抄録
In this paper, we extend an analytical method via complex fractional moment (CFM) for the response of a system under combined Gaussian and Poisson white noise excitation. CFM is a quantity which is considered as the extension of the order of the moment to a complex number and related to a Mellin transform of a probability density function (PDF). We deal with both linear and nonlinear systems. In order to obtain the PDF of the response of the system, we need to solve a generalized Fokker-Planck (FPK) equation, which includes infinite terms. So we truncate the terms of the fifth or higher order, which are considered as negligibly small. Then by applying a Mellin transform to this truncated generalized FPKeq and using the characteristics of CFM, we can calculate the CFMs of the response. Finally, applying an inverse Mellin transform to the CFMs, we can obtain the PDF of the response. The effectiveness of this method using CFM is demonstrated by comparing with the Monte Carlo simulation results. The influence of parameters of the systems and the excitation upon the accuracy of the present method is also considered.
