相关演变随机激励下响应演变谱矩阵的表达式  

General Expression of Response Evolutionary Spectrum Matrix due to correlated Evolutionary Random Excitations

作　　者：方同[1] 孙木楠[2] 张天舒[3] 

机构地区：[1]西北工业大学,西安710072 [2]南京理工大学,南京210094 [3]东华大学,上海200051

出　　处：《应用力学学报》2008年第3期351-354,共4页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(10332030)

摘　　要：引入演变频率响应矩阵的概念,时不变线性系统在矢量演变随机激励下的响应演变功率谱矩阵有十分简洁的形式,与平稳随机响应-激励功率谱矩阵的关系式十分相似。实质不同在于:此处的演变频率响应理应定义为零初始条件下、系统对演变复谐和激励的确定性瞬态响应。因此,演变随机响应问题就归结为相关演变复谐和激励下的确定性瞬态响应问题。响应演变谱矩阵的一般表达式覆盖了非均匀调制与均匀调制随机激励两种情形的结果。而同源演变随机激励情形只是其特例。Introducing the concept of evolutionary frequency response, the evolutionary spectrum matrix of the random response under zero initial conditions of a time-invariant linear system subject to correlated evolutionary random excitations can be expressed in a concise way, similar to the matrix relationship between the power spectral densities of a stationary random response and the excitation. The evolutionary frequency response is defined as the transient response of the system under an evolutionary complex harmonic excitation. Hence, the evolutionary random response problem is finally reduced into a deterministic response problem. The general matrix expression of the response evolutionary spectrum covers all the results due to uniformly or non-uniformly modulated, cognate or correlated random excitations.

关 键 词：演变随机激励 响应演变功率谱 演变频率响应 同源随机激励 

分 类 号：O324[理学—一般力学与力学基础]