基于Rayleigh-Ritz法旋转薄壁圆盘行波特性分析

Travelling wave analysis of rotating thin disks via rayleigh-ritz method

采用理论分析、实验测试与有限元仿真3种方法相互结合,分析中心固支条件的旋转薄壁圆盘的行波振动特性。基于Kirchhoff薄板基本假设,利用Lagrange方程,建立中心固支薄壁圆盘的能量方程。采用Rayleigh-Ritz法,利用多项式函数作为容许函数,建立旋转圆盘动力学分析的动力学方程,获得薄壁圆盘静止态固有特性和和旋转态行波特性的分析方法,并利用试验测试、有限元计算结果对本文所提出的解析方法进行验证。分析薄壁圆盘在静止态下的固有特性并对比分析不同旋转速度下旋转薄壁圆盘的行波特性。结果表明:前行波频率随转动速度增加而增加,后行波频率先减小后增加,当后行波频率减小为0时,前行波与后行波相互静止,即出现"驻波"现象,此时圆盘振动很容易引起共振破坏。

The analysis method, experimental method and finite element method were imported to obtain the traveling wave vibration characteristics of the rotating disk with the center fixed. Based on the Kirchoff thin plates theory and Lagrange equation, the energy equations of the central fixed rotating disk were derived. Secondly, by taking the polynomial functions as the admission function, the Rayleigh-Ritz method was introduced to derive the dynamic equations of rotating disk, in which the characteristics of no-rotating disk and the traveling wave characteristics of rotating disk were considered at the same time. The results of the test and finite element analysis are verified by the proposed method of this paper. The natural characteristic of no-rotating disk and the traveling wave characteristics of rotating disk with different rotating speeds are calculated. The results show that the vibration mode of forward traveling wave increases gradually with rotating speed while the frequency of backward traveling wave decreases at first and then increases, the standing wave phenomena is produced and the disk is easily destroyed when the frequency of backward traveling wave equals zero.