Free vibration of axially functionally graded Timoshenko cantilever beam with a large rigid body attached at its free end
Apstrakt
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.
Ključne reči:
free vibrations / longitudinal and transverse vibrations / Timoshenko beam / axially functionally graded cantelever beamIzvor:
Proceeding of 5th Serbian-Greek Symposium on Advanced Mechanics Kragujevac, Serbia, June 28-30, 2021, 2021, 444-451Izdavač:
- Beograd : Srpsko društvo za mehaniku
Finansiranje / projekti:
- Ministarstvo nauke, tehnološkog razvoja i inovacija Republike Srbije, institucionalno finansiranje - 200105 (Univerzitet u Beogradu, Mašinski fakultet) (RS-MESTD-inst-2020-200105)
- Ministarstvo nauke, tehnološkog razvoja i inovacija Republike Srbije, institucionalno finansiranje - 200108 (Univerzitet u Kragujevcu, Mašinski fakultet, Kraljevo) (RS-MESTD-inst-2020-200108)
Kolekcije
Institucija/grupa
Mašinski fakultetTY - 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 .