A TRANSIENT LOCAL ENERGY APPROACH AS AN ALTERNATIVE TO TRANSIENT SEA: WAVE AND TELEGRAPH EQUATIONS

This paper is concerned with the high-frequency dynamics of structures in the time domain. In this frequency range, a differential equation governing the vibrational energy density is proposed. This simplified equation leads to the prediction of large scale space and time evolution of the energy quantities averaged over time, frequency and space. For one-dimensional undamped structures, the energy equation is the classical wave equation whereas its generalization for damped structures leads to a telegraph-type equation. The discussion is focussed on the comparison with the diffusion equation sometimes encountered in the literature.