基于余量谐波平衡法的质点振动系统高阶近似与频率响应分析

Higher-order approximation and frequency response analysis of a particle vibration system based on a residue harmonic balance method

基于谐波平衡方法,构建了用于研究旋转抛物线上的质点运动系统的余量谐波平衡解程序。获得了系统高阶解析近似振动频率及稳态响应。研究了系统稳态下的振动频率随系统非线性项系数、初始振幅、线性刚度系数的变化趋势,给出了初始振幅、非线性项系数对系统振动频率响应的影响。研究结果表明,给出的2-阶余量谐波平衡近似比已有的方法结果更加精确,其相对误差大大降低,系统稳态下的振动频率随非线性项系数、初始振幅的增大而减少,随线性刚度系数的增大而增大。

Based on the harmonic balance method,a solution procedure of residue harmonic was developed for studying the system in which the motion of a particle is a rotating parabola.Firstly,the higher-order analytical vibration frequency and steady state response were obtained.Secondly,we study the change trend of vibration frequency as nonlinear coefficient,initial amplitude,linear stiffness coefficient of the system in steady state,the effects of initial amplitude,nonlinear coefficient on vibration frequency response were presented.The results show that the presented second-order residue harmonic balance approximations to vibration frequency and steady response are more accurate than some existing results,and that the relative error of the solution is greatly reduced,which are in good agreement with the exact ones.The vibration frequency is decreased with the increase of the nonlinear coefficient and the initial amplitude,but it increased with the increase of the linear stiffness coefficient.