Derivation of statistical energy analysis from radiative exchanges

This paper is concerned with the derivation of SEA equations from structural ray equations. Rays are assumed to be uncorrelated leading to the additivity of energy. Inside all subsystems, the energy density is the sum of a direct field from driving forces, a reflected field from the boundary and a transmitted field from adjacent subsystems. Assuming a ”rain-on-theroof” excitation and a compact shape for subsystems, actual and fictitious sources on the boundary are found to be constant. Furthermore, if the attenuation of rays during a mean free path (normalized attenuation factor) is light, the field becomes diffuse i.e. homogeneous and isotropic. The net exchanged power between two adjacent subsystems is then proportional to the difference of energy densities and therefore, to the difference of modal energies. The derived proportionality coefficient is consistent with the well-known formula for coupling loss factor in terms of transmission factors. These results are illustrated by a numerical simulation for a multi-plate system. Finally, the validity domains of SEA and the ray theory are discussed and particularly the diffuse field assumption.