Free vibration of functionally graded graphene platelet reinforced plates: A quasi 3D shear and normal deformable plate model

Present article deals with the free vibration response of composite plates which are reinforced with graphene platelets (GPLs). Each layer of the composite media may have different amount of graphene platelets which leads to a functionally graded (FG) pattern. Elastic modulus of the reinforced composite (RC) is evaluated based on the Halpin-Tsai model which captures the dimensions of the reinforcement. Following a quasi-3D plate model which captures the thickness stretching effects and non-uniform shear strains through the thickness, the complete set of governing equations dealing with free vibration response of the plate are obtained. These equations are six in number since the adopted plate theory has six unknowns. With the aid of the Navier solution suitable for plates with all edges simply supported, Fourier expansions are implemented for the essential variables of the displacement field. Closed form expressions are given to obtain the natural frequencies of FG-GPLRC plates. Present results may be valid for arbitrary thick plates. Results of the present study are compared with the available data in the open literature. After that novel results are given to obtain the frequencies of FG-GPLRC plates with arbitrary thickness. It is shown that the adopted theory accurately estimates the frequencies of FG-GPLRC plates.