Mass minimization of an AFG Timoshenko cantilever beam with a large body placed eccentrically at the beam end
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Shape optimization of an AFG Timoshenko cantilever beam of a variable cross-sectional
area, with a specified fundamental frequency, is considered. The cantilever beam has a finitedimensional
body placed eccentrically at the right end. Optimization is performed in terms of
beam mass minimization. Considerations involve the case of coupled axial and bending
oscillations, where contour conditions are the cause of coupling, which exist at the place of
junction between the cantilever beam and the body. The problem is solved applying Pontryagin’s
maximum principle, with the beam cross-sectional area being taken for control. The two-point
boundary value problem is obtained, and the shooting method is applied to solving it. The
property of self-adjoint systems is employed, where all costate variables are expressed by state
variables, which facilitates solving the appropriate differential equations. Also, the percent saving
of the beam mass is determined, achieved by using the cantile...ver beam of an optimum variable
square cross-section compared to the cantilever beam of a constant cross-section at specified
value of the fundamental frequency.
Keywords:
coupled vibrations / axially functionally graded beams / Timoshenko beam / Pontryagin's maximum principle / mass minimization / axial vibration / bending vibration / cantilever beamSource:
Procceding of 8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021, 2021, 176-183Publisher:
- Beograd : Srpsko društvo za mehaniku
Funding / projects:
- Ministry of Science, Technological Development and Innovation of the Republic of Serbia, institutional funding - 200105 (University of Belgrade, Faculty of Mechanical Engineering) (RS-MESTD-inst-2020-200105)
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Mašinski fakultetTY - CONF AU - Obradović, Aleksandar AU - Mitrović, Zoran AU - Zorić, Nemanja PY - 2021 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3984 AB - Shape optimization of an AFG Timoshenko cantilever beam of a variable cross-sectional area, with a specified fundamental frequency, is considered. The cantilever beam has a finitedimensional body placed eccentrically at the right end. Optimization is performed in terms of beam mass minimization. Considerations involve the case of coupled axial and bending oscillations, where contour conditions are the cause of coupling, which exist at the place of junction between the cantilever beam and the body. The problem is solved applying Pontryagin’s maximum principle, with the beam cross-sectional area being taken for control. The two-point boundary value problem is obtained, and the shooting method is applied to solving it. The property of self-adjoint systems is employed, where all costate variables are expressed by state variables, which facilitates solving the appropriate differential equations. Also, the percent saving of the beam mass is determined, achieved by using the cantilever beam of an optimum variable square cross-section compared to the cantilever beam of a constant cross-section at specified value of the fundamental frequency. PB - Beograd : Srpsko društvo za mehaniku C3 - Procceding of 8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021 T1 - Mass minimization of an AFG Timoshenko cantilever beam with a large body placed eccentrically at the beam end EP - 183 SP - 176 UR - https://hdl.handle.net/21.15107/rcub_machinery_3984 ER -
@conference{ author = "Obradović, Aleksandar and Mitrović, Zoran and Zorić, Nemanja", year = "2021", abstract = "Shape optimization of an AFG Timoshenko cantilever beam of a variable cross-sectional area, with a specified fundamental frequency, is considered. The cantilever beam has a finitedimensional body placed eccentrically at the right end. Optimization is performed in terms of beam mass minimization. Considerations involve the case of coupled axial and bending oscillations, where contour conditions are the cause of coupling, which exist at the place of junction between the cantilever beam and the body. The problem is solved applying Pontryagin’s maximum principle, with the beam cross-sectional area being taken for control. The two-point boundary value problem is obtained, and the shooting method is applied to solving it. The property of self-adjoint systems is employed, where all costate variables are expressed by state variables, which facilitates solving the appropriate differential equations. Also, the percent saving of the beam mass is determined, achieved by using the cantilever beam of an optimum variable square cross-section compared to the cantilever beam of a constant cross-section at specified value of the fundamental frequency.", publisher = "Beograd : Srpsko društvo za mehaniku", journal = "Procceding of 8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021", title = "Mass minimization of an AFG Timoshenko cantilever beam with a large body placed eccentrically at the beam end", pages = "183-176", url = "https://hdl.handle.net/21.15107/rcub_machinery_3984" }
Obradović, A., Mitrović, Z.,& Zorić, N.. (2021). Mass minimization of an AFG Timoshenko cantilever beam with a large body placed eccentrically at the beam end. in Procceding of 8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021 Beograd : Srpsko društvo za mehaniku., 176-183. https://hdl.handle.net/21.15107/rcub_machinery_3984
Obradović A, Mitrović Z, Zorić N. Mass minimization of an AFG Timoshenko cantilever beam with a large body placed eccentrically at the beam end. in Procceding of 8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021. 2021;:176-183. https://hdl.handle.net/21.15107/rcub_machinery_3984 .
Obradović, Aleksandar, Mitrović, Zoran, Zorić, Nemanja, "Mass minimization of an AFG Timoshenko cantilever beam with a large body placed eccentrically at the beam end" in Procceding of 8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021 (2021):176-183, https://hdl.handle.net/21.15107/rcub_machinery_3984 .