DYNAMIC RESPONSE OF LINEAR SYSTEMS TO MOVING STOCHASTIC SOURCES

Abstract

We present a generalized theory for dealing with the dynamic response of linear systems to moving sources. Stochastic characteristics of the response of linear systems to moving stochastic sources are theoretically analyzed based on the time-convolution expression established in this paper. We show that the random response of a linear system under a moving stationary stochastic source becomes a non-stationary process, for which the commonly used spectral analysis is not valid. To overcome this obstacle, the follow-up spectral analysis procedure is introduced. Statistical characteristics of the dynamic response are then given in the fixed and follow-up co-ordinates. A brief physical explanation related to time-frequency domain analysis is also provided. The theory developed in the paper can be universally applied to the moving source problem for linear systems.