Diffuse energy propagation on heterogeneous plates: Structural acoustics radiative transfer theory

The propagation of diffuse energy on an unwetted flat plate with attached heterogeneities is examined using a statistical, multiple scattering approach. The statistically homogeneous heterogeneities lightly couple the membrane and flexural waves. The problem is formulated in terms of the Bethe- Salpeter equation, which governs the field covariance. It is reduced to a radiative transfer equation in the limit that the attenuations per wave number are small, i.e., when the heterogeneities are weak. This radiative transfer equation governs the diffuse energy propagation as a function of space, time, and propagation direction. Solutions of the radiative transfer equation are presented for the simple case of attached heterogeneities in the form of delta-correlated springs excited by an extensional point source. The results show the evolution of the extensional, shear, and flexural energy densities across the plate as a function of time. A similar approach is expected to apply to the more complicated case of submerged complex structures.