On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge

A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years. The method has yielded many new analytic solutions due to its rigorousness. In this study, the first endeavor is made to further developed the symplectic superposition method for the...

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Autores principales:	Dian Xu, Zhuofan Ni, Yihao Li, Zhaoyang Hu, Yu Tian, Bo Wang, Rui Li
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Symplectic superposition method Free vibration Plates Mixed boundary constraints Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/6ce45680637a489fb0f7d40055675149
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spelling	oai:doaj.org-article:6ce45680637a489fb0f7d400556751492021-11-30T04:15:41ZOn the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge2095-034910.1016/j.taml.2021.100293https://doaj.org/article/6ce45680637a489fb0f7d400556751492021-07-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2095034921001008https://doaj.org/toc/2095-0349A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years. The method has yielded many new analytic solutions due to its rigorousness. In this study, the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge. The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied. The solution procedure incorporates separation of variables, symplectic eigen solution and superposition. The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems. The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use. The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.Dian XuZhuofan NiYihao LiZhaoyang HuYu TianBo WangRui LiElsevierarticleSymplectic superposition methodFree vibrationPlatesMixed boundary constraintsEngineering (General). Civil engineering (General)TA1-2040ENTheoretical and Applied Mechanics Letters, Vol 11, Iss 5, Pp 100293- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Symplectic superposition method Free vibration Plates Mixed boundary constraints Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	Symplectic superposition method Free vibration Plates Mixed boundary constraints Engineering (General). Civil engineering (General) TA1-2040 Dian Xu Zhuofan Ni Yihao Li Zhaoyang Hu Yu Tian Bo Wang Rui Li On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge
description	A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years. The method has yielded many new analytic solutions due to its rigorousness. In this study, the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge. The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied. The solution procedure incorporates separation of variables, symplectic eigen solution and superposition. The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems. The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use. The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.
format	article
author	Dian Xu Zhuofan Ni Yihao Li Zhaoyang Hu Yu Tian Bo Wang Rui Li
author_facet	Dian Xu Zhuofan Ni Yihao Li Zhaoyang Hu Yu Tian Bo Wang Rui Li
author_sort	Dian Xu
title	On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge
title_short	On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge
title_full	On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge
title_fullStr	On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge
title_full_unstemmed	On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge
title_sort	on the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/6ce45680637a489fb0f7d40055675149
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On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge

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