Free vibration analysis of simply-supported graphene platelets reinforced laminated piezoelectric cylindrical micro-shells

In this study, the micro-scale vibration analysis of the graphene platelets reinforced cylindrical micro-shells with piezoelectric layers is discussed. By simultaneous use of Hamilton's principle and size-dependent modified couple stress theory, the governing equations of motion and the boundary conditions are derived. The natural frequencies for graphene platelets reinforced cylindrical micro-shell with piezoelectric layers are determined by the Navier's approach. Three different graphene platelets distribution pattern are modeled in this study. The material properties of every layer of micro composite shell reinforced by graphene platelets are evaluated by Halpin-Tsai model. The present findings are validated with the available data in the literature. In addition, a parametric study is conducted to demonstrate the effects of the weight fraction, the distribution pattern, the material length scale parameter, the thickness of the piezoelectric layers, the length to radius ratio, the thickness to radius ratio, temperature change and the applied voltage on the natural frequency of piezoelectric GPL cylindrical micro-shell.