Abstract
We propose a new equation used in an analytical method via complex fractional moments (CFM) for the response distribution of a system under combined Gaussian white noise and random pulses. CFM is related to a Mellin transform of a probability density function (PDF), and by obtaining the CFMs of all order along the imaginary axis, the original PDF can be recovered. The PDF of the response of the above-mentioned system are governed by the generalized Fokker-Planck (FP) equation. By applying a Mellin transform to the generalized FP equation, the governing equations for the CFMs of the response can be derived, and by solving these equations, the CFMs are obtained. By using an inverse Mellin transform for the response CFMs, we can get the PDF of the response. However, the accuracy of the PDF obtained by such a procedure is low near the origin. In order to overcome this problem, we introduce new equation which connects PDF and its CFMs and is based on the inverse Mellin transform. By using this equation, the error of the PDF near the origin could be drastically reduced for various nonlinear systems. The effectiveness of present method is demonstrated by comparing with the Monte Carlo simulation results.
