Modeling and nonlinear dynamics of a dielectric elastomer soft sandwich cantilever plate

Abstract Inspired from the bimorph actuator which is an efficient design to flap and propel swimming vehicles, a soft actuator made of two dielectric elastomer layers and a hyperelastic material core is presented. This actuator is also termed as a soft sandwich cantilever rectangular plate, which is stimulated by the alternating voltages with a phase difference. Based on the classical plate theory and the variational method, the governing equation describing the nonlinear vibration of the soft sandwich cantilever plate is formulated. Employing the harmonic balance method and the arc-length continuation method, periodic solutions are obtained, then the convergence analyses of the numbers of discrete modes and harmonics are conducted. In order to illustrate the frequency features more clearly, a modified mode numbering scheme is developed. The numerical results manifest that, there are abundant nonlinear behaviors among mode responses of the soft sandwich cantilever plate driven by the combined voltage excitation, including the local peak and the isolated bubble aroused by the nonlinear coupling. Additionally, the fundamental mode response keeps dominating the dynamic behaviors of the soft plate. The nonlinear dynamics broaden the resonant domain significantly, which can be potentially applied to the design and manufacture of high-performance soft actuators through the vibration enhancement strategy.