Development of energy flow models for dilatation wave in elastic solids

The analysis of medium-to-high frequency vibrations of structures is particular interest in various fields, including the aviation and ship-building and automotive industries. Energy flow analysis is well known to be effective for structural acoustics problems in the medium-to-high frequency range. The aim of this paper is to develop energy flow models for a dilatation wave in three-dimensional elastic solids. The energy governing equation for the model is obtained by deriving the relation equation between simplified energy density and intensity expressions. The energy governing equation is expressed in terms of the time and space averaged energy density, which represents the vibrational energy level. 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 are compared to those obtained using NASTRAN which is based on FEM. The comparing of the results for the energy density distribution shows that the energy flow analysis for a dilatation wave in elastic solid can improve the energy flow analysis for three dimensional vibrational problems and this method is quite useful to predict the vibrational response for a three-dimensional structural analysis at a medium-to-high frequency.