB  - This paper investigates the nonlinear dynamic behavior of a nonlocal functionally graded Euler-Bernoulli beam resting on a fractional visco-Pasternak foundation and subjected to harmonic loads. The proposed model captures both, nonlocal parameter considering the elastic stress gradient field and a material length scale parameter considering the strain gradient stress field. Additionally, the von Karman strain-displacement relation is used to describe the nonlinear geometrical beam behavior. The power-law model is utilized to represent the material variations across the thickness direction of the functionally graded beam. The following steps are conducted in this research study. At first, the governing equation of motion is derived using Hamilton's principle and then reduced to the nonlinear fractional-order differential equation through the single-mode Galerkin approximation. The methodology to determine steady-state amplitude-frequency responses via incremental harmonic balance method and continuation technique is presented. The obtained periodic solutions are verified against the perturbation multiple scales method for the weakly nonlinear case and numerical integration Newmark method in the case of strong nonlinearity. It has been shown that the application of the incremental harmonic balance method in the analysis of nonlocal strain gradient theory-based structures can lead to more reliable studies for strongly nonlinear systems. In the parametric study, it is shown that, on the one hand, parameters of the visco-Pasternak foundation and power-law index remarkable affect the amplitudes responses. On the contrary, the nonlocal and the length-scale parameters are having a small influence on the amplitude-frequency response. Finally, the effects of the fractional derivative order on the system's damping are displayed at time response diagrams and subsequently discussed.
PB  - Springer, Dordrecht
T2  - Nonlinear Dynamics
T1  - Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation
EP  - 2026
IS  - 3
SP  - 2003
VL  - 107
DO  - 10.1007/s11071-021-07081-z
ER  - 

@article{
author = "Nešić, Nikola and Cajić, Milan and Karličić, Danilo and Obradović, Aleksandar and Simonović, Julijana",
year = "2022",
abstract = "This paper investigates the nonlinear dynamic behavior of a nonlocal functionally graded Euler-Bernoulli beam resting on a fractional visco-Pasternak foundation and subjected to harmonic loads. The proposed model captures both, nonlocal parameter considering the elastic stress gradient field and a material length scale parameter considering the strain gradient stress field. Additionally, the von Karman strain-displacement relation is used to describe the nonlinear geometrical beam behavior. The power-law model is utilized to represent the material variations across the thickness direction of the functionally graded beam. The following steps are conducted in this research study. At first, the governing equation of motion is derived using Hamilton's principle and then reduced to the nonlinear fractional-order differential equation through the single-mode Galerkin approximation. The methodology to determine steady-state amplitude-frequency responses via incremental harmonic balance method and continuation technique is presented. The obtained periodic solutions are verified against the perturbation multiple scales method for the weakly nonlinear case and numerical integration Newmark method in the case of strong nonlinearity. It has been shown that the application of the incremental harmonic balance method in the analysis of nonlocal strain gradient theory-based structures can lead to more reliable studies for strongly nonlinear systems. In the parametric study, it is shown that, on the one hand, parameters of the visco-Pasternak foundation and power-law index remarkable affect the amplitudes responses. On the contrary, the nonlocal and the length-scale parameters are having a small influence on the amplitude-frequency response. Finally, the effects of the fractional derivative order on the system's damping are displayed at time response diagrams and subsequently discussed.",
publisher = "Springer, Dordrecht",
journal = "Nonlinear Dynamics",
title = "Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation",
pages = "2026-2003",
number = "3",
volume = "107",
doi = "10.1007/s11071-021-07081-z"
}

Nešić, N., Cajić, M., Karličić, D., Obradović, A.,& Simonović, J.. (2022). Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation. in Nonlinear Dynamics
Springer, Dordrecht., 107(3), 2003-2026.
https://doi.org/10.1007/s11071-021-07081-z

Nešić N, Cajić M, Karličić D, Obradović A, Simonović J. Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation. in Nonlinear Dynamics. 2022;107(3):2003-2026.
doi:10.1007/s11071-021-07081-z .

Nešić, Nikola, Cajić, Milan, Karličić, Danilo, Obradović, Aleksandar, Simonović, Julijana, "Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation" in Nonlinear Dynamics, 107, no. 3 (2022):2003-2026,
https://doi.org/10.1007/s11071-021-07081-z . .

TY  - JOUR
AU  - Nešić, Nikola
AU  - Cajić, Milan
AU  - Karličić, Danilo
AU  - Obradović, Aleksandar
AU  - Simonović, Julijana
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4360
AB  - This paper investigates the nonlinear dynamic behavior of a nonlocal functionally graded Euler-Bernoulli beam resting on a fractional visco-Pasternak foundation and subjected to harmonic loads. The proposed model captures both, nonlocal parameter considering the elastic stress gradient field and a material length scale parameter considering the strain gradient stress field. Additionally, the von Karman strain-displacement relation is used to describe the nonlinear geometrical beam behavior. The power-law model is utilized to represent the material variations across the thickness direction of the functionally graded beam. The following steps are conducted in this research study. At first, the governing equation of motion is derived using Hamilton's principle and then reduced to the nonlinear fractional-order differential equation through the single-mode Galerkin approximation. The methodology to determine steady-state amplitude-frequency responses via incremental harmonic balance method and continuation technique is presented. The obtained periodic solutions are verified against the perturbation multiple scales method for the weakly nonlinear case and numerical integration Newmark method in the case of strong nonlinearity. It has been shown that the application of the incremental harmonic balance method in the analysis of nonlocal strain gradient theory-based structures can lead to more reliable studies for strongly nonlinear systems. In the parametric study, it is shown that, on the one hand, parameters of the visco-Pasternak foundation and power-law index remarkable affect the amplitudes responses. On the contrary, the nonlocal and the length-scale parameters are having a small influence on the amplitude-frequency response. Finally, the effects of the fractional derivative order on the system's damping are displayed at time response diagrams and subsequently discussed.
PB  - Springer, Dordrecht
T2  - Nonlinear Dynamics
T1  - Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation
EP  - 2026
IS  - 3
SP  - 2003
VL  - 107
DO  - 10.1007/s11071-021-07081-z
ER  - 

