Analysis by variational principles of the vibration and acoustic radiation of a vibrating elastic plate with circumferential stiffeners

Abstract

This study concerns the effects of circumferential ring stiffeners on the vibration and acoustic radiation of a submerged circular elastic plate. The disk, which is excited by an arbitrary axisymmetric harmonic force, may be supported by either a rigid annulus or by an infinite baffle. The analysis employs variational principles [J. H. Ginsberg and P. T. Chen, J. Acoust. Soc. Am. Suppl. 1 82, S1 (1987)], in which surface pressure and velocity are represented by assumed model functions. The presence of stiffeners alters the kinetic and potential energies of the plate, but it does not affect the formulation of the fluid‐structure interaction. Two structural formulations are addressed, differing by whether the connection between the plate and the stiffeners is implicitly or explicitly enforced. The results for surface response are used in conjunction with the Kirchhoff‐Helmholtz integral theorem to evaluate near‐ and farfield pressures. Results include radiation patterns showing the influence of stiffener size and location. (Work supported by ONR.)