Multiple scattering of bending waves by random inhomogeneities

This paper proposes a theory of multiple scattering for the propagation of bending waves over a flexible plate whose mass density is a random function of position. A detailed analysis of the energy transfer processes involved in scattering is presented, and the results are used to derive a kinetic (Boltzmann) equation for the distribution of random wave modes in wavenumber space. This is expected to give a valid description of multiple scattering provided that the dissipation length associated with the decay of a coherent wave is large compared with the correlation scale of the random inhomogeneities. The kinetic equation is used to study the reflection and transmission of bending waves on a beam a finite length of which contains random density inhomogeneities.