Vibration responses of graphene oxide powder reinforced hyperelastic neo-Hookean cylindrical shells under time-varying axial velocity

Hyperelastic materials are widely used in the fields of aerospace and medical engineering, such as oil transfer hoses and drug delivery systems, both of which are one kind of soft materials. The graphene oxide powder (GOP) with the advantages of high strength is commonly used as a reinforcing material in soft structures. The vibration behaviors of GOP reinforced hyperelastic cylindrical shells under time-varying axial velocity are investigated for the first time. Considering both geometric and material nonlinearities and three distribution types of the GOP including Hyper-UD, Hyper-O and Hyper-X, the dynamic equations of the hyperelastic cylindrical shells under time-varying axial velocity are constructed by the shell theory, hyperelastic neo-Hookean model, Halpin-Tsai model and Lagrange equations. The natural frequencies of the linearized system for the GOP reinforced hyperelastic cylindrical shells under constant axial velocity are presented under varying parameters. The harmonic balance method (HBM) is employed to derive the relations between the frequencies and amplitudes under different parameter values. Numerical results indicate that certain values of axially constant velocity, weight fractions of GOP and structural parameters can enable the shell to escape the unstable regions. The hardening behaviors appear in this system. Furthermore, the time-varying axial velocity significantly affects the vibration responses of the GOP reinforced hyperelastic cylindrical shells, the incorporation of GOP makes the chaotic motions appear the hysteresis phenomena.