Vibrations of arbitrary deep and thick polymeric nanocomposite cylindrical panels: Introduction of a novel quasi-3D shell model

Using the modified Reddy’s shear deformation hypothesis, the analysis of the free vibrations of the cylindrical panel reinforced with graphene platelets (GPLs) is investigated. In the used theory, in addition to the fact that the transverse shear strains are considered as a non-uniform function of the thickness, the transverse normal strain is also included in such a way that the displacement along the thickness of the shell is non-uniform. A laminated composite is considered in such a way that each layer is reinforced with a certain volume fraction of the graphene platelets. The amount of reinforcement in each layer may be different, which will lead to functionally graded material (FGM). To estimate the elastic properties of the used material, the Halpin-Tsai relationship has been used. Considering the linear strain-displacement relations and the elastic structural relation in the three-dimensional elasticity state as basic relations, Hamilton’s principle has been used to derive the equations of motion. The resulting six equations of motion are then presented in terms of displacement components using the definitions of the resultants. For simple supported boundary conditions, Navier’s solution has been used, and the stiffness and mass matrices have been presented. The obtained results can be useful for estimating the frequencies of a deep and thick shell made of FG-GPLRCs. The results of this research show that increasing the volume fraction of GPLs increases the natural frequency of the shell. It is seen that, in FG-X distribution of reinforcements, the natural frequencies of the shell can be enhanced.