Multiple scattering theory for plate with sprung masses mean and mean- square responses

Diagrammatic multiple scattering theory is applied to the case of an infinite homogeneous plate in flexure attached to a random distribution of sprung masses. This system is a prototypical example of a wave-bearing master structure with a locally reacting 'fuzzy' substructure. Results are obtained from the first order smoothing approximation, the Foldy average t-matrix approximation, and Soven's Coherent-potential approximation. It is found that the attenuation as calculated by Pierce et al differs from that of the multiple scattering theory by a fractional amount which is small if the individual sprung masses are weak. It is also found that fluctuations away from the mean are weak if the spectral and areal density of sprung masses is great. A radiative transfer equation is found to govern the flow of energy on time scales greater than the inverse of the frequency, and a diffusion equation is found to govern the flow of energy at times greater than the dwell time of energy in the substructure.Multiple Scattering Theory; Sprung Masses; Mean and Mean-Square Response