The transmission of a spherical sound wave through a thin elastic plate

Abstract

The transmission of a spherical sound wave through a thin elastic plate of infinite extent is investigated theoretically. The case considered in detail is that for which the velocity of sound in the surrounding medium is less than the velocity of the free flexural waves in the plate at the frequency of the incident wave. This situation gives rise to considerable radiation into the region on the opposite side of the plate from the incident wave. An integral representation for the transmitted sound field is initially derived and the path of integration subsequently transformed into the complex plane where the integration is then carried out in an approximate manner by means of the method of stationary phase. It is found that the transmitted sound field at any point may be decomposed into three parts; an outgoing spherical wave modified by an amplitude factor containing angular dependence and two “surface waves.” The nonradiating case where the velocity of sound in the surrounding medium is greater than the velocity of the flexural waves in the plate is also briefly discussed.