Free vibrations of Kirchhoff plates considering plate variable thickness and interaction with water including water boundaries

The natural vibrations of thin (Kirchhoff-Love) plates with constant and variable thickness and interaction with water are considered in the paper. The influence of the water free surface on natural frequencies of the coupled water-plate system is analysed too. The Finite Element Method (FEM) and the Finite Difference Method (FDM) are used to describe structural deformation and the Boundary Element Method (BEM) is applied to describe the dynamic interaction of water on a plate surface. The plate inertia forces are expressed by diagonal or consistent mass matrix. The water inertia forces are described by fully-populated mass matrix which is obtained directly from the theory of double layer potential.