变系数曲线支承矩形厚板自由振动的傅里叶分析

FOURIER ANALYSIS ON FREE VIBRATION OF RECTANGULAR THICK PLATES WITH VARIABLE ELASTIC CURVED SUPPORTS

本文给出了变系数曲线支承的Ambartsumian矩形厚板自由振动问题的级数解,将位移和剪力在板域内展成重傅里叶级数,将其导数在边界上展成单傅里叶级数,通过傅里叶交换将控制微分方程和边界条件转化成关于位移级数的系数的一组无穷线性代数方程,最终将板的自由振动问题转化为矩阵特征值问题。

This paper presents a series solution for the free vibration of Ambartsumian rectangular plates with variable elastic curved supports. Using double fourier series to represent the deflection and the stress function, the governing equations and the boundary conditions may be reduced to a set of infinite linear algebraic equations for coefficients in the series of deflection. Then the problem of free vibration of the thick plates is transformed into a matrix eigenproblem.