Dynamical Analysis of Long Fiber-Reinforced Laminated Plates with Elastically Restrained Edges

This paper presents a variational formulation for the free vibration analysis of unsymmetrically laminated composite plates with elastically restrained edges. The study includes a micromechanics approach that allows starting the study considering each layer as constituted by long unidirectional fibers in a continuous matrix. The Mori-Tanaka method is used to predict the mechanical properties of each lamina as a function of the elastic properties of the components and of the fiber volume fraction. The resulting mechanical properties for each lamina are included in a general Ritz formulation developed to analyze the free vibration response of thick laminated anisotropic plates resting on elastic supports. Comprehensive numerical examples are computed to validate the present method, and the effects of the different mechanical and geometrical parameters on the dynamical behavior of different laminated plates are shown. New results for general unsymmetrical laminates with elastically restrained edges are also presented. The analytical approximate solution obtained in this paper can also be useful as a basis to deal with optimization problems under, for instance, frequency constraints.