A derivation of the coupling loss factors used in statistical energy analysis

Abstract The conditions under which an exact theory concerning the energy/power flow relationships for a complex dynamic system may be reduced to the standard Statistical Energy Analysis (SEA) equations are considered. A definition of weak coupling is introduced which encompasses a number of previous definitions, and it is shown that the presence of weak coupling does not guarantee the validity of the standard SEA assumption that the coupling loss factor (CLF) between two subsystems is zero unless the subsystems are directly connected. The standard assumption is likely to be reasonable for systems which are both weakly coupled and reverberant. Attention is then turned to the CLF between two connected subsystems and a general result is obtained which involves a space and frequency averaged Green function. It is shown that under the appropriate assumptions a number of existing results may be derived from this expression, including those produced by both the wave and the modal approaches to SEA. The exact theory may be used as a basis for developing improved models of the system dynamics.