@article{
author = "Nešić, Nikola and Cajić, Milan and Karličić, Danilo and Obradović, Aleksandar and Simonović, Julijana",
year = "2022",
abstract = "This paper investigates the nonlinear dynamic behavior of a nonlocal functionally graded Euler-Bernoulli beam resting on a fractional visco-Pasternak foundation and subjected to harmonic loads. The proposed model captures both, nonlocal parameter considering the elastic stress gradient field and a material length scale parameter considering the strain gradient stress field. Additionally, the von Karman strain-displacement relation is used to describe the nonlinear geometrical beam behavior. The power-law model is utilized to represent the material variations across the thickness direction of the functionally graded beam. The following steps are conducted in this research study. At first, the governing equation of motion is derived using Hamilton's principle and then reduced to the nonlinear fractional-order differential equation through the single-mode Galerkin approximation. The methodology to determine steady-state amplitude-frequency responses via incremental harmonic balance method and continuation technique is presented. The obtained periodic solutions are verified against the perturbation multiple scales method for the weakly nonlinear case and numerical integration Newmark method in the case of strong nonlinearity. It has been shown that the application of the incremental harmonic balance method in the analysis of nonlocal strain gradient theory-based structures can lead to more reliable studies for strongly nonlinear systems. In the parametric study, it is shown that, on the one hand, parameters of the visco-Pasternak foundation and power-law index remarkable affect the amplitudes responses. On the contrary, the nonlocal and the length-scale parameters are having a small influence on the amplitude-frequency response. Finally, the effects of the fractional derivative order on the system's damping are displayed at time response diagrams and subsequently discussed.",
publisher = "Springer, Dordrecht",
journal = "Nonlinear Dynamics",
title = "Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation",
pages = "2026-2003",
number = "3",
volume = "107",
doi = "10.1007/s11071-021-07081-z"
}

Nešić, N., Cajić, M., Karličić, D., Obradović, A.,& Simonović, J.. (2022). Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation. in Nonlinear Dynamics
Springer, Dordrecht., 107(3), 2003-2026.
https://doi.org/10.1007/s11071-021-07081-z

Nešić N, Cajić M, Karličić D, Obradović A, Simonović J. Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation. in Nonlinear Dynamics. 2022;107(3):2003-2026.
doi:10.1007/s11071-021-07081-z .

Nešić, Nikola, Cajić, Milan, Karličić, Danilo, Obradović, Aleksandar, Simonović, Julijana, "Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation" in Nonlinear Dynamics, 107, no. 3 (2022):2003-2026,
https://doi.org/10.1007/s11071-021-07081-z . .

TY  - JOUR
AU  - Obradović, Aleksandar
AU  - Mitrović, Zoran
AU  - Šalinić, Slaviša
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4361
AB  - The paper considers a heavy homogeneous ball rolling without slipping on the outside of a real rough fixed surface of revolution, which is generated by rotating a plane curve around a vertical axis. By applying the Coulomb sliding friction law, the position is established at which slipping occurs during rolling down the surface, and thereafter this mechanical system ceases to be holonomic. Dynamic differential equations of motion are obtained using general theorems of mechanics. The paper presents the procedure of determining the tangential and normal component of the reaction of constraint depending on the height of the contact point between the ball and the surface. On the basis of the initial total mechanical energy of the system and the value of Coulomb friction coefficient, the condition is determined to prevent the ball from slipping, as well as the height interval in which the considered system behaves as a nonholonomic system. The procedure is illustrated by examples of surfaces generated by rotating segments of the circular arc, line and parabola. In the last example there is not a closed-form solution, so that numerical integration of a corresponding Cauchy problem is performed.
PB  - Elsevier Science Inc, New York
T2  - Applied Mathematics and Computation
T1  - On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution
VL  - 420
DO  - 10.1016/j.amc.2021.126906
ER  - 

@article{
author = "Obradović, Aleksandar and Mitrović, Zoran and Šalinić, Slaviša",
year = "2022",
abstract = "The paper considers a heavy homogeneous ball rolling without slipping on the outside of a real rough fixed surface of revolution, which is generated by rotating a plane curve around a vertical axis. By applying the Coulomb sliding friction law, the position is established at which slipping occurs during rolling down the surface, and thereafter this mechanical system ceases to be holonomic. Dynamic differential equations of motion are obtained using general theorems of mechanics. The paper presents the procedure of determining the tangential and normal component of the reaction of constraint depending on the height of the contact point between the ball and the surface. On the basis of the initial total mechanical energy of the system and the value of Coulomb friction coefficient, the condition is determined to prevent the ball from slipping, as well as the height interval in which the considered system behaves as a nonholonomic system. The procedure is illustrated by examples of surfaces generated by rotating segments of the circular arc, line and parabola. In the last example there is not a closed-form solution, so that numerical integration of a corresponding Cauchy problem is performed.",
publisher = "Elsevier Science Inc, New York",
journal = "Applied Mathematics and Computation",
title = "On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution",
volume = "420",
doi = "10.1016/j.amc.2021.126906"
}

Obradović, A., Mitrović, Z.,& Šalinić, S.. (2022). On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution. in Applied Mathematics and Computation
Elsevier Science Inc, New York., 420.
https://doi.org/10.1016/j.amc.2021.126906

Obradović A, Mitrović Z, Šalinić S. On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution. in Applied Mathematics and Computation. 2022;420.
doi:10.1016/j.amc.2021.126906 .

