Stochastic averaging for SDOF strongly nonlinear system under combined harmonic and Poisson white noise excitations

A stochastic averaging method for single degree of freedom(SDOF)strongly nonlinear system under combined harmonic and Poisson white noise excitations is proposed by using generalized harmonic functions. The averaged stochastic differential equations (SDEs) and the Generalized Fokker–Planck–Kolmogoro...

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Published inInternational journal of non-linear mechanics Vol. 126; p. 103574
Main Authors Liu, Weiyan, Guo, Zhongjin, Yin, Xunru
Format Journal Article
LanguageEnglish
Published New York Elsevier Ltd 01.11.2020
Elsevier BV
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ISSN0020-7462
1878-5638
DOI10.1016/j.ijnonlinmec.2020.103574

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Abstract A stochastic averaging method for single degree of freedom(SDOF)strongly nonlinear system under combined harmonic and Poisson white noise excitations is proposed by using generalized harmonic functions. The averaged stochastic differential equations (SDEs) and the Generalized Fokker–Planck–Kolmogorov (GFPK) equation for the stationary joint probability density of amplitude and phase difference are derived. Then the reduced GFPK equation is solved by using finite difference method and the successive over relation (SOR) method to obtain the approximate stationary probability density of the response. This method is applied to Duffing oscillator subject to combined harmonic and Poisson white noise excitations. In the case of primary resonance, the stochastic bifurcation of the Duffing oscillator under combined harmonic and Poisson white noise excitations as the system parameters change are examined using the stationary probability density of amplitude. At last, the analytical results obtained from the proposed method are verified by those from the Monte Carlo numerical simulation. •A stochastic averaging method for SDOF system under noise excitations is proposed.•The excitations are the combined harmonic and Poisson white noise excitations.•The GFPK equations are solved using finite difference and the SOR method.•Theoretical results agree well with those from Monte Carlo simulation.
AbstractList A stochastic averaging method for single degree of freedom(SDOF)strongly nonlinear system under combined harmonic and Poisson white noise excitations is proposed by using generalized harmonic functions. The averaged stochastic differential equations (SDEs) and the Generalized Fokker–Planck–Kolmogorov (GFPK) equation for the stationary joint probability density of amplitude and phase difference are derived. Then the reduced GFPK equation is solved by using finite difference method and the successive over relation (SOR) method to obtain the approximate stationary probability density of the response. This method is applied to Duffing oscillator subject to combined harmonic and Poisson white noise excitations. In the case of primary resonance, the stochastic bifurcation of the Duffing oscillator under combined harmonic and Poisson white noise excitations as the system parameters change are examined using the stationary probability density of amplitude. At last, the analytical results obtained from the proposed method are verified by those from the Monte Carlo numerical simulation.
A stochastic averaging method for single degree of freedom(SDOF)strongly nonlinear system under combined harmonic and Poisson white noise excitations is proposed by using generalized harmonic functions. The averaged stochastic differential equations (SDEs) and the Generalized Fokker–Planck–Kolmogorov (GFPK) equation for the stationary joint probability density of amplitude and phase difference are derived. Then the reduced GFPK equation is solved by using finite difference method and the successive over relation (SOR) method to obtain the approximate stationary probability density of the response. This method is applied to Duffing oscillator subject to combined harmonic and Poisson white noise excitations. In the case of primary resonance, the stochastic bifurcation of the Duffing oscillator under combined harmonic and Poisson white noise excitations as the system parameters change are examined using the stationary probability density of amplitude. At last, the analytical results obtained from the proposed method are verified by those from the Monte Carlo numerical simulation. •A stochastic averaging method for SDOF system under noise excitations is proposed.•The excitations are the combined harmonic and Poisson white noise excitations.•The GFPK equations are solved using finite difference and the SOR method.•Theoretical results agree well with those from Monte Carlo simulation.
ArticleNumber 103574
Author Yin, Xunru
Guo, Zhongjin
Liu, Weiyan
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Combined harmonic and Poisson white noise excitations
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Snippet A stochastic averaging method for single degree of freedom(SDOF)strongly nonlinear system under combined harmonic and Poisson white noise excitations is...
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SubjectTerms Amplitudes
Approximation
Bifurcation
Bifurcations
Combined harmonic and Poisson white noise excitations
Density
Differential equations
Duffing oscillators
Excitation
Finite difference method
Harmonic functions
Noise
Nonlinear systems
Probability theory
Response
Stochastic averaging
White noise
Title Stochastic averaging for SDOF strongly nonlinear system under combined harmonic and Poisson white noise excitations
URI https://dx.doi.org/10.1016/j.ijnonlinmec.2020.103574
https://www.proquest.com/docview/2450652295
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