Free vibration analysis of a circular plate partially in contact with a liquid

This paper provides a theoretical method for a hydroelastic vibration of a clamped circular plate partially in contact with a liquid. It is assumed that the liquid is inviscid and incompressible while the thickness of the plate is small compared to the plate radius, and the gravity effect on the system is neglected. The wet dynamic displacement of the plate is approximated by combining the orthogonal modal functions of a dry circular plate with a clamped boundary condition. The liquid displacement potential satisfying the boundary conditions is derived and the wet dynamic modal functions of the plate are derived by using a compatibility requirement along the contacting surface between the plate and the liquid. The eigenvalue equation for the system is obtained by using the Rayleigh–Ritz method in order to calculate the wet natural frequencies and the mode shapes for the symmetric and the asymmetric modes. The proposed method is verified by observing a good agreement with three-dimensional finite element analysis results. The effects of the liquid thickness and the liquid depth on the natural frequencies are also discussed.