Probabilistic solution of some multi-degree-of-freedom nonlinear systems under external independent Poisson white noises.

This paper studies the stationary probability density function (PDF) of the response of multi-degree-of-freedom nonlinear systems under external independent Poisson white noises. The PDF is governed by the high-dimensional generalized Fokker-Planck-Kolmogorov (FPK) equation. The state-space-split (3S) method is adopted to reduce the high-dimensional generalized FPK equation to a low-dimensional equation. Subsequently, the exponential-polynomial closure (EPC) method is further used to solve the reduced FPK equation for the PDF solution. Two illustrative examples are presented to examine the accuracy of the 3S-EPC solution procedure. One example involves a two-degree-of-freedom coupled nonlinear system. The other example is concerned with a ten-degree-of-freedom system with cubic terms in displacement. A Monte Carlo simulation is also performed for simulating the PDF solution of the response. The comparison with the simulated result shows that the 3S-EPC solution procedure can provide satisfactory PDF solutions. The good agreement is also observed in the tail regions of the PDF solutions.