TY  - JOUR
AU  - Maretić, R.
AU  - Glavardanov, V.
AU  - Milošević-Mitić, Vesna
PY  - 2015
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2102
AB  - Transverse vibrations of a rotating annular disk composed of two annular disks of different materials are studied in this paper. The disk is clamped at the inner edge, while at the outer edge is free. Differential equations of small vibrations are solved exactly by series expansion using the Frobenius method. The solutions are separately presented for three cases corresponding to vibration with zero, one or two nodal diameters. The influence of angular velocity, moduli of elasticity and the volume densities of the materials of disks on vibration frequency is analyzed. Vibration frequencies are obtained for the disk composed of aluminum and steel. Influences of the inner radius and the radius of the connection on the vibration frequencies are also obtained.
PB  - Springer, New York
T2  - Archive of Applied Mechanics
T1  - Vibration and stability of rotating annular disks composed of different materials
EP  - 131
IS  - 1
SP  - 117
VL  - 85
DO  - 10.1007/s00419-014-0903-5
ER  - 

@article{
author = "Maretić, R. and Glavardanov, V. and Milošević-Mitić, Vesna",
year = "2015",
abstract = "Transverse vibrations of a rotating annular disk composed of two annular disks of different materials are studied in this paper. The disk is clamped at the inner edge, while at the outer edge is free. Differential equations of small vibrations are solved exactly by series expansion using the Frobenius method. The solutions are separately presented for three cases corresponding to vibration with zero, one or two nodal diameters. The influence of angular velocity, moduli of elasticity and the volume densities of the materials of disks on vibration frequency is analyzed. Vibration frequencies are obtained for the disk composed of aluminum and steel. Influences of the inner radius and the radius of the connection on the vibration frequencies are also obtained.",
publisher = "Springer, New York",
journal = "Archive of Applied Mechanics",
title = "Vibration and stability of rotating annular disks composed of different materials",
pages = "131-117",
number = "1",
volume = "85",
doi = "10.1007/s00419-014-0903-5"
}

Maretić, R., Glavardanov, V.,& Milošević-Mitić, V.. (2015). Vibration and stability of rotating annular disks composed of different materials. in Archive of Applied Mechanics
Springer, New York., 85(1), 117-131.
https://doi.org/10.1007/s00419-014-0903-5

Maretić R, Glavardanov V, Milošević-Mitić V. Vibration and stability of rotating annular disks composed of different materials. in Archive of Applied Mechanics. 2015;85(1):117-131.
doi:10.1007/s00419-014-0903-5 .

Maretić, R., Glavardanov, V., Milošević-Mitić, Vesna, "Vibration and stability of rotating annular disks composed of different materials" in Archive of Applied Mechanics, 85, no. 1 (2015):117-131,
https://doi.org/10.1007/s00419-014-0903-5 . .

TY  - JOUR
AU  - Vesković, M.
AU  - Cović, V.
AU  - Obradović, Aleksandar
PY  - 2011
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1154
AB  - The paper discusses the equilibrium instability problem of the scleronomic nonholonomic systems acted upon by dissipative, conservative, and circulatory forces. The method is based on the existence of solutions to the differential equations of the motion which asymptotically tends to the equilibrium state of the system as t tends to negative infinity. It is assumed that the kinetic energy, the Rayleigh dissipation function, and the positional forces in the neighborhood of the equilibrium position are infinitely differentiable functions. The results obtained here are partially generalized the results obtained by Kozlov et al. (Kozlov, V. V. The asymptotic motions of systems with dissipation. Journal of Applied Mathematics and Mechanics, 58(5), 787-792 (1994). Merkin, D. R. Introduction to the Theory of the Stability of Motion (in Russian), Nauka, Moscow (1987). Thomson, W. and Tait, P. Treatise on Natural Philosophy, Part I, Cambridge University Press, Cambridge (1879)). The results are illustrated by an example.
PB  - SHANGHAI UNIV, SHANGHAI
T2  - Applied Mathematics and Mechanics-English Edition
T1  - Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces
EP  - 222
IS  - 2
SP  - 211
VL  - 32
DO  - 10.1007/s10483-011-1407-9
ER  - 