Obradović, Aleksandar, Mitrović, Zoran, Šalinić, Slaviša, "On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution" in Applied Mathematics and Computation, 420 (2022),
https://doi.org/10.1016/j.amc.2021.126906 . .

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  - JOUR
AU  - Šalinić, Slaviša
AU  - Todorović, Marko
AU  - Obradović, Aleksandar
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4098
AB  - Free vibration of eccentrically stepped beams with one step change in cross-section is considered. It is assumed that the longitudinal symmetry axes of the beam segments are translationally shifted along the vertical direction with respect to each other. The effect of that arrangement of the segments on the coupling of axial and bending vibrations of the stepped beam is analyzed. The beam segments are modeled in the frame of the Euler-Bernoulli theory of elastic beams. Two numerical examples are presented.
PB  - University of Kragujevac, Faculty of Mechanical and Civil Engineering, Kraljevo, Serbia
T2  - Engineering Today
T1  - An analytical approach for free vibration analysis of Euler-Bernoulli stepped beams with axial-bending coupling effect
EP  - 17
IS  - 4
SP  - 7
VL  - 1
DO  - 10.5937/engtoday2204007S
ER  - 

@article{
author = "Šalinić, Slaviša and Todorović, Marko and Obradović, Aleksandar",
year = "2022",
abstract = "Free vibration of eccentrically stepped beams with one step change in cross-section is considered. It is assumed that the longitudinal symmetry axes of the beam segments are translationally shifted along the vertical direction with respect to each other. The effect of that arrangement of the segments on the coupling of axial and bending vibrations of the stepped beam is analyzed. The beam segments are modeled in the frame of the Euler-Bernoulli theory of elastic beams. Two numerical examples are presented.",
publisher = "University of Kragujevac, Faculty of Mechanical and Civil Engineering, Kraljevo, Serbia",
journal = "Engineering Today",
title = "An analytical approach for free vibration analysis of Euler-Bernoulli stepped beams with axial-bending coupling effect",
pages = "17-7",
number = "4",
volume = "1",
doi = "10.5937/engtoday2204007S"
}

Šalinić, S., Todorović, M.,& Obradović, A.. (2022). An analytical approach for free vibration analysis of Euler-Bernoulli stepped beams with axial-bending coupling effect. in Engineering Today
University of Kragujevac, Faculty of Mechanical and Civil Engineering, Kraljevo, Serbia., 1(4), 7-17.
https://doi.org/10.5937/engtoday2204007S

Šalinić S, Todorović M, Obradović A. An analytical approach for free vibration analysis of Euler-Bernoulli stepped beams with axial-bending coupling effect. in Engineering Today. 2022;1(4):7-17.
doi:10.5937/engtoday2204007S .

Šalinić, Slaviša, Todorović, Marko, Obradović, Aleksandar, "An analytical approach for free vibration analysis of Euler-Bernoulli stepped beams with axial-bending coupling effect" in Engineering Today, 1, no. 4 (2022):7-17,
https://doi.org/10.5937/engtoday2204007S . .

TY  - CONF
AU  - Miličić, Luka
AU  - Obradović, Aleksandar
AU  - Todić, Ivana
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4077
AB  - Numerical techniques for solving optimal control problems fall into two general classes: indirect methods and direct methods. In an indirect method, we rely on the Pontryagin's maximum principle and other necessary conditions to obtain a two-point boundary-value problem, which is then numerically solved for optimal trajectories. However, indirect methods are frequently subject to severe convergence problems. We examine the possibility of implementing these methods in guidance algorithms using a single processor. Calculations were performed in real time and conclusions are drawn about the robustness of these methods.
PB  - Univerzitet u Beogradu, Mašinski fakultet
C3  - Abstract book : Mathematics, Numerics and Applications MNA 2022, Budva 1-3 June, 2022
T1  - Overview of numerical methods for solving optimal control problem in guidance  algorithms
EP  - 17
SP  - 17
UR  - https://hdl.handle.net/21.15107/rcub_machinery_4077
ER  - 

@conference{
author = "Miličić, Luka and Obradović, Aleksandar and Todić, Ivana",
year = "2022",
abstract = "Numerical techniques for solving optimal control problems fall into two general classes: indirect methods and direct methods. In an indirect method, we rely on the Pontryagin's maximum principle and other necessary conditions to obtain a two-point boundary-value problem, which is then numerically solved for optimal trajectories. However, indirect methods are frequently subject to severe convergence problems. We examine the possibility of implementing these methods in guidance algorithms using a single processor. Calculations were performed in real time and conclusions are drawn about the robustness of these methods.",
publisher = "Univerzitet u Beogradu, Mašinski fakultet",
journal = "Abstract book : Mathematics, Numerics and Applications MNA 2022, Budva 1-3 June, 2022",
title = "Overview of numerical methods for solving optimal control problem in guidance  algorithms",
pages = "17-17",
url = "https://hdl.handle.net/21.15107/rcub_machinery_4077"
}

Miličić, L., Obradović, A.,& Todić, I.. (2022). Overview of numerical methods for solving optimal control problem in guidance  algorithms. in Abstract book : Mathematics, Numerics and Applications MNA 2022, Budva 1-3 June, 2022
Univerzitet u Beogradu, Mašinski fakultet., 17-17.
https://hdl.handle.net/21.15107/rcub_machinery_4077

Miličić L, Obradović A, Todić I. Overview of numerical methods for solving optimal control problem in guidance  algorithms. in Abstract book : Mathematics, Numerics and Applications MNA 2022, Budva 1-3 June, 2022. 2022;:17-17.
https://hdl.handle.net/21.15107/rcub_machinery_4077 .

