Electrochemical viscoelastic modeling to predict quasi-static and dynamic response of IPMC actuators

•This proposed model was able to simulate the back-relaxation phenomenon in the IPMC actuators.•This paper provide a more comprehensive governing equation that can be used for vibration analysis and real time control applications.•The proposed model can easily extend to analysis the other types of ionic polymer actuators and sensors. A nonlinear dynamic viscoelastic model of an ionic polymer metal composite (IPMC) actuator is presented based on the viscoelastic constitutive equations and an energy-based variational approach to acquire dynamic and quasi-static response. For this purpose, the equation of motion of an IPMC actuator is obtained by considering the actuator as a cantilever viscoelastic beam and utlizing continuum mechanic relations, Euler-Bernoulli beam theory, Hamilton's principle, and electrochemical properties of ionomer. This new model can simulate time-dependent tip displacement of the IPMC actuators and predict the back-relaxation that occurs in the Nafion-based IPMC actuator under an imposed step voltage. The transfer function derived from the proposed model provides a good frequency response prediction in comparison to the experimental results.This model also can be utilized to obtain mechanical response and vibration analysis of the IPMC sensors.