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A Volterra-PEM approach for random vibration spectrum analysis of nonlinear systems

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Abstract

In this paper, the Volterra series and the pseudo-excitation method (PEM) are combined to establish a frequency domain method for the power spectral density (PSD) analysis of random vibration of nonlinear systems. The explicit expression of the multi-dimensional power spectral density (MPSD) of the random vibration response is derived analytically. Furthermore, a fast calculation strategy from MPSD to physical PSD is given. The PSD characteristics analysis of the random vibration response of nonlinear systems is effectively achieved. First, within the framework of Volterra series theory, an improved PEM is established for MPSD analysis of nonlinear systems. As a generalized PEM for nonlinear random vibration analysis, the Volterra-PEM is used to analyse the response MPSD, which also has a very concise expression. Second, in the case of computation difficulties with multi-dimensional integration from MPSD to PSD, the computational efficiency is improved by converting the multi-dimensional integral into a matrix operation. Finally, as numerical examples, the Volterra-PEM is used to estimate the response PSD for stationary random vibration of a nonlinear spring-damped oscillator and a non-ideal boundary beam with geometrical nonlinearity. Compared with Monte Carlo simulation, the results show that by constructing generalized pseudo-excitation and matrix operation methods, Volterra-PEM can be used for input PSD with arbitrary energy distribution, not only restricted to broadband white noise excitation, and accurately predict the secondary resonance phenomenon of the random vibration response of nonlinear systems in the frequency domain.

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Funding

The work is 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 (No. 2019JZZY010801).

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian, 116023, China

    Penghui Wu & Yan Zhao

  2. Ningbo Research Institute of Dalian University of Technology, Ningbo, 315016, China

    Yan Zhao

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  1. Penghui Wu
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Correspondence to Yan Zhao.

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Wu, P., Zhao, Y. A Volterra-PEM approach for random vibration spectrum analysis of nonlinear systems. Nonlinear Dyn 111, 8523–8543 (2023). https://doi.org/10.1007/s11071-023-08270-8

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