Statistical Energy Analysis for the Time-Integrated Transient Response of Vibrating Systems

Abstract

For more than twenty years, statistical energy analysis (SEA) has been used for the analysis of steady-state response distributions in complex coupled structures and sound-structure systems. However, the steady-state SEA formalism is not directly applicable to the analysis of transient vibrations. In this paper, energy relations, analogous to steady-state SEA power flow relations, are derived for the time-integrated transient response of each oscillator. These energy flow relations can be combined using statistical concepts, to obtain a set of energy balance equations for N coupled multimodal subsystems. It is shown that the time-integrated response of each subsystem can be described in terms of transient input energies and conventional SEA parameters, i.e., modal densities, loss factors and coupling loss factors. By solving the energy balance equations, the time-integrated response of each subsystem can be obtained. The results of experiments, conducted on a coupled structure consisting of two welded plates, are presented to illustrate the applicability of these relations.