Miličić, Luka, Obradović, Aleksandar, Todić, Ivana, "Overview of numerical methods for solving optimal control problem in guidance  algorithms" in Abstract book : Mathematics, Numerics and Applications MNA 2022, Budva 1-3 June, 2022 (2022):17-17,
https://hdl.handle.net/21.15107/rcub_machinery_4077 .

TY  - CONF
AU  - Obradović, Aleksandar
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3971
AB  - The paper considers mass minimization of an axially functionally graded (AFG) Timoshenko beam of a variable cross-sectional area, with a specified fundamental frequency. The analyzed case of coupled axial and bending vibrations involves contour conditions as the cause of coupling. The problem is solved applying Pontryagin’s maximum principle, where the beam cross-sectional area is taken for control. The two-point boundary value problem is obtained, and the shooting method is used to solving it. The property of self-adjoint systems is deployed. The percent saving of the beam mass is determined, achieved by using the beam of an optimum variable square cross-section as compared to the beam of a constant cross-section. The procedure developed by the author in his earlier papers is extended herein to the case of a limited cross-sectional area. The second generalization relates to the general case of contour conditions at the beam ends.
PB  - Serbian Academy of Nonlinear Sciences
C3  - Proceedings of the 2nd CONFERENCE ON NONLINEARITY, 11, October18–22, 2021,Belgrade
T1  - Mass minimization of an AFG Timoshenko beam with a coupled axial and bending vibrations
EP  - 108
SP  - 96
UR  - https://hdl.handle.net/21.15107/rcub_machinery_3971
ER  - 

@conference{
author = "Obradović, Aleksandar",
year = "2022",
abstract = "The paper considers mass minimization of an axially functionally graded (AFG) Timoshenko beam of a variable cross-sectional area, with a specified fundamental frequency. The analyzed case of coupled axial and bending vibrations involves contour conditions as the cause of coupling. The problem is solved applying Pontryagin’s maximum principle, where the beam cross-sectional area is taken for control. The two-point boundary value problem is obtained, and the shooting method is used to solving it. The property of self-adjoint systems is deployed. The percent saving of the beam mass is determined, achieved by using the beam of an optimum variable square cross-section as compared to the beam of a constant cross-section. The procedure developed by the author in his earlier papers is extended herein to the case of a limited cross-sectional area. The second generalization relates to the general case of contour conditions at the beam ends.",
publisher = "Serbian Academy of Nonlinear Sciences",
journal = "Proceedings of the 2nd CONFERENCE ON NONLINEARITY, 11, October18–22, 2021,Belgrade",
title = "Mass minimization of an AFG Timoshenko beam with a coupled axial and bending vibrations",
pages = "108-96",
url = "https://hdl.handle.net/21.15107/rcub_machinery_3971"
}

Obradović, A.. (2022). Mass minimization of an AFG Timoshenko beam with a coupled axial and bending vibrations. in Proceedings of the 2nd CONFERENCE ON NONLINEARITY, 11, October18–22, 2021,Belgrade
Serbian Academy of Nonlinear Sciences., 96-108.
https://hdl.handle.net/21.15107/rcub_machinery_3971

Obradović A. Mass minimization of an AFG Timoshenko beam with a coupled axial and bending vibrations. in Proceedings of the 2nd CONFERENCE ON NONLINEARITY, 11, October18–22, 2021,Belgrade. 2022;:96-108.
https://hdl.handle.net/21.15107/rcub_machinery_3971 .

Obradović, Aleksandar, "Mass minimization of an AFG Timoshenko beam with a coupled axial and bending vibrations" in Proceedings of the 2nd CONFERENCE ON NONLINEARITY, 11, October18–22, 2021,Belgrade (2022):96-108,
https://hdl.handle.net/21.15107/rcub_machinery_3971 .

TY  - JOUR
AU  - Milenović, Ivan Lj.
AU  - Bošnjak, Srđan
AU  - Gnjatović, Nebojša
AU  - Obradović, Aleksandar
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3732
AB  - Identification of the basic parameters of static stability (BPSS) of the slewing superstructure is the key step in solving the problem of its static stability, as well as static stability of the entire bucket wheel excavator (BWE). Specificity of the slewing superstructure examined in this paper lies in the kinematic breakdown system (KBS) which prevents the loss of static stability on the counterweight side. Development of a unique method for the formation and two-step validation of the calculation models for this particular design concept was the main objective of the presented research. A two-step validation of the analytical models is conducted based on the experimental results. As the outcome, the final calculation model formed in such manner represents an accurate basis both for the proof of static stability and for the monitoring of the BPSS during exploitation. By comparing the results of the control weighing and the referent values of the final calculation model it was concluded that the existing double-walled bucket wheel represents a 'weak point' of the considered BWE.
PB  - Polish Maintenance Soc, Lublin
T2  - Eksploatacja I Niezawodnosc-Maintenance and Reliability
T1  - Bucket wheel excavators with a kinematic breakdown system: Identification and monitoring of the basic parameters of static stability of the slewing superstructure
EP  - 370
IS  - 2
SP  - 359
VL  - 24
DO  - 10.17531/ein.2022.2.17
ER  - 

