Energy models of one-dimensional, multi-propagative systems

For a number of years, a model well suited to medium and high frequencies in structures, and called Energy Flow analysis, has been studied in order to generalize Statistical Energy Analysis. This model is based on a thermal analogy: a law analogous to Fourier's law for heat flow is involved. This relationship, which relates the energy flow to the energy density, leads to a differential equation similar to the heat conduction equation in steady state conditions. The aim of this study is to generalize previous works on one-dimensional structures. A wave approach is adopted. It is shown that Fourier's law is valid for one symmetric propagation mode (one group velocity). However this law has to be modified for non-symmetric propagation modes or multi-mode propagation. In each case, the wave approach determines the relationship betwen energy density and energy flow. Finally, the theoretical models are illustrated with several examples of waveguides: an Euler-Bernoulli beam on an elastic support, pipes carrying moving fluid and a Timoshenko beam. (C) 1997 Academic Press Limited.