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Stationary Response of MDOF Dissipated Hamiltonian Systems to Poisson White Noises

[+] Author and Article Information
Y. Wu

Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, P.R.C.

W. Q. Zhu1

Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, P.R.C.wqzhu@yahoo.com

1

Corresponding author.

J. Appl. Mech 75(4), 044502 (May 14, 2008) (5 pages) doi:10.1115/1.2912987 History: Received May 25, 2007; Revised February 22, 2008; Published May 14, 2008

The stationary response of multi-degree-of-freedom dissipated Hamiltonian systems to random pulse trains is studied. The random pulse trains are modeled as Poisson white noises. The approximate stationary probability density function and mean-square value for the response of MDOF dissipated Hamiltonian systems to Poisson white noises are obtained by solving the fourth-order generalized Fokker–Planck–Kolmogorov equation using perturbation approach. As examples, two nonlinear stiffness coupled oscillators under external and parametric Poisson white noise excitations, respectively, are investigated. The validity of the proposed approach is confirmed by using the results obtained from Monte Carlo simulation. It is shown that the non-Gaussian behavior depends on the product of the mean arrival rate of the impulses and the relaxation time of the oscillator.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Approximate stationary probability density of displacement q1 of system 16. (a) b=0.1; (b) b=1.

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Figure 2

Approximate stationary probability density of displacement q2 of system 16. (a) b=0.1; (b) b=1.

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Figure 3

Mean-square response of displacements q1 and q2 of 2DOF Duffing oscillator excited by external Poisson white noise. (a) E[Q12]; (b) E[Q22].

Grahic Jump Location
Figure 4

Approximate stationary probability density of displacements q1 and q2 of 2DOF Duffing oscillator excited by parametric Poisson white noise. ---, ——: perturbation solution; ●, ×: Monte Carlo simulation. ζ=0.05, k1=1, k2=1.5, a=1, b=5, I0=0.04.

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