Probabilistic solutions of a variable-mass system under random excitations

Abstract

The stationary probability density function (PDF) solution of a variable-mass system is calculated under Gaussian white noises and Poisson white noises, respectively. For small mass disturbance, the corresponding Fokker–Planck–Kolmogorov equation and Kolmogorov–Feller equation of the system are derived. The solution procedure based on the exponential–polynomial closure (EPC) method is formulated to obtain and study the probabilistic solutions of the strongly nonlinear variable-mass system subjected to Gaussian white noises and Poisson white noises. Both odd and even nonlinear variable-mass systems are considered. Compared with Monte Carlo simulation results, good agreement is achieved with the EPC method in the case of sixth-order polynomial. For large mass disturbance, the PDFs and logarithmic PDFs of displacement and velocity are numerically calculated via the fourth-order Runge–Kutta algorithm.