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

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

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

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

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

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

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

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

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

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

TY  - 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  - 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  - 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  - 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  - 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 . .

TY  - JOUR
AU  - Šalinić, Slaviša
AU  - Obradović, Aleksandar
AU  - Grbović, Aleksandar
PY  - 2021
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4327
AB  - This article contains some comments on "An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies", X. Liu, Ch. Sun, J.R. Banerjee, H-Ch. Dan, L. Chang. Mechanical Systems and Signal Processing, 150, 107264 (2021).
PB  - Academic Press Ltd- Elsevier Science Ltd, London
T2  - Mechanical Systems and Signal Processing
T1  - Comments on "An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies, Mechanical Systems and Signal Processing 150 (2021) 107264, by X. Liu, Ch. Sun, JR Banerjee, H-Ch. Dan, L. Chang"
VL  - 159
DO  - 10.1016/j.ymssp.2021.107844
ER  - 

@article{
author = "Šalinić, Slaviša and Obradović, Aleksandar and Grbović, Aleksandar",
year = "2021",
abstract = "This article contains some comments on "An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies", X. Liu, Ch. Sun, J.R. Banerjee, H-Ch. Dan, L. Chang. Mechanical Systems and Signal Processing, 150, 107264 (2021).",
publisher = "Academic Press Ltd- Elsevier Science Ltd, London",
journal = "Mechanical Systems and Signal Processing",
title = "Comments on "An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies, Mechanical Systems and Signal Processing 150 (2021) 107264, by X. Liu, Ch. Sun, JR Banerjee, H-Ch. Dan, L. Chang"",
volume = "159",
doi = "10.1016/j.ymssp.2021.107844"
}

Šalinić, S., Obradović, A.,& Grbović, A.. (2021). Comments on "An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies, Mechanical Systems and Signal Processing 150 (2021) 107264, by X. Liu, Ch. Sun, JR Banerjee, H-Ch. Dan, L. Chang". in Mechanical Systems and Signal Processing
Academic Press Ltd- Elsevier Science Ltd, London., 159.
https://doi.org/10.1016/j.ymssp.2021.107844

Šalinić S, Obradović A, Grbović A. Comments on "An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies, Mechanical Systems and Signal Processing 150 (2021) 107264, by X. Liu, Ch. Sun, JR Banerjee, H-Ch. Dan, L. Chang". in Mechanical Systems and Signal Processing. 2021;159.
doi:10.1016/j.ymssp.2021.107844 .

Šalinić, Slaviša, Obradović, Aleksandar, Grbović, Aleksandar, "Comments on "An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies, Mechanical Systems and Signal Processing 150 (2021) 107264, by X. Liu, Ch. Sun, JR Banerjee, H-Ch. Dan, L. Chang"" in Mechanical Systems and Signal Processing, 159 (2021),
https://doi.org/10.1016/j.ymssp.2021.107844 . .

TY  - JOUR
AU  - Obradović, Aleksandar
AU  - Šalinić, Slaviša
AU  - Grbović, Aleksandar
PY  - 2021
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3628
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 . .

TY  - JOUR
AU  - Šalinić, Slaviša
AU  - Obradović, Aleksandar
AU  - Grbović, Aleksandar
PY  - 2021
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3603
AB  - This article contains some comments on "An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies", X. Liu, Ch. Sun, J.R. Banerjee, H-Ch. Dan, L. Chang. Mechanical Systems and Signal Processing, 150, 107264 (2021).
PB  - Academic Press Ltd- Elsevier Science Ltd, London
T2  - Mechanical Systems and Signal Processing
T1  - Comments on "An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies, Mechanical Systems and Signal Processing 150 (2021) 107264, by X. Liu, Ch. Sun, JR Banerjee, H-Ch. Dan, L. Chang"
VL  - 159
DO  - 10.1016/j.ymssp.2021.107844
ER  - 

