Abstract:
The propose of this thesis is to present the application of the finite element method to solve the problein of free vibration and buckling of a thick plate on 2-parameters elastic foundations. Thick plate with shear deformation according to the Mindlin'sthick plate theory is used for analysis. Two parameters of elastic foundation are considered. The first one is Winkler's model, the second one is known as Filonenko-Borodich's model. The total energy of plate and elastic foundation are formulated and Hamilton's principle is used to derive the equation of motion. The analysis in this study is applied to the rectangular plate with various support conditions. In the finite eleinent method, nine-node plate bending eleinent is used to formulate thetotal stiffness and mass matrices. Eigenvalue problein is then solved for the natural frequency, buckling load, and their corresponding mode shapes. The obtained numerical results are coinpared with those given in the literature, they are found to be in good agreement. Parametric studies related to the plate geometry, in-plane load ratio, and the foundation parameters are demonstrated.