单自由度随机系统的幅频与相频特性变异性分析

采用Monte Carlo方法,引入相对均差函数的概念,对单自由度线性随机系统的位移响应的幅频与相频特性的变异规律进行了定量研究.结果表明,系统动力学参数中,刚度和质量随机都会引起幅频特性均值曲线的峰值降低、位置前移、半功率带宽值增加;而阻尼系数随机会引起幅频特性均值曲线峰值升高,半功率带宽值减小.与刚度随机时的影响相比,质量随机时的半功率带宽增加幅度较小,峰值位置前移幅度较大;刚度随机时对低频段影响较大,质量随机时对高频段影响较大.刚度与质量参数随机时相频特性均值曲线的拐点位置不变,只是拐点附近曲线陡峭度减小.与刚度和质量随机相比,阻尼系数随机时幅频与相频特性的变异较小.

The Analysis of Variance of Amplitude-frequency and Phase-frequency Characteristic on SDOF Stochastic System

Using Monte-Carlo method to study quantitatively the variation rules of Amplitude frequency and Phase-frequency characteristic of displacement response on SDOF linear stochastic system.In this paper,the concept of relative mean value deviation function is proposed.The numerical simulation results indicate the peak value decreasing,site front moving,and the half-power bandwidth increasing on Amplitude-frequency characteristic mean value curve with random stiffness or mass;and the peak value increasing,half-power bandwidth decreasing with random damping coefficient.Compared the influence with random stiffness,the increment of half-power bandwidth are smaller,the front moving amplitude of peak is bigger with random mass.Random stiffness has more influence over low-frequency stage of the curve.However,random mass has more influence over high-frequency stage of the curve.The position of knee point of Phase-frequency characteristic mean value curve is invariant,but the kurtosis of the curve near the knee point decreases.And,the variation of Amplitude-frequency and Phase-frequency characteristic caused by random damp coefficient is more weaker than that caused by random mass or stiffness.