Spectral characteristics of non-stationary random processes: Theory and applications to linear structural models

The spectral characteristics are important quantities in describing random processes. Proper definitions of these quantities are available for real-valued stationary and non-stationary processes. In this paper, the well-established definitions of spectral characteristics for real-valued stationary and non-stationary processes are extended to general complex-valued non-stationary random processes. This extension allows to derive the exact solution in closed-form for the classical problem of computing the time-variant central frequency and bandwidth parameter of the response processes of single-degree-of-freedom (SDOF) and both classically and non-classically damped multi-degree-of-freedom (MDOF) linear elastic systems subjected to white noise excitation from at rest initial conditions. These new exact closed-form solutions are also used to gain deeper insight into the time-variant and stationary behavior of the central frequency and bandwidth parameter of these linear response processes.