Nonlinear free and forced vibrations analysis of graphene origami-enabled auxetic metamaterial cylindrical shells

Graphene origami-enabled (GOri) auxetic metamaterial (GOEAM) are novel materials that have recently been introduced and have attracted considerable attention due to their tunable mechanical properties and negative Poisson’s ratio. In this study, the nonlinear free and forced vibrations of GOEAM cylindrical shells are investigated. First, the mechanical properties of the shell are calculated, and the effects of GOri folding degree and weight fraction on the shell’s Poisson’s ratio are studied to identify the regions with positive or negative values. The nonlinear governing equations of the system are derived based on the first-order shear deformation theory (FSDT) and large deformation assumptions. A new hybrid algorithm is used to solve the equations. To this end, the generalized differential quadrature method is employed to obtain the linear natural frequencies and mode shapes of the system under different boundary conditions. Then, after deriving the system’s ordinary differential equations using the Galerkin method, the static condensation technique and multiple time scales method are used for the analytical solution. After validating the results, for the first time, the effects of system parameters on nonlinear natural frequency, vibration amplitude, and hardening behavior of the shell are explored. The results show that the dynamic and vibrational characteristics of the shell are strongly influenced by the parameters of the GOEAM. The findings of this study can serve as a benchmark for researchers working on the vibrational behavior of such advanced metamaterial structures.