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

• Published in: International journal of non-linear mechanics Vol. 126; p. 103574
• Main Authors: Liu, Weiyan, Guo, Zhongjin, Yin, Xunru
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.11.2020; Elsevier BV
• Subjects: 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; Response; Bifurcation; Stochastic averaging; Combined harmonic and Poisson white noise excitations
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2020.103574

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.