Power spectral density analysis for nonlinear systems based on Volterra series  被引量:2

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作  者:Penghui WU Yan ZHAO Xianghong XU 

机构地区:[1]State Key Laboratory of Structural Analysis for Industrial Equipment,Faculty of Vehicle Engineering and Mechanics,Dalian University of Technology,Dalian 116023,Liaoning Province,China [2]State Key Laboratory of Nonlinear Mechanics,Institute of Mechanics,Chinese Academy of Sciences,Beijing 100190,China

出  处:《Applied Mathematics and Mechanics(English Edition)》2021年第12期1743-1758,共16页应用数学和力学(英文版)

基  金:the National Natural Science Foundation of China(Nos.11772084 and U1906233);the National High Technology Research and Development Program of China(No.2017YFC0307203);the Key Technology Research and Development Program of Shandong Province of China(No.2019JZZY010801)。

摘  要:A consequence of nonlinearities is a multi-harmonic response via a monoharmonic excitation.A similar phenomenon also exists in random vibration.The power spectral density(PSD)analysis of random vibration for nonlinear systems is studied in this paper.The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function(GFRF).For a class of nonlinear systems,the growing exponential method is used to determine the first 3 rd-order GFRFs.The proposed approach is used to achieve the nonlinear system’s output PSD under a narrow-band stationary random input.The relationship between the peak of PSD and the parameters of the nonlinear system is discussed.By using the proposed method,the nonlinear characteristics of multi-band output via single-band input can be well predicted.The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system’s output PSD.This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.

关 键 词:Volterra series nonlinear system generalized frequency response function(GFRF) power spectrum density(PSD) 

分 类 号:O324[理学—一般力学与力学基础]

 

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