Symplectic Superposition Solution of Free Vibration of Fully Clamped Orthotropic Rectangular Thin Plate on Two-Parameter Elastic Foundation

Author:

Su Xin1,Bai Eburilitu1,Chen Alatancang2

Affiliation:

1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China

2. Mathematics Science College, Inner Mongolia Normal University, Hohhot 010022, P. R. China

Abstract

Based on the method of separation of variables in Hamiltonian system and superposition method, the series expansion solution of the free vibration problem of orthotropic rectangular thin plates (ORTPs) with four clamped edges (CCCC) on two-parameter elastic foundation is obtained. The original vibration problem is decomposed into two subproblems with two opposite sides simply supported, and the general solution of each subproblem is obtained by using the expansion of symplectic eigenvectors. Then by superposing these two general solutions, the series expansion solution of the original problem is obtained. The advantage of this method is that the solution process is carried out in symplectic space, and the validity of variable separation and symplectic eigenvectors expansion ensures the rationality of the solution process, while avoiding the presetting of the solution form. Finally, the correctness of symplectic superposition solution obtained in this paper is verified by calculating three concrete examples of fully clamped rectangular thin plates.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mechanical Engineering,Ocean Engineering,Aerospace Engineering,Building and Construction,Civil and Structural Engineering

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