A modal plate excited by an airborne field and its consequences for SEA

In this paper a plate excited by a diffuse airborne field is analyzed directly using a modal approach, thus including both so called forced and resonant vibrations, and the results are compared with classical Statistical Energy Analys is (SEA) results. The background is that in SEA two important assumptions are that 1) the subsyste ms excitation are spatially uniformly distributed and uncorrelated, and 2) the principle of reciprocity . The first assumption is realized as a so called ’rain-on-the-roof’ excitation, with a large number of uncorrelated point excitations, distributed spatially over the subsystem. In this way is it gua ranteed that in the considered frequency band all the modes is excited equally we ll. However, the ’rain-on-the-roof’ excitation excludes the important excitation of a diffuse airborne sound field, where each plane wave is projected on the plate. The second condition says that if the receiver and excitation positions are exchanged, the ratio between excitation and response should be the same. This concerns point positions, but as this applies for a pair of points and as ’rain-on-the-roof’ excitation is assumed, it will also apply for the mean value, which is used in SEA. Thus, using these two conditions the forced field (or non-resonant field) is missing in the analysis. It is therefore ad hoc included separately using, e.g., the mass law. Comparing the classical SEA results with the direct full modal approach indicates that SEA in general works fine, but that deviations occur around the critical frequency, where SEA predicts a too sharp influence of the coincidence phenomena.