Analytical solutions of free vibration for rectangular thin plate and right-angle triangle plate on the Winkler elastic foundation based on the symplectic superposition method

IF 1.5 4区工程技术 Q3 MECHANICS

Journal of Mechanics Pub Date : 2023-11-09 DOI:10.1093/jom/ufad032

Hao-Jie Jiang, Tong-Bo Chen, Yu-Xiang Ren, Ning-Hua Gao

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引用次数: 0

Abstract

Abstract Based on the symplectic superposition method, the free vibration models of rectangular and right-angle triangle plates on the Winkler elastic foundation are established in present paper, and the modes and frequencies are studied. In addition, the theoretical calculation model and finite element analysis model of rectangular thin plate and right-angle triangle plate on elastic foundation are established by using Mathematica software and ABAQUS software. It proves that the symplectic superposition method converges very fast and has a good consistency with the finite element simulation results. Analytical results show that foundation stiffness, aspect ratio and boundary condition have great influences on vibration frequency and mode shape for structures. This paper solved the free vibration problem of rectangular plate and right-angle triangle plate on elastic foundation by using symplectic superposition method. Compared with the inverse or semi-inverse method, this method avoids the process of assuming the form about the solution, hence the result of this method is completely rational.

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基于辛叠加法的Winkler弹性地基上矩形薄板和直角三角形板自由振动解析解

基于辛叠加法，建立了Winkler弹性地基上矩形板和直角三角形板的自由振动模型，并对其振型和频率进行了研究。此外，利用Mathematica软件和ABAQUS软件建立了弹性基础上矩形薄板和直角三角形板的理论计算模型和有限元分析模型。结果表明，辛叠加法收敛速度快，与有限元仿真结果有较好的一致性。分析结果表明，基础刚度、展弦比和边界条件对结构振动频率和振型有较大影响。本文用辛叠加法求解弹性基础上矩形板和直角三角形板的自由振动问题。与逆法或半逆法相比，该方法避免了对解的形式进行假设的过程，因此该方法的结果是完全合理的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mechanics 物理-力学

CiteScore

3.20

自引率

11.80%

发文量

审稿时长

6 months

期刊介绍： The objective of the Journal of Mechanics is to provide an international forum to foster exchange of ideas among mechanics communities in different parts of world. The Journal of Mechanics publishes original research in all fields of theoretical and applied mechanics. The Journal especially welcomes papers that are related to recent technological advances. The contributions, which may be analytical, experimental or numerical, should be of significance to the progress of mechanics. Papers which are merely illustrations of established principles and procedures will generally not be accepted. Reports that are of technical interest are published as short articles. Review articles are published only by invitation.