薄板振动分析的辛空间波传播方法

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振动与冲击 ›› 2014, Vol. 33 ›› Issue (12) : 1-6.

论文

薄板振动分析的辛空间波传播方法

张亚辉，马永彬

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A wave propagation method in symplectic space for the vibration analysis of thin plates

ZHANG Ya-hui, Ma Yong-bin

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文章历史 +

摘要

基于弹性力学问题求解的辛方法，结合波传播理论，提出一个薄板结构稳态动力响应分析的新思路。首先，将薄板振动的控制方程导入辛对偶体系，应用分离变量法得到薄板波传播问题的本征值方程，求解得到本征值（波传播参数）与本征向量（波形）；然后将物理空间求解体系转换到波空间，进而结合波传播以及波反射关系求解薄板结构的受迫振动问题。算例给出了矩形薄板在四边简支（SSSS）和一对边固支、另一对边简支（CCSS）两种边界条件下的输入点导纳以及动能和应变能；四边简支的结果与模态叠加法给出的解析解以及波有限元法的结果做了对比，对边固支-对边简支边界下的结果与有限元程序系统ABAQUS的参考解以及波有限元法结果做了对比，对比结果验证了本文方法的精确性与有效性。

Abstract

A new approach is presented for the steady state vibration analysis of thin plates which is based on the symplectic method of elasticity problem and the theory of wave propagation. The governing equations of thin plates are introduced into the symplectic duality system, the eigenvalue equations are formulated by applying the method of variable separation, and the eigenvalues (wave propagation parameters) and eigenvectors (wave modes) can be obtained. The equations of motion in physical domain are then transformed into “wave co-ordinates”, and the forced responses of thin plates are deduced by using the incident and reflection wave components. Taking a rectangular thin plate as an illustrative example, numerical results of the input mobility, kinetic energy and strain energy of the plate based on two combinations of simply supported (S) and clamped (C) boundary conditions, CCSS and SSSS, are computed. The accuracy and efficiency of the method are validated by comparing with the analytic solutions of the mode superposition method, the wave finite element method and ABAQUS software.

导出引用

张亚辉;马永彬. 薄板振动分析的辛空间波传播方法[J]. 振动与冲击, 2014, 33(12): 1-6

ZHANG Ya-hui;Ma Yong-bin. A wave propagation method in symplectic space for the vibration analysis of thin plates[J]. Journal of Vibration and Shock, 2014, 33(12): 1-6