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Stochastic Averaging of Strongly Nonlinear Oscillators under Poisson White Noise Excitation

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IUTAM Symposium on Nonlinear Stochastic Dynamics and Control

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 29))

Abstract

A stochastic averaging method for single-degree-of-freedom (SDOF) strongly nonlinear oscillators under Poisson white noise excitation is proposed by using the so-called generalized harmonic functions. The stationary averaged generalized Fokker-Planck-Kolmogorov (GFPK) equation is solved by using the classical perturbation method. Then the procedure is applied to estimate the stationary probability density of response of a Duffing-van der Pol oscillator under Poisson white noise excitation. Theoretical results agree well with Monte Carlo simulations.

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Authors and Affiliations

  1. Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, China

    Y. Zeng & W. Q. Zhu

Authors
  1. Y. Zeng
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  2. W. Q. Zhu
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Editor information

Editors and Affiliations

  1. Zhejiang University, Zhe Da Road 38, 310027, Hangzhou, People’s Republic of China

    W. Q. Zhu

  2. College of Engineering and Computer Science, Florida Atlantic University , 33431, Boca Raton, Florida, USA

    Y. K. Lin

  3. College of Engineering and Computer Science , Florida Atlantic University, 33431, Boca Raton, Florida, USA

    G. Q. Cai

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Zeng, Y., Zhu, W.Q. (2011). Stochastic Averaging of Strongly Nonlinear Oscillators under Poisson White Noise Excitation. In: Zhu, W.Q., Lin, Y.K., Cai, G.Q. (eds) IUTAM Symposium on Nonlinear Stochastic Dynamics and Control. IUTAM Bookseries, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0732-0_15

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  • DOI: https://doi.org/10.1007/978-94-007-0732-0_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-0731-3

  • Online ISBN: 978-94-007-0732-0

  • eBook Packages: EngineeringEngineering (R0)

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