Determination of Natural Frequencies of Multilayered Plates by Mixed Finite Elements

Abstract

Natural frequencies for multilayer plates are calculated by mixed finite element method. The main object of this paper is to use the mixed model for multilayer plates, analyzing each layer as an isolated plate, where the continuity of displacements is achieved by Lagrange multipliers (representing static variables). This procedure allows us to work with any model for single plate (so as to ensure the proper behavior of each layer),and the complexity of the multilayer system is avoided by ensuring the condition of displacements by the Lagrange multipliers (static variables). The plate is discretized by finite element modeling based on a primary hybrid model, where the domain is divided by quadrilateral, both for the displacement field and static variables. This mixed element for plates was implemented and several examples of vibrations have been verified successfully by the results obtained by other methods in the literature