@article{
author = "Milenović, Ivan Lj. and Bošnjak, Srđan and Gnjatović, Nebojša and Obradović, Aleksandar",
year = "2022",
abstract = "Identification of the basic parameters of static stability (BPSS) of the slewing superstructure is the key step in solving the problem of its static stability, as well as static stability of the entire bucket wheel excavator (BWE). Specificity of the slewing superstructure examined in this paper lies in the kinematic breakdown system (KBS) which prevents the loss of static stability on the counterweight side. Development of a unique method for the formation and two-step validation of the calculation models for this particular design concept was the main objective of the presented research. A two-step validation of the analytical models is conducted based on the experimental results. As the outcome, the final calculation model formed in such manner represents an accurate basis both for the proof of static stability and for the monitoring of the BPSS during exploitation. By comparing the results of the control weighing and the referent values of the final calculation model it was concluded that the existing double-walled bucket wheel represents a 'weak point' of the considered BWE.",
publisher = "Polish Maintenance Soc, Lublin",
journal = "Eksploatacja I Niezawodnosc-Maintenance and Reliability",
title = "Bucket wheel excavators with a kinematic breakdown system: Identification and monitoring of the basic parameters of static stability of the slewing superstructure",
pages = "370-359",
number = "2",
volume = "24",
doi = "10.17531/ein.2022.2.17"
}

Milenović, I. Lj., Bošnjak, S., Gnjatović, N.,& Obradović, A.. (2022). Bucket wheel excavators with a kinematic breakdown system: Identification and monitoring of the basic parameters of static stability of the slewing superstructure. in Eksploatacja I Niezawodnosc-Maintenance and Reliability
Polish Maintenance Soc, Lublin., 24(2), 359-370.
https://doi.org/10.17531/ein.2022.2.17

Milenović IL, Bošnjak S, Gnjatović N, Obradović A. Bucket wheel excavators with a kinematic breakdown system: Identification and monitoring of the basic parameters of static stability of the slewing superstructure. in Eksploatacja I Niezawodnosc-Maintenance and Reliability. 2022;24(2):359-370.
doi:10.17531/ein.2022.2.17 .

Milenović, Ivan Lj., Bošnjak, Srđan, Gnjatović, Nebojša, Obradović, Aleksandar, "Bucket wheel excavators with a kinematic breakdown system: Identification and monitoring of the basic parameters of static stability of the slewing superstructure" in Eksploatacja I Niezawodnosc-Maintenance and Reliability, 24, no. 2 (2022):359-370,
https://doi.org/10.17531/ein.2022.2.17 . .

TY  - CONF
AU  - Obradović, Aleksandar
AU  - Mitrović, Zoran
AU  - Zorić, Nemanja
PY  - 2021
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3984
AB  - Shape optimization of an AFG Timoshenko cantilever beam of a variable cross-sectional
area, with a specified fundamental frequency, is considered. The cantilever beam has a finitedimensional
body placed eccentrically at the right end. Optimization is performed in terms of
beam mass minimization. Considerations involve the case of coupled axial and bending
oscillations, where contour conditions are the cause of coupling, which exist at the place of
junction between the cantilever beam and the body. The problem is solved applying Pontryagin’s
maximum principle, with the beam cross-sectional area being taken for control. The two-point
boundary value problem is obtained, and the shooting method is applied to solving it. The
property of self-adjoint systems is employed, where all costate variables are expressed by state
variables, which facilitates solving the appropriate differential equations. Also, the percent saving
of the beam mass is determined, achieved by using the cantilever beam of an optimum variable
square cross-section compared to the cantilever beam of a constant cross-section at specified
value of the fundamental frequency.
PB  - Beograd : Srpsko društvo za mehaniku
C3  - Procceding of 8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021
T1  - Mass minimization of an AFG Timoshenko cantilever beam with a large body placed eccentrically at the beam end
EP  - 183
SP  - 176
UR  - https://hdl.handle.net/21.15107/rcub_machinery_3984
ER  - 

@conference{
author = "Obradović, Aleksandar and Mitrović, Zoran and Zorić, Nemanja",
year = "2021",
abstract = "Shape optimization of an AFG Timoshenko cantilever beam of a variable cross-sectional
area, with a specified fundamental frequency, is considered. The cantilever beam has a finitedimensional
body placed eccentrically at the right end. Optimization is performed in terms of
beam mass minimization. Considerations involve the case of coupled axial and bending
oscillations, where contour conditions are the cause of coupling, which exist at the place of
junction between the cantilever beam and the body. The problem is solved applying Pontryagin’s
maximum principle, with the beam cross-sectional area being taken for control. The two-point
boundary value problem is obtained, and the shooting method is applied to solving it. The
property of self-adjoint systems is employed, where all costate variables are expressed by state
variables, which facilitates solving the appropriate differential equations. Also, the percent saving
of the beam mass is determined, achieved by using the cantilever beam of an optimum variable
square cross-section compared to the cantilever beam of a constant cross-section at specified
value of the fundamental frequency.",
publisher = "Beograd : Srpsko društvo za mehaniku",
journal = "Procceding of 8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021",
title = "Mass minimization of an AFG Timoshenko cantilever beam with a large body placed eccentrically at the beam end",
pages = "183-176",
url = "https://hdl.handle.net/21.15107/rcub_machinery_3984"
}

Obradović, A., Mitrović, Z.,& Zorić, N.. (2021). Mass minimization of an AFG Timoshenko cantilever beam with a large body placed eccentrically at the beam end. in Procceding of 8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021
Beograd : Srpsko društvo za mehaniku., 176-183.
https://hdl.handle.net/21.15107/rcub_machinery_3984

Obradović A, Mitrović Z, Zorić N. Mass minimization of an AFG Timoshenko cantilever beam with a large body placed eccentrically at the beam end. in Procceding of 8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021. 2021;:176-183.
https://hdl.handle.net/21.15107/rcub_machinery_3984 .

Obradović, Aleksandar, Mitrović, Zoran, Zorić, Nemanja, "Mass minimization of an AFG Timoshenko cantilever beam with a large body placed eccentrically at the beam end" in Procceding of 8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021 (2021):176-183,
https://hdl.handle.net/21.15107/rcub_machinery_3984 .

