Numerical and Theoretical Solutions for the Free Vibration Analysis of Moderately Thick Plates

The vibrations of plates are a topic of undoubted interest in the field of civil engineering and aeronautics. Today, we find many examples where this type of phenomena occur, and there are structural elements that we can study as plates or shells. The analytical solutions for the governing equations for the dynamics of higher order plates are very difficult or impossible to obtain so we have to resort to numerical methods. The Finite Element Method (FEM) has been and is a very powerful tool to solve differential or integral equations. The method of Galerkin is another interesting possibility that can be applied without difficulty and that has not been given as much interest as the FEM. As with the FEM, there are different techniques to relieve numerical instabilities (shear locking of the stiffness matrix) for the solutions of thin plates. In this communication, we studied this phenomenon by making use of a higher order shear deformation plate theory deduced by the author. We made use of D'Alembert's principle and used a modified method of Galerkin. The results obtained are in very good agreement with those present in the literature.