Nonlinear modeling and dynamic analysis of bioengineering hyper-elastic tubes based on different material models

In this research, nonlinear vibrations of a hyper-elastic tube accounting for large deflection and moderate rotation have been examined. The hyper-elastic tube is assumed to be surrounded by a nonlinear hardening elastic medium. Different types of hyper-elastic material models are presented and discussed including neo-Hookean, Mooney–Rivlin, Ishihara and Yeoh models. The efficacy of these models in nonlinear vibration modeling and analysis of hyper-elastic tubes has been examined. Modified von-Karman strain is used to consider both large deflection and moderate rotation. The governing equations are obtained based on strain energy function of above-mentioned hyper-elastic material models. The nonlinear governing equation of the tube contains cubic and quantic terms which is solved via extended Hamiltonian method leading to a closed form of nonlinear vibration frequency. The effect of hyper-elastic models and their material parameters on nonlinear vibrational frequency of tubes has been studied.