A hybrid finite element and radiative energy transfer method for predicting the vibrational energy distribution of coupled systems in the mid-frequency range

Abstract

This study proposes a hybrid approach integrating the finite element method (FEM) and radiative energy transfer method (RETM) to predict the local energy characteristics of short-wavelength subsystems in mid-frequency coupled systems. Long-wavelength subsystems are modeled using FEM, and RETM governs short-wavelength components, where energy density originates from three contributions: incoherent rays emitted by deterministic boundaries, physical sources, and fictitious sources. Power transfer amongst RETM subsystems via FE interfaces is quantified using reciprocity relationships between direct field radiation and blocked reverberant forces. Local energy transfer coefficients characterize the interactions amongst fictitious sources across deterministic boundaries. Second-type Fredholm equations are formulated by balancing the outgoing fictitious source energy against the incident energy from physical sources, neighboring fictitious sources, and adjacent boundaries to determine the fictitious source intensities. The diffuse directional emissions from fictitious and point sources enhance boundary condition robustness. Numerical validations involving comparisons with Monte Carlo FE solutions demonstrate the effectiveness of hybrid FE-RETM. Results confirm its capability to accurately capture energy distribution patterns in short-wavelength subsystems across mid-frequency ranges and its ability to resolve the overlapping frequency limitations of wave-bearing and energy-based methods. The proposed methodology offers a systematic approach for mid-frequency analysis of coupled systems with mixed wavelength behaviors.