Free vibrations of planar serial frame structures in the case of axially functionally graded materials
Апстракт
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 conditio...ns at the right and left ends of such structures, as illustrated by an appropriate numerical example.
Кључне речи:
planar serial frame structures / free vibrations / axially functionally graded materialsИзвор:
Theoretical and Applied Mechanics, 2020, 47, 2, 221-239Издавач:
- Srpsko društvo za mehaniku, Beograd
Финансирање / пројекти:
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200105 (Универзитет у Београду, Машински факултет) (RS-200105)
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200108 (Универзитет у Крагујевцу, Машински факултет, Краљево) (RS-200108)
DOI: 10.2298/TAM2000017O
ISSN: 1450-5584
WoS: 000607924500005
Scopus: 2-s2.0-85099589762
Колекције
Институција/група
Mašinski fakultetTY - 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 . .