Transient SEA: Mean and Variance Predictions

Statistical Energy Analysis (SEA) has been used for many years to predict the response of complex systems to high frequency steady-state harmonic or random excitation. The method has also been applied to shock loading, in which case it is referred to as Transient SEA (TSEA), although the validity of the approach is less certain for this case since the TSEA equations mix time and frequency descriptions of the response in a non-rigorous manner. In this paper, the TSEA equations are derived in a new way by employing an analogy of the Priestley description of a non-stationary random process. The shock loading is deterministic, but the random ensemble of responses arises from random structural properties rather than random loading, and this requires a reinterpretation of the Priestley description. For calculation of the mean subsystem energies, the method enables the appropriate initial conditions on the equations to be established, and bounds on the prediction error are found from Parseval's theorem. In addition to the mean subsystem energies, a method is derived for calculating the variance of the subsystem energies across the ensemble. The derived equations are applied to numerical and experimental examples involving plates, which provide strong validation.