A derivation of the Transient Statistical Energy Analysis (TSEA) equations with benchmark applications to plate systems

Abstract

Statistical Energy Analysis (SEA) is a well-established method for predicting the response of complex systems to high frequency steady-state harmonic or random excitation. The method has also been applied to transient and 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 an ad-hoc way. 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. A key feature is that shock loading is deterministic, so that the random ensemble of responses arises from random structural properties rather than random loading, and this requires a reinterpretation of the Priestley description. The present derivation of TSEA enables the appropriate initial conditions on the equations to be established and bounds on the prediction error are found from Parseval′s theorem. The derived equations are applied to numerical and experimental examples involving plates.