Free Vibrations of Iso- and Orthotropic Plates Considering Plate Variable Thickness and Interaction with Water

Abstract

The natural vibrations of thin (Kirchhoff-Love) plates with constant and variable thickness are considered in the paper. Isotropic and orthotropic rectangular plates with different boundary conditions are analysed. The Finite Element Method and the Finite Difference Method are used to describe structural deformation. The elements of stiffness matrix are derived numerically using author’s approaches of localization of integration points. The plate inertia forces are expressed by diagonal, lumped mass matrix or consistent mass matrix. The presence of the external medium, which can be a fluid, is described by the fluid velocity potential of double layer and the fundamental solution of Laplace equation which leads to the fully-populated mass matrix. The influence of external additional liquid mass on natural frequencies of plate is analysed, too.