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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