A general derivation of the statistical energy analysis equations for coupled dynamic systems

Abstract The response of a multi-coupled dynamic system to random excitation is considered, with the aim of providing a theoretical derivation of the Statistical Energy Analysis (SEA) approach to vibration prediction. It is shown that the general form of the principal SEA equation is widely applicable provided that the coupling between the subsystems is conservative and a suitable definition of the subsystem energy is used. Under the assumption of weak coupling the standard SEA equations are recovered. Expressions for the coupling loss factors are obtained in terms of the frequency and space averaged Green functions of the coupled system.