Large-Strain Vibrations of Axially Stretched Hyperelastic Rods

Abstract

Fast-moving soft robotics usually suffer large-strain deformation with a relatively high velocity. To improve their performance, it is necessary to study the underly dynamical mechanism. However, the inherent strong material nonlinearity brings considerable difficulties in modeling and calculating the soft structure’s nonlinear dynamics. This work focuses on the large-strain vibrations of the hyperelastic rod under an axial tensile force. Several typical hyperelastic models, including the neo-Hookean, Mooney, and Yeoh models, are used to derive the equations governing the rod’s dynamics. The equations based on these models are relatively complex, and their corresponding numerical calculation diverges in some cases. Therefore, a reference stretch ratio(s) polynomial fitting (RSRPF) model is proposed to derive the concise governing equation. Such a governing equation is effectively solved by the combination of the Galerkin discretization and the fourth-order Runge–Kutta integration algorithm. The correctness of the developed model and the employed algorithm is verified by comparing with the previous data of a hyperelastic membrane. In most cases, the rod periodically vibrates under a periodic tensile force. However, when the structural damping is small and the load frequency approaches the resonant frequency, the hyperelastic rod may quasi-periodically vibrate. The revealed large-strain vibration mechanism is supposed to be useful for guiding the dynamical design of soft structures.