任意形状Mindlin板的弯曲自振特性分析

Free Vibration Analysis of Mindlin Plates with Arbitrary Shapes

将改进的Rayleigh-Ritz法拓展到对任意形状中厚板的弯曲自振特性分析中。将位移试函数的函数域拓展到曲边域外的矩形区域,并选用改进的傅里叶级数作为试函数。采用刚度可调的弹簧模型模拟复杂边界条件,并引入数值方法将边界离散,对微段的弹性势能求和得到整体边界的弹性势能,解决了任意形状带来的曲边的复杂边界条件的问题。基于能量变分原理和Mindlin理论建立求解方程。通过将直边板和曲边板的算例与文献及有限元结果对比,证明本方法的准确性,为实际工程问题提供参考。

The improved Rayleigh-Ritz method was extended to the analysis of bending vibration characteristics of Mindlin plates in arbitrary shapes. The domain of displacement test function was extended to the rectangular region outside the curve region, and the improved Fourier series was selected as the test function. The complex boundary conditions were simulated by adopting the linear springs whose stiffness is adjustable. The numerical method was introduced to disperse the boundary edges and by summing up the elastic potential energy of each micro section the elastic potential energy of the whole boundary was obtained. Then, the problems of complex boundary conditions of curved edges brought by arbitrary shape problems can be solved. The equation was established based on the energy variation principle and Mindlin theory. By comparing the results of present method of the straight edge and curved edge plates with the results of the reference and the finite element results, the accuracy of this method is proved, which provides reference for the practical engineering problems.