TY  - BOOK
AU  - Vuković, Josif
AU  - Simonović, Milivoje
AU  - Obradović, Aleksandar
AU  - Marković, Saša
PY  - 2021
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6577
AB  - Dug vek ove zbirke i veliki broj ponovljenih izdanja ukazuje na činjenicu da je ona imala značajnu ulogu u nastavi Mehanike na Mašinskom fakultetu u Beogradu. Potreba za novim izdanjem uzrokovana je i trenutnim potpunim odsustvom, u aktivnoj prodaji, zbirki iz dinamike namenjenih studentima mašinskih fakulteta u Srbiji. Bez obzira što je pisana za potrebe studija po starim programima, ona je i sada neophodna za potrebe nastave Mehanike po važećim programima predmeta na Mašinskom fakultetu u Beogradu. Prvo, drugo i sedmo poglavlje čine deo programa predmeta Mehanika 2, na osnovnim akademskim studijama. Deveto, dvanaesto i petnaesto poglavlje nalaze se u okviru programa predmeta Mehanika M na master akademskim studijama, kao i pojedini delovi četvrtog poglavlja. Preostala poglavlja obuhvataju u celini program predmeta Mehanika 3 na osnovnim akademskim studijama.
PB  - Univerzitet u Beogradu, Mašinski fakultet
T2  - Univerzitet u Beogradu, Mašinski fakultet
T1  - Zbirka zadataka iz dinamike
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6577
ER  - 

@book{
author = "Vuković, Josif and Simonović, Milivoje and Obradović, Aleksandar and Marković, Saša",
year = "2021",
abstract = "Dug vek ove zbirke i veliki broj ponovljenih izdanja ukazuje na činjenicu da je ona imala značajnu ulogu u nastavi Mehanike na Mašinskom fakultetu u Beogradu. Potreba za novim izdanjem uzrokovana je i trenutnim potpunim odsustvom, u aktivnoj prodaji, zbirki iz dinamike namenjenih studentima mašinskih fakulteta u Srbiji. Bez obzira što je pisana za potrebe studija po starim programima, ona je i sada neophodna za potrebe nastave Mehanike po važećim programima predmeta na Mašinskom fakultetu u Beogradu. Prvo, drugo i sedmo poglavlje čine deo programa predmeta Mehanika 2, na osnovnim akademskim studijama. Deveto, dvanaesto i petnaesto poglavlje nalaze se u okviru programa predmeta Mehanika M na master akademskim studijama, kao i pojedini delovi četvrtog poglavlja. Preostala poglavlja obuhvataju u celini program predmeta Mehanika 3 na osnovnim akademskim studijama.",
publisher = "Univerzitet u Beogradu, Mašinski fakultet",
journal = "Univerzitet u Beogradu, Mašinski fakultet",
title = "Zbirka zadataka iz dinamike",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6577"
}

Vuković, J., Simonović, M., Obradović, A.,& Marković, S.. (2021). Zbirka zadataka iz dinamike. in Univerzitet u Beogradu, Mašinski fakultet
Univerzitet u Beogradu, Mašinski fakultet..
https://hdl.handle.net/21.15107/rcub_machinery_6577

Vuković J, Simonović M, Obradović A, Marković S. Zbirka zadataka iz dinamike. in Univerzitet u Beogradu, Mašinski fakultet. 2021;.
https://hdl.handle.net/21.15107/rcub_machinery_6577 .

Vuković, Josif, Simonović, Milivoje, Obradović, Aleksandar, Marković, Saša, "Zbirka zadataka iz dinamike" in Univerzitet u Beogradu, Mašinski fakultet (2021),
https://hdl.handle.net/21.15107/rcub_machinery_6577 .

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  - CONF
AU  - Šalinić, Slaviša
AU  - Obradović, Aleksandar
PY  - 2021
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3970
AB  - Free in-plane vibration analysis of circular arches with varying cross-sections is studied by means of the symbolicnumeric
method of initial parameters. The effects of axial extension, transverse shear deformation and rotatory inertia are
considered. For various boundary conditions, natural frequencies of free in-plane vibration of circular arches with varying
cross-sections are obtained. By comparing obtained results with previous ones available in the literature the effectiveness
of application of the symbolic-numeric method of initial parameters to the problem considered is proven.
PB  - FACULTY OF MECHANICAL AND CIVIL ENGINEERING IN KRALJEVO UNIVERSITY OF KRAGUJEVAC
C3  - X International Conference “Heavy Machinery-HM 2021”, Vrnjačka Banja, 23– 25 June 2021
T1  - Contribution to the problem of in-plane vibration of circular arches with varying cross-sections
EP  - D32
SP  - D27
UR  - https://hdl.handle.net/21.15107/rcub_machinery_3970
ER  - 

@conference{
author = "Šalinić, Slaviša and Obradović, Aleksandar",
year = "2021",
abstract = "Free in-plane vibration analysis of circular arches with varying cross-sections is studied by means of the symbolicnumeric
method of initial parameters. The effects of axial extension, transverse shear deformation and rotatory inertia are
considered. For various boundary conditions, natural frequencies of free in-plane vibration of circular arches with varying
cross-sections are obtained. By comparing obtained results with previous ones available in the literature the effectiveness
of application of the symbolic-numeric method of initial parameters to the problem considered is proven.",
publisher = "FACULTY OF MECHANICAL AND CIVIL ENGINEERING IN KRALJEVO UNIVERSITY OF KRAGUJEVAC",
journal = "X International Conference “Heavy Machinery-HM 2021”, Vrnjačka Banja, 23– 25 June 2021",
title = "Contribution to the problem of in-plane vibration of circular arches with varying cross-sections",
pages = "D32-D27",
url = "https://hdl.handle.net/21.15107/rcub_machinery_3970"
}

