Joseph A. Turner
Richard L. Weaver
Dept. Theoret. and Appl. Mech., Univ. of Illinois, Urbana, IL 61801
The propagation of diffuse energy on an unwetted heterogeneous plate is examined using a diagrammatic approach. The heterogeneities are assumed to lightly couple the membrane and flexural waves. The energy propagation is formulated in terms of the Bethe--Salpeter equation. This equation is further reduced to a radiative transfer equation in limit that the attenuations per wave number are small, i.e., when the heterogeneities are weak. This approach allows the diffuse energy propagation to be calculated as a function of space, time, and propagation direction. Solutions of the derived 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 launched in a single direction. The results show the evolution and mode conversion 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. [Work supported by ONR.]