Vibration and acoustic radiation of elastically supported rectangular plates

A Green function solution is developed for the steady-state vibrations of an elastically supported rectangular plate coupled to a semi-infinite acoustic medium. Rotational motion at the plate boundaries is controlled by continuous distributions of rotary springs. The solution takes the form of that for a simply supported rectangular plate. The coefficients are determined from systems of simultaneous algebraic equations that include the coupling due to non-homogeneous boundary conditions and the acoustic surface impedance. The solution is also extended to cover the case of an arbitrary load distribution and an expression is derived for the power balance in the coupled plate-fluid system. Results of a numerical evaluation of the modal coupling factors due to fluid loading are compared with low frequency approximations. Effects of the support conditions on the low frequency sound radiation from a plate are illustrated by an example.