@article{
author = "Vesković, M. and Cović, V. and Obradović, Aleksandar",
year = "2011",
abstract = "The paper discusses the equilibrium instability problem of the scleronomic nonholonomic systems acted upon by dissipative, conservative, and circulatory forces. The method is based on the existence of solutions to the differential equations of the motion which asymptotically tends to the equilibrium state of the system as t tends to negative infinity. It is assumed that the kinetic energy, the Rayleigh dissipation function, and the positional forces in the neighborhood of the equilibrium position are infinitely differentiable functions. The results obtained here are partially generalized the results obtained by Kozlov et al. (Kozlov, V. V. The asymptotic motions of systems with dissipation. Journal of Applied Mathematics and Mechanics, 58(5), 787-792 (1994). Merkin, D. R. Introduction to the Theory of the Stability of Motion (in Russian), Nauka, Moscow (1987). Thomson, W. and Tait, P. Treatise on Natural Philosophy, Part I, Cambridge University Press, Cambridge (1879)). The results are illustrated by an example.",
publisher = "SHANGHAI UNIV, SHANGHAI",
journal = "Applied Mathematics and Mechanics-English Edition",
title = "Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces",
pages = "222-211",
number = "2",
volume = "32",
doi = "10.1007/s10483-011-1407-9"
}

Vesković, M., Cović, V.,& Obradović, A.. (2011). Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces. in Applied Mathematics and Mechanics-English Edition
SHANGHAI UNIV, SHANGHAI., 32(2), 211-222.
https://doi.org/10.1007/s10483-011-1407-9

Vesković M, Cović V, Obradović A. Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces. in Applied Mathematics and Mechanics-English Edition. 2011;32(2):211-222.
doi:10.1007/s10483-011-1407-9 .

Vesković, M., Cović, V., Obradović, Aleksandar, "Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces" in Applied Mathematics and Mechanics-English Edition, 32, no. 2 (2011):211-222,
https://doi.org/10.1007/s10483-011-1407-9 . .

TY  - JOUR
AU  - Cović, V.
AU  - Djurić, D.
AU  - Vesković, M.
AU  - Obradović, Aleksandar
PY  - 2011
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1219
AB  - Lyapunov's first method, extended by Kozlov to nonlinear mechanical systems, is applied to study the instability of the equilibrium position of a mechanical system moving in the field of conservative and dissipative forces. The cases with a tensor of inertia or a matrix of coefficients of the Rayleigh dissipative function are analyzed singularly in the equilibrium position. This fact renders the impossible application of Lyapunov's approach in the analysis of the stability because, in the equilibrium position, the conditions of the existence and uniqueness of the solutions to the differential equations of motion are not fulfilled. It is shown that Kozlov's generalization of Lyapunov's first method can also be applied in the mentioned cases on the conditions that, besides the known algebraic expression, more are fulfilled. Three theorems on the instability of the equilibrium position are formulated. The results are illustrated by an example.
PB  - Shanghai Univ, Shanghai
T2  - Applied Mathematics and Mechanics-English Edition
T1  - Lyapunov-Kozlov method for singular cases
EP  - 1220
IS  - 9
SP  - 1207
VL  - 32
DO  - 10.1007/s10483-011-1494-6
ER  - 

@article{
author = "Cović, V. and Djurić, D. and Vesković, M. and Obradović, Aleksandar",
year = "2011",
abstract = "Lyapunov's first method, extended by Kozlov to nonlinear mechanical systems, is applied to study the instability of the equilibrium position of a mechanical system moving in the field of conservative and dissipative forces. The cases with a tensor of inertia or a matrix of coefficients of the Rayleigh dissipative function are analyzed singularly in the equilibrium position. This fact renders the impossible application of Lyapunov's approach in the analysis of the stability because, in the equilibrium position, the conditions of the existence and uniqueness of the solutions to the differential equations of motion are not fulfilled. It is shown that Kozlov's generalization of Lyapunov's first method can also be applied in the mentioned cases on the conditions that, besides the known algebraic expression, more are fulfilled. Three theorems on the instability of the equilibrium position are formulated. The results are illustrated by an example.",
publisher = "Shanghai Univ, Shanghai",
journal = "Applied Mathematics and Mechanics-English Edition",
title = "Lyapunov-Kozlov method for singular cases",
pages = "1220-1207",
number = "9",
volume = "32",
doi = "10.1007/s10483-011-1494-6"
}

Cović, V., Djurić, D., Vesković, M.,& Obradović, A.. (2011). Lyapunov-Kozlov method for singular cases. in Applied Mathematics and Mechanics-English Edition
Shanghai Univ, Shanghai., 32(9), 1207-1220.
https://doi.org/10.1007/s10483-011-1494-6

Cović V, Djurić D, Vesković M, Obradović A. Lyapunov-Kozlov method for singular cases. in Applied Mathematics and Mechanics-English Edition. 2011;32(9):1207-1220.
doi:10.1007/s10483-011-1494-6 .

Cović, V., Djurić, D., Vesković, M., Obradović, Aleksandar, "Lyapunov-Kozlov method for singular cases" in Applied Mathematics and Mechanics-English Edition, 32, no. 9 (2011):1207-1220,
https://doi.org/10.1007/s10483-011-1494-6 . .