Coupling of sound and structural vibrations

Abstract

Vibrational properties of hull plates of ships are considerably modified by the presence of the water. A simple model problem is presented that accounts for the fluid-loading, i.e. the coupling of the plate’s flexural vibrations and the acoustic field in the fluid. This model, consisting of a thin, transversely vibrating plate with a compressible fluid at one side and excited by a time-harmonic load, is analyzed in some detail. The model equations are solved 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 integral transform technique and by evaluating numerically the inverse transform in the complex wavenumber plane. For the two-dimensional case the boundary integral equations degenerate to a system of algebraic equations, thus yielding an exact representation for the solution. Numerical results show the fluid-loading effect on the resonance 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.