一类非线性系统的随机振动频率响应分析研究  

RANDOM VIBRATION FREQUENCY RESPONSE ANALYSIS OF NONLINEAR SYSTEMS BASED ON VOLTERRA SERIES

作　　者：程长明[1] 彭志科[1] 孟光[1] 

机构地区：[1]上海交通大学机械系统与振动国家重点实验室,上海200240

出　　处：《力学学报》2011年第5期905-913,共9页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10902068;10732060);上海市浦江人才支持计划(10PJ1406000);教育部新世纪优秀人才支持计划(NCET-10-0548)资助项目~~

摘　　要：Volterra级数是研究非线性系统的一种重要数学工具,它可看作线性系统理论中的卷积运算在非线性系统分析中的推广.基于Volterra级数,给出了受高斯白噪声激励下的非线性系统输出功率谱的计算公式.公式表明,该系统输出功率谱可用激励强度的多项式函数来表示,其结果为研究激励强度对非线性系统输出功率谱的影响提供了有效途径.Volterra series is a powerful mathematical tool for nonlinear system analysis, which is essentially an extension of the convolution operation from linear systems to nonlinear systems. In this study, based on the Volterra series, an analytical expression is derived to calculate the power spectrum density （PSD） for the output of nonlinear systems subjected to Gaussian white noise excitation. This expression reveals that the PSD of the nonlinear system can be expressed as polynomial function of the input intensity. This expression provides an efficient way to study the effect of the input intensity of a Gaussian white noise excitation on the PSD of nonlinear system output.

关 键 词：VOLTERRA级数 非线性系统 随机振动 功率谱 广义频率响应函数 

分 类 号：O322[理学—一般力学与力学基础] O324[理学—力学]