Vibrational energy flow models for dilatational wave in elastic solids

The analysis of medium- to high-frequency vibrations of structures is of particular interest in various fields, including the aviation and ship-building industries. Energy flow analysis is well known to be effective for structural acoustics problems in the medium- to high-frequency range, with sufficient detail to include all significant information of the vibrational energy levels or global variation in vibrational energy densities. The aim of this article is to develop energy flow models for a dilatational wave in three-dimensional elastic solids. The energy governing equation derived for the model is expressed in terms of the time- and space-averaged energy density, which represents the global variation of the energy density quite well. Numerical analyses are performed to verify the validity and accuracy of the model for a cube-shaped structure vibrating at a single frequency, and the results of the analysis of energy density distributions from the energy flow analysis that is developed are compared to those obtained using NASTRAN. The energy flow models for the elastic solids, which are useful in the prediction of the vibrational response for a three-dimensional structural analysis at a medium-to-high frequency, are newly derived.