Analysis of the response of linear dynamic systems to product random processes

Abstract

A method is presented for the analysis of the response of linear dynamic systems to product random processes, with application to processes with random amplitude modulation. The Fokker-Planck equation is used to develop equations for the statistical moments of the system response, including relations for the moments of all orders of the response of systems which have linear time-invariant state equations. The quasi-steady approximation, which omits the dynamic properties of the random amplitude modulation, is developed as a limiting case of the exact solution for the moments of the system response. The quasi-steady approximation is generally accurate for well-damped systems, but can be inaccurate for lightly damped systems.