基于三角小波的弹性薄板高精度分析方法

摘要

Taking trigonometric Hermite wavelet that has both good approximation characteristics of trig- onometric function and multi-resolution, local characteristics of wavelet as trial function, the bending, vibration and stability of rectangle elastic thin plate under different boundary conditions are solved based on the principle of minimum potential energy. Furthermore, two approaches, hierarchical and multi-reso- lution approach, are presented to improve accuracy of calculation. Numerical examples show that trigono- metric wavelet method can process kinds of boundary conditions conveniently and performs well in solving the bending,vibration and stability of rectangle elastic thin plate,especially for natural vibration feature analysis, and hierarchical and multi-resolution approaches can improve the analysis precision effectively.%采用同时具有三角函数良好逼近特性和小波多分辨率与局部特性的Hermite插值型三角小波，基于二维张量积三角小波，推导了求解各种不同边界条件下的矩形弹性薄板的弯曲、振动和屈曲问题的统一列式，同时给出了两种提高计算精度的方法一升阶法和多分辨率法。数值算例表明，三角小波法求解弹性薄板的弯曲、振动和屈曲问题时，能方便地处理各类边界条件，计算效果良好；自振特性分析更具优势，升阶法和多分辨率法能有效地提高分析精度。