Size-Dependent Vibration of Circular Cylindrical Polymeric Microshells Reinforced with Graphene Platelets

This paper investigates size-dependent vibration of graphene platelet (GPL) reinforced circular cylindrical polymeric microshells. The microshells are composed of multilayers with GPL fillers uniformly dispersed in each individual layer, but GPL weight fraction changes layer-by-layer along the thickness direction. The effective Young's modulus is predicted by the modified Halpin-Tsai model, while effective Poisson's ratio and mass density are determined by the rule of mixture. Four different patterns of GPL dispersion are considered to achieve the functionally graded property of the microshells. Based on Love's thin shell theory and the modified couple stress theory, the governing equations are derived by using Hamilton's principle. Then, the Navier and Galerkin methods are utilized to solve natural frequencies of GPL reinforced polymeric (GPLRP) microshells. A parametric study is conducted, with a particular focus on the effects of the GPL distribution pattern, the weight fraction, the geometries of the GPL and the microshells, as well as the total number of layers of the microshells.