A Comprehensive Investigation on the Effect of Graphene Nanoplatelets Characteristics on the Natural Frequency Responses of Shear Deformable Cylindrical Shell

In the present research, shear-deformable modeling is extended for natural frequency analysis of functionally graded graphene nanoplatelets reinforced cylindrical shell. The main novelty of this work is investigating impact of various distributions of the graphene nanoplatelets and amount of them on the variation in the natural frequencies of the reinforced shell. Furthermore, an investigation on the effect of various boundary conditions on the natural frequency responses is presented. After presenting the effective relations for material properties such as modulus of elasticity, density and Poisson’s ratio, the governing equations of motion are derived based on Hamilton’s principle. The governing equations of motion are analytically solved using the Navier’s technique. The natural frequencies are obtained using a solution of the characteristic equation. The results are verified using a comparative study with results from the available literature. The natural frequencies are presented with variation in significant characteristics and parameters of material composition and geometry. The results show that the highest and lowest natural frequencies are obtained for FG-X and FG-O distributions of reinforcement, respectively. Furthermore, it is deduced that a 1% addition of the graphene nanoplatelets to the pure matrix leads to a 50% increase in natural frequencies of the cylindrical shell. One can use the results of this analysis to arrive at an optimized design of reinforced structures for application in technical equipment.