Strain–Stress Estimation of Vibrational Beam and Plate Using Radiative Energy Transfer Method

Abstract

This study aims to present simple conversion expressions of strains–stresses and the energy density for beams and plates subjected to high-frequency random forces using the radiative energy transfer method (RETM). Euler–Bernoulli beam theory and Kirchhoff plate theory are introduced to describe the deflections of beam and plate. The conversion expressions of strains–stresses and energy density for a single propagation wave are quickly established by dispersion relations. For multi-cylindrical wave fields, the strains–stresses are superimposed by the wave fields generated by the actual source in the domain and the wave fields reflected by the fictitious sources at boundaries according to Huygens’ superposition principle. The conversion expressions of strains–stresses and energy density in the energy finite element method (EFEM), which supposes that the superposition of plane waves forms the wave field, are also derived. Numerical examples indicate that in damping-frequency space, the conversion expressions obtained by RETM have a wider application region than those obtained by EFEM and can be applied to a low-frequency band than the corresponding energy algorithm itself.