正交异性环形板非线性振动的有限元分析

本文用有限元法研究了正交异性环形板非线性振动的频率随振幅的变化规律。由于结构和运动的对称性，三节点九自由度环形单元被采用，计算表明这神单元是高度有效的．系统的动力学方程借助于拉格朗日方程来获得．由于刚度阵中含有非线性项，计算中使用迭代逐步逼近方程的解．与类似方法相比，本文在对非线性刚度阵的线性化方面作了改进，用能量平衡原理求得线性化系数，使计算结果更趋合理．

Finite Element Analysis for Non-linear Vibration of a Orthogonal Annular Plate

This paper has analyzed the non-linear axisymmetrical vibration of a orthogonal annular plateby the finite element method. The three node annular elements used here are very effective and only afew elements are needed to obtain high precision of the calculations. The non-linear terms of thestiffness matrix are functions of the displacements and change continuously within a period. This paperlinearised the terms by averagins them over a period according to the energy ballance principle andobtained better results. The method used here and the obtained results are valuable for the designer toestimate the frequencies of linear and non-linear vibrations of composite annular plates.