Mass minimization of an AFG Timoshenko beam with a coupled axial and bending vibrations
Апстракт
The paper considers mass minimization of an axially functionally graded (AFG) Timoshenko beam of a variable cross-sectional area, with a specified fundamental frequency. The analyzed case of coupled axial and bending vibrations involves contour conditions as the cause of coupling. The problem is solved applying Pontryagin’s maximum principle, where the beam cross-sectional area is taken for control. The two-point boundary value problem is obtained, and the shooting method is used to solving it. The property of self-adjoint systems is deployed. The percent saving of the beam mass is determined, achieved by using the beam of an optimum variable square cross-section as compared to the beam of a constant cross-section. The procedure developed by the author in his earlier papers is extended herein to the case of a limited cross-sectional area. The second generalization relates to the general case of contour conditions at the beam ends.
Извор:
Proceedings of the 2nd CONFERENCE ON NONLINEARITY, 11, October18–22, 2021,Belgrade, 2022, 96-108Издавач:
- Serbian Academy of Nonlinear Sciences
Финансирање / пројекти:
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200105 (Универзитет у Београду, Машински факултет) (RS-MESTD-inst-2020-200105)
Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Obradović, Aleksandar PY - 2022 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3971 AB - The paper considers mass minimization of an axially functionally graded (AFG) Timoshenko beam of a variable cross-sectional area, with a specified fundamental frequency. The analyzed case of coupled axial and bending vibrations involves contour conditions as the cause of coupling. The problem is solved applying Pontryagin’s maximum principle, where the beam cross-sectional area is taken for control. The two-point boundary value problem is obtained, and the shooting method is used to solving it. The property of self-adjoint systems is deployed. The percent saving of the beam mass is determined, achieved by using the beam of an optimum variable square cross-section as compared to the beam of a constant cross-section. The procedure developed by the author in his earlier papers is extended herein to the case of a limited cross-sectional area. The second generalization relates to the general case of contour conditions at the beam ends. PB - Serbian Academy of Nonlinear Sciences C3 - Proceedings of the 2nd CONFERENCE ON NONLINEARITY, 11, October18–22, 2021,Belgrade T1 - Mass minimization of an AFG Timoshenko beam with a coupled axial and bending vibrations EP - 108 SP - 96 UR - https://hdl.handle.net/21.15107/rcub_machinery_3971 ER -
@conference{ author = "Obradović, Aleksandar", year = "2022", abstract = "The paper considers mass minimization of an axially functionally graded (AFG) Timoshenko beam of a variable cross-sectional area, with a specified fundamental frequency. The analyzed case of coupled axial and bending vibrations involves contour conditions as the cause of coupling. The problem is solved applying Pontryagin’s maximum principle, where the beam cross-sectional area is taken for control. The two-point boundary value problem is obtained, and the shooting method is used to solving it. The property of self-adjoint systems is deployed. The percent saving of the beam mass is determined, achieved by using the beam of an optimum variable square cross-section as compared to the beam of a constant cross-section. The procedure developed by the author in his earlier papers is extended herein to the case of a limited cross-sectional area. The second generalization relates to the general case of contour conditions at the beam ends.", publisher = "Serbian Academy of Nonlinear Sciences", journal = "Proceedings of the 2nd CONFERENCE ON NONLINEARITY, 11, October18–22, 2021,Belgrade", title = "Mass minimization of an AFG Timoshenko beam with a coupled axial and bending vibrations", pages = "108-96", url = "https://hdl.handle.net/21.15107/rcub_machinery_3971" }
Obradović, A.. (2022). Mass minimization of an AFG Timoshenko beam with a coupled axial and bending vibrations. in Proceedings of the 2nd CONFERENCE ON NONLINEARITY, 11, October18–22, 2021,Belgrade Serbian Academy of Nonlinear Sciences., 96-108. https://hdl.handle.net/21.15107/rcub_machinery_3971
Obradović A. Mass minimization of an AFG Timoshenko beam with a coupled axial and bending vibrations. in Proceedings of the 2nd CONFERENCE ON NONLINEARITY, 11, October18–22, 2021,Belgrade. 2022;:96-108. https://hdl.handle.net/21.15107/rcub_machinery_3971 .
Obradović, Aleksandar, "Mass minimization of an AFG Timoshenko beam with a coupled axial and bending vibrations" in Proceedings of the 2nd CONFERENCE ON NONLINEARITY, 11, October18–22, 2021,Belgrade (2022):96-108, https://hdl.handle.net/21.15107/rcub_machinery_3971 .