非比例阻尼线性体系平稳随机地震响应计算的虚拟激励法

应用复振型分解方法,将非比例阻尼线性体系在地震作用下的动力方程求解问题转化为若干个广义复振子的求解与叠加问题。通过假定地震地面运动为一零均值的平稳随机激励,应用虚拟激励法原理,推导得到了广义复振子动力坐标的解析计算公式,进而得到了以复振型为基础的非比例阻尼线性体系随机地震响应计算的一般实数解析解答。算例证实了这种方法的可靠性及高效率。

Pseudo-excitation method for stationary random responses of non-proportionally damped MDOF systems

In terms of the complex mode superposition method,the motion equations of general multiple degrees of freedom(MDOF) discrete system can be transferred into the combination of many complex oscillators.Assuming that the earthquake ground motion is a zero-mean-valued stationary random excitation,the analytic solutions of these complex oscillators are derived in virtue of the principle of pseudo-excitation method;then a delicate general solution of non-proportionally damped MDOF systems subjected to earthquake ground motion,complete in real value form,is presented in this paper.Comparing with the traditional pesudo-excitation method,to ensure the accuracy in the dynamic response analysis of non-proportionally damped MDOF systems,the less modes in complex conjugate pairs is required in using the proposed pseudo-excitation method in this paper,so that the computing efficiency is mproved greatly.A numerical example is given to demonstrate the validity and efficiency of the algorithm.