Šalinić, S.,& Obradović, A.. (2021). Contribution to the problem of in-plane vibration of circular arches with varying cross-sections. in X International Conference “Heavy Machinery-HM 2021”, Vrnjačka Banja, 23– 25 June 2021
FACULTY OF MECHANICAL AND CIVIL ENGINEERING IN KRALJEVO UNIVERSITY OF KRAGUJEVAC., D27-D32.
https://hdl.handle.net/21.15107/rcub_machinery_3970

Šalinić S, Obradović A. Contribution to the problem of in-plane vibration of circular arches with varying cross-sections. in X International Conference “Heavy Machinery-HM 2021”, Vrnjačka Banja, 23– 25 June 2021. 2021;:D27-D32.
https://hdl.handle.net/21.15107/rcub_machinery_3970 .

Šalinić, Slaviša, Obradović, Aleksandar, "Contribution to the problem of in-plane vibration of circular arches with varying cross-sections" in X International Conference “Heavy Machinery-HM 2021”, Vrnjačka Banja, 23– 25 June 2021 (2021):D27-D32,
https://hdl.handle.net/21.15107/rcub_machinery_3970 .

TY  - CONF
AU  - Zorić, Nemanja
AU  - Jazarević, Vladimir
AU  - Obradović, Aleksandar
PY  - 2021
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3994
AB  - This paper presents the design of a thrust controller for a single-shaft turbofan engine at the
operation point defined with following parameters: altitude = 0, Mach number = 0, angle of attack
= 0. In that case, the dynamics of the engine depends only of the shaft angular velocity.
Mathematical model for controller synthesis is obtained by solution of the set of nonlinear
equations. Due to complexity of the engine, parameter uncertainties and exposure to various
disturbances during exploitation, the H∞ methodology for controller synthesis is applied. Since H∞
based controller presents linear controller, it requires linear model of the plant for synthesis. Due
to that, the plant needs to be linearized. From nonlinear simulation, the 1st order transfer functions
can be obtained for selected intervals of shaft angular velocities. For controller synthesis, the fuel
supply system is also included as the 1st order transfer function. Since obtained controllers present
higher order controllers which may not be feasible for a real-time implementation because of
hardware limitations, they are reduced to proportional-integral (PI) controllers by using the
balanced reduction. Obtained controllers are then combined via gain-scheduling approach and
simulation is performed.
PB  - Beograd : Srpsko društvo za mehaniku
C3  - 8th International Congress of Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30 2021
T1  - H∞ Proportional-Integral Control of a Turbofan Engine
EP  - 315
SP  - 306
UR  - https://hdl.handle.net/21.15107/rcub_machinery_3994
ER  - 

@conference{
author = "Zorić, Nemanja and Jazarević, Vladimir and Obradović, Aleksandar",
year = "2021",
abstract = "This paper presents the design of a thrust controller for a single-shaft turbofan engine at the
operation point defined with following parameters: altitude = 0, Mach number = 0, angle of attack
= 0. In that case, the dynamics of the engine depends only of the shaft angular velocity.
Mathematical model for controller synthesis is obtained by solution of the set of nonlinear
equations. Due to complexity of the engine, parameter uncertainties and exposure to various
disturbances during exploitation, the H∞ methodology for controller synthesis is applied. Since H∞
based controller presents linear controller, it requires linear model of the plant for synthesis. Due
to that, the plant needs to be linearized. From nonlinear simulation, the 1st order transfer functions
can be obtained for selected intervals of shaft angular velocities. For controller synthesis, the fuel
supply system is also included as the 1st order transfer function. Since obtained controllers present
higher order controllers which may not be feasible for a real-time implementation because of
hardware limitations, they are reduced to proportional-integral (PI) controllers by using the
balanced reduction. Obtained controllers are then combined via gain-scheduling approach and
simulation is performed.",
publisher = "Beograd : Srpsko društvo za mehaniku",
journal = "8th International Congress of Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30 2021",
title = "H∞ Proportional-Integral Control of a Turbofan Engine",
pages = "315-306",
url = "https://hdl.handle.net/21.15107/rcub_machinery_3994"
}

Zorić, N., Jazarević, V.,& Obradović, A.. (2021). H∞ Proportional-Integral Control of a Turbofan Engine. in 8th International Congress of Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30 2021
Beograd : Srpsko društvo za mehaniku., 306-315.
https://hdl.handle.net/21.15107/rcub_machinery_3994

Zorić N, Jazarević V, Obradović A. H∞ Proportional-Integral Control of a Turbofan Engine. in 8th International Congress of Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30 2021. 2021;:306-315.
https://hdl.handle.net/21.15107/rcub_machinery_3994 .

Zorić, Nemanja, Jazarević, Vladimir, Obradović, Aleksandar, "H∞ Proportional-Integral Control of a Turbofan Engine" in 8th International Congress of Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30 2021 (2021):306-315,
https://hdl.handle.net/21.15107/rcub_machinery_3994 .

