弹性地基上矩形板自由振动的GDQ法求解

摘要

According to the theory of vibration of elastic bodies and starting from the governing differential equation of free vibration of rectangular plates on elastic foundations,the governing differential equation and the different boundary conditions were made discrete and the frequency characteristics of free vibration were studied numerically by using the generalized differential quadrature(GDQ) method. The dimension-less fundamental frequencies for rectangular plates are obtained at different aspect ratios and at different foundation parameters.which is compared with the available value of the exact solution of the plates with four simply supported edges. The results show that the GDQ method is applicable and precise and its results can provide some references to the analysis of engineering vibrations of structures.%依据弹性体振动理论,从弹性地基上矩形板自由振动的控制微分方程出发,运用广义微分求积法(GDQ法)将控制微分方程及不同边界条件进行离散.数值研究了弹性地基上矩形板自由振动的频率特性；给出了矩形板不同长宽比和不同地基参数之间无量纲振动基频的关系;并将四边简支边界条件下的计算结果与其精确解进行了比较,显示了GDQ法的适用性和精确性,其计算结果可为结构的工程振动分析提供参考.