Abstract
This chapter discusses the response of a particular nonlinear system to a combination of Gaussian and Poisson white noises to assess the sensitivity of the solution and subsequent moment calculations to the relative weight of each. A numerical method developed for the solution of stochastic systems excited by Poisson white noise will be applied to several dynamical systems. The stationary probability density function of the response process for the single degree-of-freedom Duffing oscillator will be obtained by solving the Fourier-transformed forward generalized Kolmogorov equation directly for the characteristic function, followed by numerical Fourier inversion to recover the probability density function. The excitation process is modeled as a sum of Gaussian and Poisson white noises. The resulting second and fourth order moments of response are examined to assess the relative effects of the two inputs.
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