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Connection between Volterra series and perturbation method in nonlinear systems analyses

  • Research Paper
  • Dynamics, Vibration, and Control
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Abstract

This paper is concerned with the connection between the Volterra series and the regular perturbation method in nonlinear systems analyses. It is revealed for the first time that, for a forced polynomial nonlinear system, if its derived linear system is a damped dissipative system, the steady response obtained through the regular perturbation method is exactly identical to the response given by the Volterra series. On the other hand, if the derived linear system is an undamped conservative system, then the Volterra series is incapable of modeling the forced polynomial nonlinear system. Numerical examples are further presented to illustrate these points. The results provide a new criterion for quickly judging whether the Volterra series is applicable for modeling a given polynomial nonlinear system.

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Authors and Affiliations

  1. Institute of Vibration Shock & Noise, Shanghai Jiao Tong University, 200240, Shanghai, China

    Xing-Jian Dong, Zhi-Ke Peng, Wen-Ming Zhang & Guang Meng

Authors
  1. Xing-Jian Dong
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  2. Zhi-Ke Peng
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  3. Wen-Ming Zhang
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  4. Guang Meng
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Corresponding author

Correspondence to Xing-Jian Dong.

Additional information

The project was supported by the National Science Fund for Distinguished Young Scholars (11125209), and the National Natural Science Foundation of China (51121063 and 10702039).

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Dong, XJ., Peng, ZK., Zhang, WM. et al. Connection between Volterra series and perturbation method in nonlinear systems analyses. Acta Mech Sin 30, 600–606 (2014). https://doi.org/10.1007/s10409-014-0010-4

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  • DOI: https://doi.org/10.1007/s10409-014-0010-4

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