Power spectral density analysis for nonlinear systems based on Volterra series

doi:10.1007/s10483-021-2794-7

Applied Mathematics and Mechanics (English Edition) ›› 2021, Vol. 42 ›› Issue (12): 1743-1758.doi: https://doi.org/10.1007/s10483-021-2794-7

Power spectral density analysis for nonlinear systems based on Volterra series

Penghui WU¹, Yan ZHAO¹, Xianghong XU²

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

收稿日期:2021-07-07 修回日期:2021-09-01 发布日期:2021-11-23
通讯作者: Yan ZHAO ,E-mail:yzhao@dlut.edu.cn
基金资助:
the National Natural Science Foundation of China (Nos. 11772084 and U1906233), the National High Technology Research and Development Program of China (No. 2017YFC0307203), and the Key Technology Research and Development Program of Shandong Province of China (No. 2019JZZY010801)

Power spectral density analysis for nonlinear systems based on Volterra series

Penghui WU¹, Yan ZHAO¹, Xianghong XU²

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

Received:2021-07-07 Revised:2021-09-01 Published:2021-11-23
Contact: Yan ZHAO ,E-mail:yzhao@dlut.edu.cn
Supported by:
the National Natural Science Foundation of China (Nos. 11772084 and U1906233), the National High Technology Research and Development Program of China (No. 2017YFC0307203), and the Key Technology Research and Development Program of Shandong Province of China (No. 2019JZZY010801)

摘要/Abstract

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 3rd-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)

Abstract: 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 3rd-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.

Key words: Volterra series, nonlinear system, generalized frequency response function (GFRF), power spectrum density (PSD)

中图分类号:

74H50

Penghui WU, Yan ZHAO, Xianghong XU. Power spectral density analysis for nonlinear systems based on Volterra series[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(12): 1743-1758.

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Power spectral density analysis for nonlinear systems based on Volterra series

Power spectral density analysis for nonlinear systems based on Volterra series

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