Surface variational principle analysis of the response of an eccentrically loaded submerged disk in a baffle

Abstract

As an initial step in the extension of the surface variational principle (SVP) to an assumed mode analysis of vibratory displacement and surface pressure on submerged axisymmetric structures subjected to arbitrary nonsymmetric loading, the present study considers a harmonic point force applied at an arbitrary location of an elastic plate supported by an infinite, rigid baffle. Fourier series expansions of the azimuthal dependence of pressure and displacement are shown to be uncoupled, with each harmonic being governed by equations that are similar in form to those for the analogous axisymmetric problem [J. H. Ginsberg, P. T. Chen, and A.D. Pierce, J. Acoust. Soc. Am. 88, 548–559 (1990)]. Recursion relations using coefficients developed in the course of solving the axisymmetric problem are shown to substantially expedite the evaluation of the additional azimuthal harmonics. Results for a force located at r=a/2 when ka = 3.35, where a is the radius of the plate, are presented in terms of the radial variation associated with each harmonic, as well as overall surface distributions. It is shown that m = 0 to m = 4 azimuthal harmonics are comparable in magnitude, and that other harmonics are insignificant. In addition, radiated power is evaluated as a function of m. [Work supported by ONR, Code 1132‐SA.]