A hybrid radiative energy transfer and image source method for high-frequency vibrational coupled plates

Abstract

A hybrid approach composed of the radiative energy transfer method (RETM) and image source method (ISM) is proposed in this study for estimating the vibrational energy of coupled plates loaded by high-frequency point excitation. The vibrational energy at a receiver is represented by energy density and intensity, which are superposed by incoherent rays emitted by the load point in the analyzed domain and reflected/transmitted by the domain boundaries. The energy rays reflected/transmitted at the boundaries are described by two modes: diffuse reflection/transmission, which is a basic assumption in RETM, and the other obeys Snell’s law of reflection/refraction, which is deduced by Fermat’s principle and often applied in ISM. The local energy response distribution in the loading subsystem is described by ISM. The energies in other subsystems are described by RETM. The energy transfer relationship between subsystems is expressed by the energy transfer coefficient. At the boundary of coupled plates, a Fredholm equation of the second type is established through the balance among the outgoing energy of the diffuse reflection fictitious sources and the incident energy of actual sources, other diffuse reflection sources, and specular reflection image sources, which can be used to determine the intensity of the diffuse reflection fictitious sources. The average energy transfer coefficient in the transmission direction half-space is used to express the energy transfer relationship associated with diffuse reflection sources, while the energy transfer relationship associated with specular reflection sources is expressed directly by the energy transfer coefficient. Numerical tests show that the energy distributions and energy flow fields of typical coupled plates are well predicted by the proposed hybrid RETM-ISM approach. Compared with RETM, hybrid RETM-ISM is more consistent with the FEM solution.