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Power Spectrum Analysis and Optimization Design of Nonlinear Energy Sink Under Random Excitation

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Abstract

Purpose

The vibration problem of nonlinear structures is very challenging, especially for random excitations.

Methods

This paper investigates the power spectral characteristics of the random vibration response of a structure with a nonlinear energy sink (NES) in the frequency domain. Using the statistical characteristics of system response, an optimized objective function is constructed, and a stochastic optimization method is established to realize the parameter optimization of the NES attachment of the structure under random excitation. The random excitation is modeled as a complex exponential series represented by random variables, and the multi-harmonic balance method (MHBM) is used to analyze the random vibration of the multi-degree-of-freedom (MDOF) coupled nonlinear system.

Results

By introducing the alternating frequency time (AFT) approach, the analytical derivation of nonlinear constitutive equations in the frequency domain is avoided, and the iterative calculation of power spectral density (PSD) analysis of random vibration based on the frequency domain is effectively realized. Moreover, the peak shift and multi-peak response of the response PSD of the system coupled with NES are discussed. To solve the nonlinear optimization problem of NES system parameters, an MHBM–GA optimization approach is proposed, which realizes the parameter optimization of the nonlinear coupled system under random excitation.

Conclusions

This study provides a new method for the vibration analysis and optimization design of NES under random excitation.

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Data availability

The data supporting the findings of this study are available within the article.

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Acknowledgements

Project 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), the Key Technology Research and Development Program of Shandong (No. 2019JZZY010801), the Fundamental Research Funds for the Central Universities (DUT22ZD209, DUT21ZD209).

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Authors and Affiliations

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

    Penghui Wu & Yan Zhao

  2. Beijing Aerospace System Engineering Institute, Beijing, 100076, China

    Jin Xiao

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

    Yan Zhao

Authors
  1. Penghui Wu
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  2. Jin Xiao
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  3. Yan Zhao
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Correspondence to Yan Zhao.

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Wu, P., Xiao, J. & Zhao, Y. Power Spectrum Analysis and Optimization Design of Nonlinear Energy Sink Under Random Excitation. J. Vib. Eng. Technol. 12, 5663–5673 (2024). https://doi.org/10.1007/s42417-023-01210-1

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  • DOI: https://doi.org/10.1007/s42417-023-01210-1

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