关于虚拟激励法的一个注记  

A note on the pseudo-excitation method

作　　者：陈建兵[1] 彭勇波[2] 李杰[1] 

机构地区：[1]同济大学土木工程防灾国家重点实验室,上海200092 [2]同济大学上海防灾救灾研究所,上海200092

出　　处：《计算力学学报》2011年第2期163-167,共5页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(90715033;10872148);土木工程防灾国家重点实验室系统性研究(SLDRCE08-A-01);探索性研究课题(SLDRCE10-B-02)资助项目

摘　　要：从具有随机频率与随机相位的随机谐和函数出发,证明了当随机频率与相位均为均匀分布而随机幅值与功率谱密度平方根成正比时,该随机过程的功率谱即精确地等于目标功率谱。进而表明:只需遍历频率区间,即可由单一谐和函数激励下的响应幅值给出响应的功率谱密度,从而揭示了虚拟激励法的物理意义。研究还表明:为了给出结构响应的功率谱密度,实际上仅需要虚拟激励法中一半的计算工作量即可。文中的算例分析验证了这一结果。A stochastic harmonic function of random frequency and phase is introduced in the present paper.The power spectral density of a stochastic process represented by the stochastic harmonic function is proved to be exactly the target power spectral density if the random frequency and phase of the harmonic function both follow uniform distributions,while its amplitude is proportion to the square root of target power spectral density.It is thus noted that the power spectral density of structural response can be obtained by figuring out the square of the amplitude of steady-state response of the structure excited by harmonic processes traversing the values of frequency domain of interest.This interpreted the physical meaning of the pseudo-excitation method.Numerical investigations,meanwhile,reveal that actually only half of the computational efforts in the pseudo-excitation method are adequate.

关 键 词：随机谐和函数 功率谱密度 虚拟激励法 平稳响应 

分 类 号：O324[理学—一般力学与力学基础]