A unified expression for the multivariate joint probability density function of the output fluctuation of an arbitrary linear vibratory system with arbitrary random excitation

Abstract

It is well-known that full information on the statistical properties of state variables can be derived by finding the multivariate joint probability density function. From this point of view, a new theoretical expression for the multivariate joint probability density function of an output response is derived exactly, without any simplification of the problem or analytical approximation, in the case when a general random signal having an arbitrary probability distribution and correlation properties is passed through an arbitrary linear vibratory system of finite order. The result is given as an explicit solution, in a general series expansion form, with functional dependence on the input statistics and vibratory system parameters. Effects of the random input and system characteristics on the output multivariate joint distribution form are explicity reflected in the coefficients of this series expansion expression. The theoretical results for several multivariate joint moments of the output fluctuation are confirmed by comparing with experimental results obtained by a digital simulation technique.