Resonant vibrations of fluid-loaded plates. Axisymmetric case.

Abstract

Vibrational properties of hull plates of ships are considerably modified by the presence of water. A simple model problem is presented, consisting of a thin, transversely vibrating plate with a compressible fluid at one side and clamped along a circular contour. The forced vibrations are studied by means of a Green integral representation along with a set of coupled boundary integral equations. The kernel of the integral representation is found by using the Fourier–Hankel integral transform technique and by evaluating numerically the inverse transform in the complex wave-number plane. For the axisymmetric case the boundary integral equations collapse down into a system of algebraic equations, thus yielding an exact representation for the solution. The integration along the circular contour is performed analytically by employing addition theorems for cylinder functions. The Green kernels thus obtained correspond to the response of an infinite plate subject to fluid-loading and ring-driven by constant forces and moments. Numerical results are presented that show the fluid-loading effect on the resonant frequencies of the plate, which are shifted downwards relative to the in-vacuo natural frequencies, while acoustic radiation contributes to the damping of the plate’s resonant modes. [Work supported by the TNO Institute of Applied Physics, Delft, The Netherlands.]