Nonlinear vibration of a conical PVC gel actuator under electrical excitation

Polyvinyl chloride (PVC) gel is an electroactive polymer material with low cost, large deformability, light weight and fatigue resistance. It has two-way electromechanical coupling performance and has important application prospects in intelligent sensing and flexible driving. The material is often prepared into a conical structure for driving soft robots, flexible pumps, etc. However, limited research exists on the theoretical modeling of PVC gel conical structures and their nonlinear deformation behavior under dynamic loads, hindering broader applications. This study addressed this gap by developing an electromechanical coupling model for the spatial conical structure actuator and establishing its nonlinear vibration control equation using the Euler-Lagrange framework. The Helmholtz free energy was used to describe the system energy change of the conical PVC gel actuator. The Gent constitutive model of the hyperelastic material was used to characterize the elastic strain of the PVC gel material, and the nonlinear dynamic behavior of the PVC gel cone structure was analyzed. The damping ratio effect, tensile limit factor, and external factors, such as pre-stretching mechanical external force, external periodic sinusoidal voltage, and spring stiffness coefficient, were considered. The critical threshold for the transition from steady-state to chaotic vibration of PVC gel cone-shaped structure actuator under different parameters was explored. The threshold was qualitatively and quantitatively defined and analyzed by bifurcation diagram and Lyapunov exponent. This study provides a theoretical basis for the further application of PVC gel conical structure actuators.