一角点支撑对边两边固支正交各向异性矩形薄板振动的辛叠加方法

A Symplectic Superposition Method for Vibration of the Orthotropic Rectangular Thin Plate Point-Supported at a Corner and Clamped at its Opposite Edges

运用辛叠加方法研究了一角点支撑对边两边固支的正交各向异性矩形薄板的振动问题.首先由边界条件出发,将原振动问题分解为两个对边简支的子振动问题,再根据Hamilton体系的分离变量法分别得到两个子振动问题的级数展开解,然后利用叠加方法得到原振动问题的辛叠加解.为了在具体计算中确定所得辛叠加的级数展开项,对该解计算正交各向异性矩形薄板的情形进行了收敛性分析.应用所得辛叠加解分别计算了一角点支撑对边两边固支的各向同性和正交各向异性矩形薄板的振动频率,进而给出了正交各向异性方形薄板的前8阶振动频率所对应的模态.

The symplectic superposition method was used to study the vibration problem of the orthotropic rec-tangular thin plate point-supported at a corner and clamped at its opposite edges.Firstly,based on the bounda-ry conditions,the original vibration problem was decomposed into 2 subproblems with 2 opposite edges simply supported.Next,the series expansion solutions to the 2 sub-vibration problems were obtained based on the separation variable method in the Hamiltonian system.Then the symplectic superposition solution to the original vibration problem was obtained with the superposition method.To determine the terms of the series expansion of the obtained symplectic superposition solution in specific calculations,the convergence analysis of the solu-tion for calculating orthotropic rectangular thin plates was performed.The symplectic superposition solution was also used to calculate the vibration frequencies of the isotropic and orthotropic rectangular thin plate point-supported at a corner and clamped at its opposite edges,respectively,and to give the modes corresponding to the 1st 8 vibration frequencies of an orthotropic square thin plate.