On the Vibration Characteristics of Graphene Platelet Reinforced Composite Super-elliptical Plates via Chebyshev-Ritz Method

Current investigation deals with the free vibration response of super elliptical plates which is not discussed so far in the open literature. Super elliptical plates are known as advanced shape of plates with round corners to avoid the stress concentrations in the corners. Plate is reinforced with graphene platelets. It is also made from a composite laminated media where the amount of reinforcement may be different through the layers which leads to a functionally graded media. The basic governing equations of the plate are established using the first order shear deformation theory of plates which is known to be valid for thin and moderately thick plates. Elastic properties of the media are estimated by means of the Halpin-Tsai rule while the mass density and Poisson's ratio are obtained via the rule of mixtures approach. The total potential and kinetic energies of the plate are estab-lished. Using the general idea of Ritz method where the shape functions are estimated via the Chebyshev polynomials, the energies are discretized and minimized to establish a set of homogeneous time-dependent second order equations. This set may be studied to analyse the vibration behavior of super-elliptical plates with arbitrary boundary conditions. Results of this study are studied for simple cases to assure the validity and correctness of the formulation and solution method. After that, novel numerical results are given to explore the effects of number of layers, boundary conditions, graded pattern, weight fraction and geometric characteristics of the plate. It is highlighted that with introduction of GPLs in the matrix, frequencies may be enhanced significantly.