Electromechanical coupling induced multiple excitation mechanisms in conical dielectric elastomer resonators

Resonant actuation of the dielectric elastomer resonators (DERs) allows them to achieve outstanding output performance comparable to biological muscles and facilitates numerous applications of the DERs in robotics. However, the electromechanical coupling mechanism of the DERs introduces complicated nonlinear correlations between the input signals, system states, and excitation forces at resonances, which are overlooked in previous studies. In this paper, we adopt a conical DER (CDER) configuration, and by decomposing the electromechanical coupling term in this nonlinear dynamic system, we reveal that the resonances in this system are excited both externally and parametrically and at two frequencies. The forcing mechanisms include four excitation components: The external excitation components with the frequencies of 1:1 and 2:1 to the actuation frequency (fe_ext1 and fe_ext2, respectively) and parametric excitation components with the frequencies of 1:1 and 2:1 to the actuation frequency (fe_par1 and fe_par2, respectively). Using an energy balance approach, we theoretically investigate the contributions of these four excitation components to the resonances in the CDER. We show that the primary resonance is mainly excited by fe_ext1 and fe_par2, the super-harmonic resonance is mainly excited by fe_ext2, and the subharmonic resonance is excited by fe_par1. We reveal that the strengths of these excitation components are strongly influenced by the out-of-plane deformation of the membrane and the ratios of the voltage components. Power studies suggest that parametric excitation is heavily affected by damping, while the super-harmonic and primary resonances excited by the external excitation components show good robustness against the increasing payload.