Radiative energy transfer model for finite anisotropic plates

Abstract

This study aims to extend the radiative energy transfer method (RETM) to anisotropic plates loaded by transverse point force at high frequencies. The flexural wave field of a medium is represented by energy density and intensity. The energy variables are superposed by incoherent rays emitted by actual source in the analyzed domain and fictitious sources on the domain boundary. By applying Fermat’s principle, we theoretically prove that ray paths are straight lines for rays traveling in unbounded homogeneous anisotropic media. The kernel functions of the energy transfer in the domain are derived by considering the energy balance at the loading point. To represent the radiative intensity in a free field, we define a directivity function, which can be determined by the stationary phase approximation of the far field solution. The diffuse reflection of rays at free boundaries leads to a Fredholm integral equation, from which the fictitious sources are determined. Numerical examples show that the energy flow fields and energy distributions of typical anisotropic plates are well predicted by the proposed approach.