@article{
author = "Šalinić, Slaviša and Obradović, Aleksandar and Grbović, Aleksandar",
year = "2021",
abstract = "This article contains some comments on "An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies", X. Liu, Ch. Sun, J.R. Banerjee, H-Ch. Dan, L. Chang. Mechanical Systems and Signal Processing, 150, 107264 (2021).",
publisher = "Academic Press Ltd- Elsevier Science Ltd, London",
journal = "Mechanical Systems and Signal Processing",
title = "Comments on "An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies, Mechanical Systems and Signal Processing 150 (2021) 107264, by X. Liu, Ch. Sun, JR Banerjee, H-Ch. Dan, L. Chang"",
volume = "159",
doi = "10.1016/j.ymssp.2021.107844"
}

Šalinić, S., Obradović, A.,& Grbović, A.. (2021). Comments on "An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies, Mechanical Systems and Signal Processing 150 (2021) 107264, by X. Liu, Ch. Sun, JR Banerjee, H-Ch. Dan, L. Chang". in Mechanical Systems and Signal Processing
Academic Press Ltd- Elsevier Science Ltd, London., 159.
https://doi.org/10.1016/j.ymssp.2021.107844

Šalinić S, Obradović A, Grbović A. Comments on "An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies, Mechanical Systems and Signal Processing 150 (2021) 107264, by X. Liu, Ch. Sun, JR Banerjee, H-Ch. Dan, L. Chang". in Mechanical Systems and Signal Processing. 2021;159.
doi:10.1016/j.ymssp.2021.107844 .

Šalinić, Slaviša, Obradović, Aleksandar, Grbović, Aleksandar, "Comments on "An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies, Mechanical Systems and Signal Processing 150 (2021) 107264, by X. Liu, Ch. Sun, JR Banerjee, H-Ch. Dan, L. Chang"" in Mechanical Systems and Signal Processing, 159 (2021),
https://doi.org/10.1016/j.ymssp.2021.107844 . .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

TY  - CONF
AU  - Obradović, Aleksandar
AU  - Šalinić, Slaviša
PY  - 2020
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3992
AB  - The problem of brachistochronic motion of a heavy uniform ball rolling without slip along the upper outside surface of an imperfect rough stationary sphere, is solved. The control forces are located in the tangential plane, and their total power equals zero. In the first part of the paper the determination of the brachistochronic motion is solved as the problem of optimal control using Pontryagin’s maximum principle. This solution corresponds to the motion of the heavy ball along a perfect rough sphere. The second part provides the case when the constraint between the sphere and the ball is imperfectly rough. Here, the problem of optimal control is formulated in such way that the tangential component of the reaction of constraint is taken for the control, with the restriction resulting from Coulomb’s laws of sliding friction. The problem thus formulated belongs to the theory of singular optimal controls, and the solution that satisfies the Maximum principle consists of a singular part and a nonsingular part.
PB  - SERBIAN ACADEMY OF NONLINEAR SCIENCES
C3  - Proceedings of the 1st CONFERENCE ON NONLINEARITY, October11–12, 2019, Belgrade, Serbia
T1  - The brachistochronic motion of a heavy ball rolling along an imperfect rough surface
EP  - 128
SP  - 112
UR  - https://hdl.handle.net/21.15107/rcub_machinery_3992
ER  - 

@conference{
author = "Obradović, Aleksandar and Šalinić, Slaviša",
year = "2020",
abstract = "The problem of brachistochronic motion of a heavy uniform ball rolling without slip along the upper outside surface of an imperfect rough stationary sphere, is solved. The control forces are located in the tangential plane, and their total power equals zero. In the first part of the paper the determination of the brachistochronic motion is solved as the problem of optimal control using Pontryagin’s maximum principle. This solution corresponds to the motion of the heavy ball along a perfect rough sphere. The second part provides the case when the constraint between the sphere and the ball is imperfectly rough. Here, the problem of optimal control is formulated in such way that the tangential component of the reaction of constraint is taken for the control, with the restriction resulting from Coulomb’s laws of sliding friction. The problem thus formulated belongs to the theory of singular optimal controls, and the solution that satisfies the Maximum principle consists of a singular part and a nonsingular part.",
publisher = "SERBIAN ACADEMY OF NONLINEAR SCIENCES",
journal = "Proceedings of the 1st CONFERENCE ON NONLINEARITY, October11–12, 2019, Belgrade, Serbia",
title = "The brachistochronic motion of a heavy ball rolling along an imperfect rough surface",
pages = "128-112",
url = "https://hdl.handle.net/21.15107/rcub_machinery_3992"
}

