Energy transport velocity of flexural waves in a random medium

Abstract

A novel effective medium theory is derived for the Euler-Bernoulli equation, allowing the transport behaviour of flexural waves encountering random variations in density to be found. As an example the energy transport velocities for multiply scattered, flexural waves propagating in a thin plate with circular inclusions of different density are computed. Small transport velocities are observed for small to moderate density anomalies implying suppression of the wave diffusion constant. For large-density anomalies the diffusive description is found to fail when the localization parameter falls below a critical value.