A simple analytical model for free vibration of orthotropic and functionally graded rectangular plates

Abstract

With the widespread application of composite structures in engineering, the static and dynamic analyses of these structures have become important in the past years. Composite and functionally graded plates have been frequently being used and are important parts of many engineering structures. Numerous plate theories and solution procedures have been presented to predict the linear dynamic response of composite and functionally graded plates. This study aims to develop a simple analytical model to predict the free vibration response of orthotropic and functionally graded rectangular plates with clamped and simply-supported boundary conditions. To this end, Mindlin’s shear deformation plate theory has been used to obtain the equations of motion in terms of transverse displacement and rotations of mid-plane of the plate. After expressing the rotation parameters in terms of the transverse displacement, they have been substituted into equation of transverse motion of the plate. Then, for each boundary condition, an appropriate function has been assumed for the transverse displacement of the plate. Using the orthogonality of these functions, the natural frequencies of the plate have been determined. Some examples have been provided to validate the proposed model. Keywords: Orthotropic, Functionally graded, Rectangular plate, Mindlin plate theory, Clamped, Simply-supported