Analysis using variational principles of the surface pressure and displacement along an axisymmetrically excited disk in a baffle

Abstract

A discussion of the singularities that arise in a variational principle for the surface pressure resulting from a specified harmonic motion of an arbitrary surface leads to the observation that essentially the same formulation may be employed to study a thin disk in an annular baffle and a disk in an infinite baffle. This variational principle is implemented jointly with Hamilton’s principle for structural displacement to study the response of an axisymmetrically excited flexible disk (membrane or elastic plate) in a baffle. Surface pressure, as well as displacement, are represented in a series of assumed modal functions. The system equations reduce to a set of simultaneous equations for the complex amplitudes of the assumed modes, in which the inhomogeneous terms are the modal generalized forces, whereas the coefficients of the homogeneous terms arise from the isolated responses of the fluid and structural media, and from the fluid–structure coupling. The coefficients associated with surface pressure are obtained from numerical integrations over the surface. The technique for performing such integrations in conjunction with analytical basis functions is reviewed and extended to interpolating functions spanning segments of the surface. Results obtained for the infinite baffle case are shown to be in close agreement with an earlier analytical solution, except for differences stemming from discrepancies in the in vacuo resonant frequencies predicted by conventional and Timoshenko plate theory.