On the vibrational conductivity approach to high frequency dynamics for two-dimensional structural components

Abstract

Abstract The vibrational conductivity approach to high frequency dynamics is applied here to the case of two-dimensional structural components: with this approach an equation which is analogous to the steady state heat conduction equation is used to model the spatial variation of the energy density of the structure. It is shown that the standard derivation of the method is incomplete, in the sense that the steady state heat conduction equation admits a class of solution which is not encompassed by the assumed form of response, and a revised derivation is presented. It is further shown that the associated boundary conditions for coupled structural components may be expressed in terms of the coupling loss factors which are used in statistical energy analysis. A variational principle for the differential equation and the associated boundary conditions is then derived which permits the application of the Rayleigh-Ritz technique to coupled problems, and it is shown that a one-term Rayleigh-Ritz solution leads to standard statistical energy analysis. The method is applied to a single plate and to two coupled plates, and it is found that the technique is unable to provide an accurate estimate of the direct field due to point loading. This difficulty is traced to the fact that the assumptions employed in the derivation become self-contradictory for this case. Finally, the usefulness or otherwise of the approach as an engineering tool is discussed.