Parametric characteristic of the random vibration response of nonlinear systems  

作　　者：Xing-Jian Dong Zhi-Ke Peng Wen-Ming Zhang Guang Meng Fu-Lei Chu 

机构地区：[1]State Key Laboratory of Mechanical System and Vibration,Shanghai Jiao Tong University [2]Department of Precision Instruments,Tsinghua University

出　　处：《Acta Mechanica Sinica》2013年第2期267-283,共17页力学学报（英文版）

基　　金：supported by the National Science Fund for Distinguished Young Scholars (11125209);the National Natural Science Foundation of China (10902068,51121063 and 10702039);the Shanghai Pujiang Program (10PJ1406000);the Opening Project of State Key Laboratory of Mechanical System and Vibration (MSV201103)

摘　　要：Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.

关 键 词：Volterra series·Nonlinear system·Random vibration·Power spectrum density·Generalized frequency response functions 

分 类 号：O324[理学—一般力学与力学基础]