Obradović, A.,& Šalinić, S.. (2020). The brachistochronic motion of a heavy ball rolling along an imperfect rough surface. in Proceedings of the 1st CONFERENCE ON NONLINEARITY, October11–12, 2019, Belgrade, Serbia
SERBIAN ACADEMY OF NONLINEAR SCIENCES., 112-128.
https://hdl.handle.net/21.15107/rcub_machinery_3992

Obradović A, Šalinić S. The brachistochronic motion of a heavy ball rolling along an imperfect rough surface. in Proceedings of the 1st CONFERENCE ON NONLINEARITY, October11–12, 2019, Belgrade, Serbia. 2020;:112-128.
https://hdl.handle.net/21.15107/rcub_machinery_3992 .

Obradović, Aleksandar, Šalinić, Slaviša, "The brachistochronic motion of a heavy ball rolling along an imperfect rough surface" in Proceedings of the 1st CONFERENCE ON NONLINEARITY, October11–12, 2019, Belgrade, Serbia (2020):112-128,
https://hdl.handle.net/21.15107/rcub_machinery_3992 .

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

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

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

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

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

TY  - JOUR
AU  - Jeremić, Bojan
AU  - Radulović, Radoslav
AU  - Obradović, Aleksandar
AU  - Šalinić, Slaviša
AU  - Dražić, Milan
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3045
AB  - In this paper, the brachistochronic motion of a mechanical system composed of variable-mass particles is analysed. Workless (ideal) holonomic and linear nonholonomic constraints are imposed on the system. It is assumed that the system moves in an arbitrary field of known potential and nonpotential forces with prescribed both laws of the time-rate of mass variation of the particles and relative velocities of the expelled (or gained) masses. The first time-derivatives of quasi-velocities are taken as control variables. Using Pontryagin's maximum principle and singular optimal control theory, the problem of brachistochronic motion of the nonholonomic variable-mass mechanical system is solved as a two-point boundary value problem. In addition, a discussion about the realization of control forces is given. The results are illustrated via an example.
PB  - Sage Publications Ltd, London
T2  - Mathematics and Mechanics of Solids
T1  - Brachistochronic motion of a nonholonomic variable-mass mechanical system in general force fields
EP  - 298
IS  - 1
SP  - 281
VL  - 24
DO  - 10.1177/1081286517738307
ER  - 

@article{
author = "Jeremić, Bojan and Radulović, Radoslav and Obradović, Aleksandar and Šalinić, Slaviša and Dražić, Milan",
year = "2019",
abstract = "In this paper, the brachistochronic motion of a mechanical system composed of variable-mass particles is analysed. Workless (ideal) holonomic and linear nonholonomic constraints are imposed on the system. It is assumed that the system moves in an arbitrary field of known potential and nonpotential forces with prescribed both laws of the time-rate of mass variation of the particles and relative velocities of the expelled (or gained) masses. The first time-derivatives of quasi-velocities are taken as control variables. Using Pontryagin's maximum principle and singular optimal control theory, the problem of brachistochronic motion of the nonholonomic variable-mass mechanical system is solved as a two-point boundary value problem. In addition, a discussion about the realization of control forces is given. The results are illustrated via an example.",
publisher = "Sage Publications Ltd, London",
journal = "Mathematics and Mechanics of Solids",
title = "Brachistochronic motion of a nonholonomic variable-mass mechanical system in general force fields",
pages = "298-281",
number = "1",
volume = "24",
doi = "10.1177/1081286517738307"
}

Jeremić, B., Radulović, R., Obradović, A., Šalinić, S.,& Dražić, M.. (2019). Brachistochronic motion of a nonholonomic variable-mass mechanical system in general force fields. in Mathematics and Mechanics of Solids
Sage Publications Ltd, London., 24(1), 281-298.
https://doi.org/10.1177/1081286517738307

Jeremić B, Radulović R, Obradović A, Šalinić S, Dražić M. Brachistochronic motion of a nonholonomic variable-mass mechanical system in general force fields. in Mathematics and Mechanics of Solids. 2019;24(1):281-298.
doi:10.1177/1081286517738307 .

