Numerical investigation of non-local elasticity theory for free vibration of polymer embedded multi-layer graphene sheets

Abstract

The present study investigates the free vibration behavior of multi-layered graphene sheets with various shapes embedded in a polymer matrix under different boundary conditions based on Eringen non local elasticity. The governing equations are obtained through the minimization of potential energy or Newton’s law which is not only equivalent to Hamilton’s principle and mutually can be derived from each other. Differential Quadrature and pb2 Rayleigh Ritz procedures are applied to Multi-layered Graphene sheets employing Eringen’s elasticity and classical plate theory. Results indicate that the resonant frequencies of the sheets are overestimated up to 60% using the classical elastic model. Depending on the shapes of Graphene sheets, small-scale parameters, boundary conditions, stiffness of polymer matrix, the number of layers and van der Waal’s interaction on the vibrational characteristics of graphene sheets are studied, and the results are tabulated. Conclusions are drawn and recommendations are provided for future work.