环向正交异性变厚度圆板非线性分析渐近法

本文提出了解决环向正交异性变厚度圆板非线性静、动态分析的另一种渐近方法。方法的实质是在板的应变能中引入一新参量 I_e,得到了一组以 I_e 进行简单耦合的控制方程。通过迭代或迭代-变分方法求解方程,得出环向正交异性变厚度圆板的一般非线性运动方程和非线性振动相对周期的近似表达式,将所得的部分数值结果与现有结果相较,证明本文结果精度是满意的。

A GRADUAL APPROXIMATION APPLIED TO THE NON-LINEAR ANALYSIS OF POLARLY ORTHOTROPIC CIRCULAR PLATES WITH VARYING THICKNESS

A new gradual approximation is presented in this paper for thenon-linear analysis of static and dynamic behaviours of polarly orth-otropic circular plate with varying thickness.The essence of thismethod is that a new parameter Ie is introduced into the energyexpression of the plate in order to obtain a set of simple differential goveaning equations coupled by Ie.By using iteration-variation method to solve the above equations,we can obtain approximate general non-linear dynamic equations andthe relative period expression of non-linear vibration of a plate,com-paring some numerical results with current ones obtained by othermethods has been proved that the results in this paper are Satisfactoy.