Jeremić, Bojan, Radulović, Radoslav, Obradović, Aleksandar, Šalinić, Slaviša, Dražić, Milan, "Brachistochronic motion of a nonholonomic variable-mass mechanical system in general force fields" in Mathematics and Mechanics of Solids, 24, no. 1 (2019):281-298,
https://doi.org/10.1177/1081286517738307 . .

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

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

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

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

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

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

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

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

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

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

TY  - JOUR
AU  - Radulović, Radoslav
AU  - Jeremić, Bojan
AU  - Šalinić, Slaviša
AU  - Obradović, Aleksandar
AU  - Dražić, Milan
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2931
AB  - We consider the brachistochrone problem of the particle with a preselected interval for the normal reaction force value as well as the terminal position of the particle lying on an arbitrary planar curve. We use optimal control theory to solve the formulated brachistochrone problem. Here we treat the brachistochrone curve as a bilateral ideal constraint. We study the cases of symmetrically and unsymmetrically preselected intervals for the normal reaction force value. We show that in the case of a symmetrically preselected interval for the normal reaction force value, the brachistochrone curve is a two-segment curve, and in the case of an unsymmetrically preselected interval, it is a three-segment curve. We present a numerical procedure for the identification of the global minimum time of motion. Finally, we present several examples to illustrate the approach proposed in the paper.
PB  - Pergamon-Elsevier Science Ltd, Oxford
T2  - International Journal of Non-Linear Mechanics
T1  - A new approach for the determination of the global minimum time for the brachistochrone with preselected interval for the normal reaction force value
EP  - 35
SP  - 26
VL  - 101
DO  - 10.1016/j.ijnonlinmec.2018.02.001
ER  - 

@article{
author = "Radulović, Radoslav and Jeremić, Bojan and Šalinić, Slaviša and Obradović, Aleksandar and Dražić, Milan",
year = "2018",
abstract = "We consider the brachistochrone problem of the particle with a preselected interval for the normal reaction force value as well as the terminal position of the particle lying on an arbitrary planar curve. We use optimal control theory to solve the formulated brachistochrone problem. Here we treat the brachistochrone curve as a bilateral ideal constraint. We study the cases of symmetrically and unsymmetrically preselected intervals for the normal reaction force value. We show that in the case of a symmetrically preselected interval for the normal reaction force value, the brachistochrone curve is a two-segment curve, and in the case of an unsymmetrically preselected interval, it is a three-segment curve. We present a numerical procedure for the identification of the global minimum time of motion. Finally, we present several examples to illustrate the approach proposed in the paper.",
publisher = "Pergamon-Elsevier Science Ltd, Oxford",
journal = "International Journal of Non-Linear Mechanics",
title = "A new approach for the determination of the global minimum time for the brachistochrone with preselected interval for the normal reaction force value",
pages = "35-26",
volume = "101",
doi = "10.1016/j.ijnonlinmec.2018.02.001"
}

Radulović, R., Jeremić, B., Šalinić, S., Obradović, A.,& Dražić, M.. (2018). A new approach for the determination of the global minimum time for the brachistochrone with preselected interval for the normal reaction force value. in International Journal of Non-Linear Mechanics
Pergamon-Elsevier Science Ltd, Oxford., 101, 26-35.
https://doi.org/10.1016/j.ijnonlinmec.2018.02.001

Radulović R, Jeremić B, Šalinić S, Obradović A, Dražić M. A new approach for the determination of the global minimum time for the brachistochrone with preselected interval for the normal reaction force value. in International Journal of Non-Linear Mechanics. 2018;101:26-35.
doi:10.1016/j.ijnonlinmec.2018.02.001 .

Radulović, Radoslav, Jeremić, Bojan, Šalinić, Slaviša, Obradović, Aleksandar, Dražić, Milan, "A new approach for the determination of the global minimum time for the brachistochrone with preselected interval for the normal reaction force value" in International Journal of Non-Linear Mechanics, 101 (2018):26-35,
https://doi.org/10.1016/j.ijnonlinmec.2018.02.001 . .

