A closed-form solution for asymmetric free vibration analysis of composite cylindrical shells with metamaterial honeycomb core layer based on shear deformation theory

Asymmetric free vibration analysis of composite cylindrical shells with a honeycomb core layer and adjustable Poisson’s ratio is performed analytically in this study. The equations of motion which are a system of coupled partial differential equations are extracted using Hamilton’s principle by employing the first-order shear deformation theory and they are solved analytically. To study the sensitivity of the results to the different parameters of the honeycomb structure, geometrical parameters, and boundary conditions, a parametric study is presented. It is concluded that for the auxetic composite shell with a negative Poisson’s ratio, by decreasing the Poisson ratio, the frequency decreases. Also, it is shown that by employing the composite shells the weight decreases significantly, while the asymmetric frequency will not change remarkably. By adjusting the Poisson ratio, the frequency variations are studied for a composite shell with a honeycomb core layer. The results are compared with the finite element method and some other references