Closed-form solutions for the time-variant spectral characteristics of non-stationary random processes

Spectral characteristics are important quantities in describing stationary and non-stationary random processes. In this paper, the spectral characteristics for complex-valued random processes are evaluated and closed-form solutions for the time-variant statistics of the response of linear single-degree-of-freedom ( S D O F ) and both classically and non-classically damped multi-degree-of-freedom ( M D O F ) systems subjected to modulated Gaussian colored noise are obtained. The time-variant central frequency and bandwidth parameter of the response processes of linear S D O F and M D O F elastic systems subjected to Gaussian colored noise excitation are computed exactly in closed-form. These quantities are useful in problems which require the use of complex modal analysis, such as random vibrations of non-classically damped M D O F linear structures, and in structural reliability applications. Monte Carlo simulation has been used to confirm the validity of the proposed solutions.