TY  - JOUR
AU  - Šalinić, Slaviša
AU  - Obradović, Aleksandar
AU  - Dunjić, Momčilo
AU  - Sekulić, Dragan
AU  - Lazarević, Željko
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2838
AB  - Free vibration of an Euler-Bernoulli beam with rigid bodies connected to the beam ends by both revolute joints and torsional springs is considered. The mass centers of rigid bodies have both the transverse and the axial eccentricity relative to the neutral axis of the undeformed beam. The coupling of the partial differential equations of axial and bending vibrations of the beam due to boundary conditions is considered. The frequency equation and the mode shape orthogonality condition of the system are derived. In order to illustrate the effect of the transverse and the axial eccentricity on the vibration behavior of the beam, a numerical example is provided.
PB  - Wiley-V C H Verlag Gmbh, Weinheim
T2  - Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik
T1  - Contribution to the free vibration problem of a free-free beam with large end masses
EP  - 847
IS  - 5
SP  - 840
VL  - 98
DO  - 10.1002/zamm.201600300
ER  - 

@article{
author = "Šalinić, Slaviša and Obradović, Aleksandar and Dunjić, Momčilo and Sekulić, Dragan and Lazarević, Željko",
year = "2018",
abstract = "Free vibration of an Euler-Bernoulli beam with rigid bodies connected to the beam ends by both revolute joints and torsional springs is considered. The mass centers of rigid bodies have both the transverse and the axial eccentricity relative to the neutral axis of the undeformed beam. The coupling of the partial differential equations of axial and bending vibrations of the beam due to boundary conditions is considered. The frequency equation and the mode shape orthogonality condition of the system are derived. In order to illustrate the effect of the transverse and the axial eccentricity on the vibration behavior of the beam, a numerical example is provided.",
publisher = "Wiley-V C H Verlag Gmbh, Weinheim",
journal = "Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik",
title = "Contribution to the free vibration problem of a free-free beam with large end masses",
pages = "847-840",
number = "5",
volume = "98",
doi = "10.1002/zamm.201600300"
}

Šalinić, S., Obradović, A., Dunjić, M., Sekulić, D.,& Lazarević, Ž.. (2018). Contribution to the free vibration problem of a free-free beam with large end masses. in Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik
Wiley-V C H Verlag Gmbh, Weinheim., 98(5), 840-847.
https://doi.org/10.1002/zamm.201600300

Šalinić S, Obradović A, Dunjić M, Sekulić D, Lazarević Ž. Contribution to the free vibration problem of a free-free beam with large end masses. in Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik. 2018;98(5):840-847.
doi:10.1002/zamm.201600300 .

Šalinić, Slaviša, Obradović, Aleksandar, Dunjić, Momčilo, Sekulić, Dragan, Lazarević, Željko, "Contribution to the free vibration problem of a free-free beam with large end masses" in Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik, 98, no. 5 (2018):840-847,
https://doi.org/10.1002/zamm.201600300 . .

TY  - JOUR
AU  - Radulović, Radoslav
AU  - Obradović, Aleksandar
AU  - Šalinić, Slaviša
AU  - Mitrović, Zoran
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4362
AB  - The paper considers the brachistochronic motion of a wheeled vehicle on a horizontal plane surface. The objective is to transfer the vehicle from the specified initial position with given initial kinetic energy to the specified terminal position in minimum time with conserved total mechanical energy of the vehicle. The problem is solved by applying Pontryagin's maximum principle and singular optimal control theory. The projection of the reaction force of the horizontal plane applied on the front vehicle wheels onto the axis of the front vehicle axle is taken for a control variable. The cases of unbounded and bounded value of this projection are considered. The shooting method is used to solve the two-point boundary value problem arising from Pontryagin's maximum principle and singular optimal control theory.
PB  - Springer, Dordrecht
T2  - Nonlinear Dynamics
T1  - The brachistochronic motion of a wheeled vehicle
EP  - 205
IS  - 1
SP  - 191
VL  - 87
DO  - 10.1007/s11071-016-3035-3
ER  - 

@article{
author = "Radulović, Radoslav and Obradović, Aleksandar and Šalinić, Slaviša and Mitrović, Zoran",
year = "2017",
abstract = "The paper considers the brachistochronic motion of a wheeled vehicle on a horizontal plane surface. The objective is to transfer the vehicle from the specified initial position with given initial kinetic energy to the specified terminal position in minimum time with conserved total mechanical energy of the vehicle. The problem is solved by applying Pontryagin's maximum principle and singular optimal control theory. The projection of the reaction force of the horizontal plane applied on the front vehicle wheels onto the axis of the front vehicle axle is taken for a control variable. The cases of unbounded and bounded value of this projection are considered. The shooting method is used to solve the two-point boundary value problem arising from Pontryagin's maximum principle and singular optimal control theory.",
publisher = "Springer, Dordrecht",
journal = "Nonlinear Dynamics",
title = "The brachistochronic motion of a wheeled vehicle",
pages = "205-191",
number = "1",
volume = "87",
doi = "10.1007/s11071-016-3035-3"
}

