PDF Solutions of Nonlinear Oscillators under Poisson Impulse with Non-Gaussian Amplitude

摘要

It is a challenging problem in obtaining the probabilistic solutions of nonlinear stochastic dynamic (NSD) systems.A new method named exponential-polynomial closure (EPC) method was proposed in 1998 for obtaining the probability density function (PDF) of the responses of various NSD systems [1-3].Recently, the EPC method was extended to analyze the PDF solution of nonlinear stochastic oscillators subject to Poisson white noise with Gaussian amplitudes [4,5].In this paper, the EPC method is applied to analyze the PDF solution of nonlinear stochastic oscillators excited by Poisson white noises with non-Gaussian amplitude.The oscillators with two types of impulse amplitude distribution are investigated,respectively. One is the oscillator excited by the Poisson impulse with uniform impulse amplitude distribution and another is the oscillator excited by the Poisson impulse with shifted Rayleigh impulse amplitude distribution. Different levels of oscillator nonlinearities are also examined.In both cases of impulse amplitude distribution,it is numerically shown that the tails of the PDFs obtained with the equivalent linearization (EQL) procedure deviate significantly from the results from Monte Carlo simulation even when the oscillator nonlinearity is slight.On the other hand, the solutions from the EPC method are in good agreement with the simulation,especially in the tail regions which are important in reliability analysis.It is proved numerically that the EPC method is effective for the nonlinear oscillators excited by Poisson white noise regardless of system nonlinearity and the patterns of impulse amplitude distribution. The numerical results also show that the PDF solutions of displacement of the oscillator is still symmetricallly distributed with respect to it zero-mean in both cases though the shifted Rayleigh distribution is not symmetric.