Free vibration analysis of functionally graded multilayer hybrid composite cylindrical shell panel reinforced by GPLs and CNTs surrounded by Winkler elastic foundation

Natural frequency characteristics of functionally graded multilayer hybrid composite cylindrical shell panel reinforced by graphene platelets (GPLs) and carbon nanotubes (CNTs) are scrutinized in the present study for the first time. Effective material properties of the composite media are evaluated using a modified micromechanical model based on the Halpin-Tsai approach and rule of mixtures. First order shear deformation theory of shells, Hamilton’s principle and finite element procedure are applied to obtain the effective stiffness and mass matrices of the structure. After validating accuracy of the presented solution procedure with the published literatures, influence of broad range of factors such as number of multilayers, weight fraction and distribution pattern of GPLs and CNTs reinforcements, CNTs and GPLs volume fraction index for the nonlinear distributions, thickness and length ratio of the shell panel, span angle, Winkler elastic foundation stiffness parameter and different boundary condition are presented and their trends are discussed in several tabular and graphical data in detail. Results denotes that cylindrical shells composed of three phases can make use of the advantages of both CNTs and GPLs reinforcing elements and can significantly improve the free vibration behavior of shell.