Radulović, R., Obradović, A., Šalinić, S.,& Mitrović, Z.. (2017). The brachistochronic motion of a wheeled vehicle. in Nonlinear Dynamics
Springer, Dordrecht., 87(1), 191-205.
https://doi.org/10.1007/s11071-016-3035-3

Radulović R, Obradović A, Šalinić S, Mitrović Z. The brachistochronic motion of a wheeled vehicle. in Nonlinear Dynamics. 2017;87(1):191-205.
doi:10.1007/s11071-016-3035-3 .

Radulović, Radoslav, Obradović, Aleksandar, Šalinić, Slaviša, Mitrović, Zoran, "The brachistochronic motion of a wheeled vehicle" in Nonlinear Dynamics, 87, no. 1 (2017):191-205,
https://doi.org/10.1007/s11071-016-3035-3 . .

TY  - JOUR
AU  - Radulović, Radoslav
AU  - Obradović, Aleksandar
AU  - Šalinić, Slaviša
AU  - Mitrović, Zoran
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2554
AB  - The paper considers the brachistochronic motion of a wheeled vehicle on a horizontal plane surface. The objective is to transfer the vehicle from the specified initial position with given initial kinetic energy to the specified terminal position in minimum time with conserved total mechanical energy of the vehicle. The problem is solved by applying Pontryagin's maximum principle and singular optimal control theory. The projection of the reaction force of the horizontal plane applied on the front vehicle wheels onto the axis of the front vehicle axle is taken for a control variable. The cases of unbounded and bounded value of this projection are considered. The shooting method is used to solve the two-point boundary value problem arising from Pontryagin's maximum principle and singular optimal control theory.
PB  - Springer, Dordrecht
T2  - Nonlinear Dynamics
T1  - The brachistochronic motion of a wheeled vehicle
EP  - 205
IS  - 1
SP  - 191
VL  - 87
DO  - 10.1007/s11071-016-3035-3
ER  - 

@article{
author = "Radulović, Radoslav and Obradović, Aleksandar and Šalinić, Slaviša and Mitrović, Zoran",
year = "2017",
abstract = "The paper considers the brachistochronic motion of a wheeled vehicle on a horizontal plane surface. The objective is to transfer the vehicle from the specified initial position with given initial kinetic energy to the specified terminal position in minimum time with conserved total mechanical energy of the vehicle. The problem is solved by applying Pontryagin's maximum principle and singular optimal control theory. The projection of the reaction force of the horizontal plane applied on the front vehicle wheels onto the axis of the front vehicle axle is taken for a control variable. The cases of unbounded and bounded value of this projection are considered. The shooting method is used to solve the two-point boundary value problem arising from Pontryagin's maximum principle and singular optimal control theory.",
publisher = "Springer, Dordrecht",
journal = "Nonlinear Dynamics",
title = "The brachistochronic motion of a wheeled vehicle",
pages = "205-191",
number = "1",
volume = "87",
doi = "10.1007/s11071-016-3035-3"
}

Radulović, R., Obradović, A., Šalinić, S.,& Mitrović, Z.. (2017). The brachistochronic motion of a wheeled vehicle. in Nonlinear Dynamics
Springer, Dordrecht., 87(1), 191-205.
https://doi.org/10.1007/s11071-016-3035-3

Radulović R, Obradović A, Šalinić S, Mitrović Z. The brachistochronic motion of a wheeled vehicle. in Nonlinear Dynamics. 2017;87(1):191-205.
doi:10.1007/s11071-016-3035-3 .

Radulović, Radoslav, Obradović, Aleksandar, Šalinić, Slaviša, Mitrović, Zoran, "The brachistochronic motion of a wheeled vehicle" in Nonlinear Dynamics, 87, no. 1 (2017):191-205,
https://doi.org/10.1007/s11071-016-3035-3 . .