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

被引:1
|
作者
Jiang, Hao-Jie [1 ,2 ]
Chen, Tong-Bo [1 ]
Ren, Yu-Xiang [1 ]
Gao, Ning-Hua [3 ]
机构
[1] Zhejiang Univ Technol, Coll Mech Engn, Hangzhou, Zhejiang, Peoples R China
[2] Hunan Univ, State Key Lab Adv Design & Mfg Vehicle Body, Changsha, Peoples R China
[3] Zhejiang Univ Sci & Technol, Sch Sci, Dept Big Data Sci, Hangzhou, Peoples R China
基金
中国国家自然科学基金;
关键词
symplectic superposition method; free vibration; right-angle triangle plate; Winkler elastic foundation; Hamilton system; BUCKLING SOLUTIONS; VARIABLE THICKNESS; BENDING SOLUTIONS; FORCED VIBRATION; EDGES; MODEL;
D O I
10.1093/jom/ufad032
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
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 the 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.
引用
收藏
页码:395 / 415
页数:21
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