A unified study on the output probability distribution of arbitrary linear vibratory systems with arbitrary random excitation

New theoretical expressions of probability density and cumulative distribution functions for the output response are exactly derived without any simplification of the problem and any approximation of analysis in the case when a general random signal with arbitrary probability distribution and correlation functions is passed through an arbitrary linear vibratory system with finite order. The result is given as an explicit solution of expansion series in a functional form of input statistics and vibratory system parameters, and not given as a mere numerical solution by use of a recurrence algorithm. An effect of random input and system characteristics is concretely reflected in the expansion coefficients. The experimental results obtained by digital simulation are in good agreement with the theory. Thus, the above theory is experimentally confirmed for some typical examples by the method of digital simulation.