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Probabilistic solution of a multi-degree-of-freedom Duffing system under nonzero mean Poisson impulses

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Abstract

This paper investigates the probability density function (PDF) of multi-degree-of-freedom nonlinear systems excited by nonzero mean Poisson impulses. The PDF solution is governed by the Kolmogorov–Feller equation which is also called the generalized Fokker–Planck–Kolmogorov (FPK) equation. First the high-dimensional generalized FPK equation is reduced to a low-dimensional equation by a state-space-split method. The reduced FPK equation is further solved by an exponential-polynomial closure method. In numerical analysis, a ten-degree-of-freedom Duffing system is further investigated under nonzero mean Poisson impulses. The PDF distribution of impulse amplitudes is adopted with either a nonzero mean Gaussian distribution or a nonzero mean Rayleigh distribution. Comparison with the simulated results shows that the proposed solution procedure is effective to obtain a satisfactory PDF solution, especially in the tail region. The nonzero mean PDF of displacement is formulated due to nonzero mean Poisson impulses. The obtained PDF of displacement is not symmetrically distributed about its mean.

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  1. State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin, 300072, People’s Republic of China

    H. T. Zhu

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  1. H. T. Zhu
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Zhu, H.T. Probabilistic solution of a multi-degree-of-freedom Duffing system under nonzero mean Poisson impulses. Acta Mech 226, 3133–3149 (2015). https://doi.org/10.1007/s00707-015-1372-9

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  • DOI: https://doi.org/10.1007/s00707-015-1372-9

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