The natural frequencies of annular plates on an aperture of an infinit
e rigid wall and in contact with a fluid on one side are theoretically
obtained by using the added mass approach. The fluid is assumed to be
incompressible and inviscid and the velocity potential describes its
irrotational motion. The Hankel transform is applied to solve the flui
d-plate coupled system; boundary conditions are expressed by integral
equations. Mode shapes are first assumed not to be modified by the flu
id. Accurate numerical results are given for different plate boundary
conditions; they are suitable for engineering applications. The accura
cy of the assumed-modes approach is theoretically studied by using the
Rayleigh-Ritz method that removes the simplifying hypothesis that dry
and wet mode shapes are the same. Eigenfunctions of the plate vibrati
ng in vacuum are assumed as admissible functions and the Rayleigh quot
ient for coupled vibration is used to obtain a Galerkin equation. It w
as found that the fundamental mode and frequency, for all the plate bo
undary conditions considered, is well estimated by the assumed-modes a
pproach; higher modes are computed with less accuracy by this formulas
and for some enhanced applications the Rayleigh-Ritz approach is nece
ssary. (C) 1996 Academic Press Limited