Sound reflection from a plate with periodic inhomogeneities

The scattering of sound by a thin plane elastic plate with small periodic inhomogeneities is investigated analytically, extending the theory developed by Lapin (1984) for a wall with elastic-reactance acoustic impedance. An equation describing the vibration of the plate is derived, and the problem of the conversion of bulk waves to surface waves is solved by combining the free and forced solutions for an infinite periodic structure. Allowance is made for three-mode interactions, and the inclusion of higher-level interactions is shown to have no significant effect on the results.