Statistical energy analysis: coupling loss factors, indirect coupling and system modes

The distribution of energy among the subsystems of a system can be found in terms of the modes of the system. If there are enough modes in the frequency band of interest then the system can be described by an SEA model. However, in general this is a “quasi-SEA” model, which involves both direct and indirect coupling loss factors, whose values depend on the modal overlap. This paper explores the conditions under which the indirect coupling loss factors are zero, so that the system is described by a “proper-SEA” model. It also investigates the dependence of the direct and indirect coupling loss factors on the modal properties of the system and on the modal overlap. In summary, the indirect coupling loss factors are zero, so that a proper-SEA model can be formed, either if all the system modes are local or in the weak coupling regime as the modal overlap becomes large. It is seen that in the low modal overlap limit the coupling loss factors are proportional to the damping loss factor and equipartition of energy only occurs if all modes are global. For higher modal overlap the SEA parameters depend on the detailed statistics of the modes and the situation is complicated. However, if all the modes are local the indirect coupling loss factors are all zero. In the high modal overlap limit the coupling loss factors asymptote to constants, with indirect coupling loss factors becoming zero. This behaviour occurs because of mode shape correlation at the boundary between two directly connected subsystems.