TY  - BOOK
AU  - Radovanović, Milan
AU  - Obradović, Aleksandar
AU  - Misita, Mirjana
AU  - Zubić, Adrijana
PY  - 2021
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6581
PB  - Univerzitet u Beogradu, Mašinski fakultet
T2  - Univerzitet u Beogradu, Mašinski fakultet
T1  - Bibliografija doktorskih disertacija odbranjenih na Mašinskom fakultetu Univerziteta u Beogradu : 1. 1. 1955. -31. 12. 2020.
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6581
ER  - 

@book{
author = "Radovanović, Milan and Obradović, Aleksandar and Misita, Mirjana and Zubić, Adrijana",
year = "2021",
publisher = "Univerzitet u Beogradu, Mašinski fakultet",
journal = "Univerzitet u Beogradu, Mašinski fakultet",
title = "Bibliografija doktorskih disertacija odbranjenih na Mašinskom fakultetu Univerziteta u Beogradu : 1. 1. 1955. -31. 12. 2020.",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6581"
}

Radovanović, M., Obradović, A., Misita, M.,& Zubić, A.. (2021). Bibliografija doktorskih disertacija odbranjenih na Mašinskom fakultetu Univerziteta u Beogradu : 1. 1. 1955. -31. 12. 2020.. in Univerzitet u Beogradu, Mašinski fakultet
Univerzitet u Beogradu, Mašinski fakultet..
https://hdl.handle.net/21.15107/rcub_machinery_6581

Radovanović M, Obradović A, Misita M, Zubić A. Bibliografija doktorskih disertacija odbranjenih na Mašinskom fakultetu Univerziteta u Beogradu : 1. 1. 1955. -31. 12. 2020.. in Univerzitet u Beogradu, Mašinski fakultet. 2021;.
https://hdl.handle.net/21.15107/rcub_machinery_6581 .

Radovanović, Milan, Obradović, Aleksandar, Misita, Mirjana, Zubić, Adrijana, "Bibliografija doktorskih disertacija odbranjenih na Mašinskom fakultetu Univerziteta u Beogradu : 1. 1. 1955. -31. 12. 2020." in Univerzitet u Beogradu, Mašinski fakultet (2021),
https://hdl.handle.net/21.15107/rcub_machinery_6581 .

TY  - JOUR
AU  - Obradović, Aleksandar
AU  - Šalinić, Slaviša
AU  - Grbović, Aleksandar
PY  - 2021
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4331
AB  - The problem of determining the optimum shape of a homogeneous Euler-Bernoulli beam of a circular cross-section, in which the coupled axial and bending vibrations arose due to complex boundary conditions, is considered. The beam mass is minimized at prescribed fundamental frequency. The problem is solved applying Pontryagin's maximum principle, with the beam cross-sectional diameter derivative with respect to longitudinal coordinate taken for control variable. This problem involves first-order singular optimal control, the calculations of which allowed the application of the Poisson bracket formalism and the fulfillment of the Kelley necessary condition on singular segments. Numerical solution of the two-point boundary value problem is obtained by the shooting method. An inequality constraint is imposed to the beam diameter derivative. Depending on the size of the diameter derivative boundaries, the obtained solutions are singular along the entire beam or consist of singular and non-singular segments, where the diameter derivative is at one of its boundaries. It is shown that such system is self-adjoint, so that only one differential equation of the costate equations system was integrated and the rest costate variables were expressed via the state variables. Also, the paper shows the fulfillment of necessary conditions for the optimality of junctions between singular and non-singular segments, as well as the percent saving of the beam mass compared to the beams of constant diameter at identical value of the fundamental frequency.
PB  - Elsevier Sci Ltd, Oxford
T2  - Engineering Structures
T1  - Mass minimization of an Euler-Bernoulli beam with coupled bending and axial vibrations at prescribed fundamental frequency
VL  - 228
DO  - 10.1016/j.engstruct.2020.111538
ER  - 

@article{
author = "Obradović, Aleksandar and Šalinić, Slaviša and Grbović, Aleksandar",
year = "2021",
abstract = "The problem of determining the optimum shape of a homogeneous Euler-Bernoulli beam of a circular cross-section, in which the coupled axial and bending vibrations arose due to complex boundary conditions, is considered. The beam mass is minimized at prescribed fundamental frequency. The problem is solved applying Pontryagin's maximum principle, with the beam cross-sectional diameter derivative with respect to longitudinal coordinate taken for control variable. This problem involves first-order singular optimal control, the calculations of which allowed the application of the Poisson bracket formalism and the fulfillment of the Kelley necessary condition on singular segments. Numerical solution of the two-point boundary value problem is obtained by the shooting method. An inequality constraint is imposed to the beam diameter derivative. Depending on the size of the diameter derivative boundaries, the obtained solutions are singular along the entire beam or consist of singular and non-singular segments, where the diameter derivative is at one of its boundaries. It is shown that such system is self-adjoint, so that only one differential equation of the costate equations system was integrated and the rest costate variables were expressed via the state variables. Also, the paper shows the fulfillment of necessary conditions for the optimality of junctions between singular and non-singular segments, as well as the percent saving of the beam mass compared to the beams of constant diameter at identical value of the fundamental frequency.",
publisher = "Elsevier Sci Ltd, Oxford",
journal = "Engineering Structures",
title = "Mass minimization of an Euler-Bernoulli beam with coupled bending and axial vibrations at prescribed fundamental frequency",
volume = "228",
doi = "10.1016/j.engstruct.2020.111538"
}

Obradović, A., Šalinić, S.,& Grbović, A.. (2021). Mass minimization of an Euler-Bernoulli beam with coupled bending and axial vibrations at prescribed fundamental frequency. in Engineering Structures
Elsevier Sci Ltd, Oxford., 228.
https://doi.org/10.1016/j.engstruct.2020.111538

Obradović A, Šalinić S, Grbović A. Mass minimization of an Euler-Bernoulli beam with coupled bending and axial vibrations at prescribed fundamental frequency. in Engineering Structures. 2021;228.
doi:10.1016/j.engstruct.2020.111538 .

Obradović, Aleksandar, Šalinić, Slaviša, Grbović, Aleksandar, "Mass minimization of an Euler-Bernoulli beam with coupled bending and axial vibrations at prescribed fundamental frequency" in Engineering Structures, 228 (2021),
https://doi.org/10.1016/j.engstruct.2020.111538 . .