Acoustic harmonic radiation from fluid-loaded infinite elastic plates using elasticity theory

The classical integral transform technique is used to develop the exact formal solution to the problem of harmonic two-dimensional radiation from a fluid-loaded infinite elastic plate subjected to arbitrary loading. Since the theory of elasticity is used to model the plate, no restrictive assumptions are made about the frequency–plate thickness product. The general formulation is then used to address the case of acoustic radiation from a line force-driven plate. A simple expression for the far-field pressure is presented using the stationary phase method. Numerical results are then presented for the far-field pressure patterns for a line force-driven plate at low, intermediate, and high frequencies. The highly directive features of the patterns are related to the in-vacuo dispersion curves of the elastic plate. A comparison of pressure patterns obtained from elasticity and Timoshenko–Mindlin plate theory illustrates the limitations of the latter. Finally the relationship between the plate mode spectrum predicted by the theory of elasticity, the spectral input line admittance of the plate, and the far-field directionality pattern is presented.