Vibration of circular plates on a free fluid surface: Effect of surface waves

The effect of free-surface waves on free vibrations of circular plates resting on a free fluid surface is studied. The solution is achieved by using a perturbation technique and the Hankel transformation method which give a couple of dual integral equations of Titchmarsh type. The fluid is considered inviscid and incompressible and the velocity potential describes its motion. The Kirchhoff theory of plates is used to model the elastic thin plate. The theory is suitable for all axisymmetric plate boundary conditions. Numerical results are given in non-dimensional form for modes up to five nodal circles and diameters for clamped, simply supported and free-edge plates, to be ready-to-use in applications. The effect of free-surface waves on the plate's natural frequencies is significant only when bluging and sloshing modes of the system have close natural frequencies. (C) 1999 Academic Press.