Acoustic radiation properties of an elastic plate with an infinite baffle and cavity

A cavity (0 < x < a, 0 < y < b, -d < z < 0) set in an otherwise rigid plane surface (z = 0) is covered by a rectangular elastic plate (of dimensions a x b) that is simply supported at its edges. The back face of the cavity is fixed and its side walls are taken to be acoustically soft. Two related problems are analysed. First, the system is considered to be irradiated by a plane time harmonic wave of radian frequency omega and incoming direction -n, and an estimate is sought for the transverse velocity of the plate and for the induced interior pressure. Mean square values are averaged over spatial variables and over all incidence directions n, in order to represent the case of a random external field. The second problem is that of a sound field induced by a time harmonic point source within the cavity and an estimate is given for the mean square velocity of the plate and for the radiated sound power, averaged over a frequency band and with respect to all source positions.