Scattering of flexural waves by random density fluctuations in a plate

The scattering of flexural waves by random density fluctuations in a plate strip is studied by using a statistical modal analysis. Equations are derived governing the two-point coherence functions of the propagating modes using a parabolic approximation. The governing equations reduce to a coupled set of ordinary differential equations for the self-modes and an uncoupled set for the cross-modes. A sample solution is presented to show the order of magnitude of the rate of decay of the cross-modes and the distance at which mode coupling begins for the self-modes. It is further shown that fluid loading may also be considered in the same framework by using the parabolic approximation to simplify the integral term that is introduced by the fluid loading. Finally, the application of this work to cylindrical shells is discussed.