线性随机系统振动模态参数变异规律的研究

采用MonteCarlo随机有限元方法,对多自由度线性振动系统中由于结构参数的随机变异而引起的模态参数(模态频率、模态振型和模态阻尼比)变异的规律进行了研究.文中首次提出了相对均差系数的概念,应用相对均差系数和变异系数这两个无量纲量,从不同角度定量分析随机系统模态参数的变异性.数值试验结果表明,对于小阻尼比例模型,随着结构参数变异性的增大,系统模态频率均值单调变化,较低阶模态频率均值单调减小,高阶模态频率均值单调增加;模态阻尼比均值单调增加;第一阶模态振型相对均值系统的变化很小.一般地,结构参数的随机变异对模态振型均值的影响大于对模态频率、模态阻尼比均值的影响.

Research of Variability of Stochastic Modal Parameters About Linear Random System

The variation of modal parameters is caused by random variation of structural parameters in linear vibration of multiple-degree-of-freedom system. The variable rules of modal parameters including modal frequency, mode and modal damping ratio are studied by means of Monte-Carlo stochastic finite element method. In this paper, the concept of relative mean value deviation factor is first put forward. And, relative mean value deviation factor and variation factor, from different points of view, are used for analyzing the modal parameters variability quantitatively in stochastic structure vibration system. The results of numerical experimentations show that, with the creasing of structural parameters variation, the varies of mean values of modal frequencies are monotonic, the mean value of low-order modal frequency is monotonic decreasing, the mean value of high-order model frequency is monotonic increasing, all the mean values of modal damping ratios are monotonic increasing for the small damping scale-model, and the relative mean value deviation factors of first order mode are very small. In general, the variation of structure parameters has more effect on the mean values of mode than those of modal frequencies and modal damping ratios.