Specular and diffuse reflections of rays in coupled thin plates at high frequencies

The flexural energy distribution in two right-angled point-excited thin plates at high frequencies is investigated by means of an integral energy flow approach. The fields of energy averaged over time and frequency are described by the superposition of uncorrelated cylindrical waves stemming from both boundaries and direct sources. Specular and diffuse laws are considered for the reflection and transmission of rays, giving rise to two kinds of energy equations. The diffuse law leads to a Fredholm integral equation over the boundary sources while the specular law is shown to allow an image source solution when the plates have identical propagation properties. The algorithm for computing the image position, magnitude and directivities is described. Then, some comparisons between the results from the both energy formulations and also from the statistical energy analysis and the numerical solution of the equations of motion are performed with two damped plates at high frequency. The non-diffuse pattern of the averaged flexural energy fields is well described by the energy flow approaches.