Geometrically nonlinear frequency analysis of composite cylinders with metamaterial honeycomb layer and adjustable Poisson’s ratio using the multiple scale method

This article presents an analytical method to study the nonlinear frequency of composite cylindrical shells with metamaterial honeycomb core layer and adjustable Poisson’s ratio. The governing equations for the axisymmetric case, which are coupled nonlinear partial differential equations, are obtained based on the Mirsky–Hermantheory and the von-Karman nonlinear relations. These equations are solved analytically using the multiple scale method and the linear and nonlinear frequencies are determined. By conducting a parametric study, the effects of different mechanical and geometrical parameters are investigated on composite shells. It is observed that by changing the geometrical parameters of the honeycomb layer, a vast domain of the Poisson ratios from negative, zero, and positive values are accessible to achieve a composite structure with metamaterial behavior. Since the linear natural frequency, the coefficient of nonlinear frequency, and the weight of the shell will be changed by variations of the Poisson ratio, it will give us this opportunity to adjust them to a suitable value by changing the geometrical parameters of the honeycomb structure. To study the accuracy of the presented method, the results are compared with some other references and the finite element analysis.