Letters to the Editor: Coupling Loss Factors for Coupled Anisotropic Plates

Statistical energy analysis (SEA) represents a framework for analyzing the high-frequency response of complex structures to mechanical or acoustical excitation [1]. In SEA, a structure is divided into subsystems and the energy #ow between these subsystems is described using coupling loss factors. In case of coupled plate subsystems, coupling loss factors are often expressed in terms of wave transmission coe$cients [1, 2]. Expression for coupling loss factors are derived by combining the transmission coe$cient and the intensity incident upon the junction on the source plate. The incident intensity depends on the distribution of the total energy over all directions in the source plate and is found to be proportional to the product of the energy density (energy per unit area) and the group velocity of the corresponding wave type [1]. For anisotropic plates, the derivation of the coupling loss factor should take into account the angle dependence of the wavenumber. This dependence a!ects the energy distribution over all directions in a reverberant "eld, as well as the direction of the energy #ow associated with wave propagation. Auld [3] described the energy #ow in anisotropic media in terms of a Poynting vector. This vector, which is parallel to the heading of the group velocity, is oriented normal to the curve obtained by plotting the wavenumber as a function of the wave heading. As illustrated in Figure 1, the wave heading is not parallel to the heading of the group velocity c , except for some discrete values of . This behaviour is not restricted to anisotropic media, since it can also be observed for cylindrical shells consisting of isotropic materials [4]. In fact, a general expression for the coupling loss factor applicable to anisotropic components has "rst been derived by Langley [5] for junctions of curves panels. The expression was obtained by following the procedure brie#y discussed above and the result was written in terms of the wave transmission coe$cient, the group velocity and the phase velocity on the source plate. Later, Bosmans et al. [6, 7] presented a di!erent expression which could be calculated directly from the transmission coe$cient without requiring an evaluation of the group velocity. Although their results was derived for orthotropic plates, it can easily be extended to anisotropic