Radiation from the Forced Harmonic Vibrations of a Clamped Circular Plate in an Acoustic Fluid

Abstract

The forced harmonic vibrations of a solid circular plate clamped to a rigid infinite baffle and bounded on one side of an inviscid fluid of infinite extent is considered. The motion in the plate is described by the Mindlin-Timoshenko theory, which includes the effects of transverse shear and rotatory inertia. The external force, which is applied from the in vacuo side of the plate, can have any spatial distribution. The solution is obtained with the use of orthogonal functions which result from transforming the polar cylindrical coordinates describing the fluid motion into oblate spheroidal coordinates and the solution to the in vacuo vibrations of the clamped plate. This method of solution removes all previous restrictions regarding the solution of this problem, namely, boundary conditions of the plate, symmetry of loading, applicable frequency range, and extensive numerical calculations for the determination of the complete nearfield pressure. Expressions are obtained for the near- and farfield pressure in the fluid and the radiated power from the plate-fluid surface. A numerical case for a concentrated load at the center of the plate is presented.