Hysteretic Constitutive Equations Based Continuous Dynamic Modeling of Bending Piezoelectric Actuators

Piezoelectric bending actuators have been extensively utilized in recent years. Two major modeling methods, lumped and continuous, have been generally proposed in previous researches for these actuators. The lumped method can only express the transverse vibration of one specified point on the actuator. In addition, the effect of higher vibrational modes has been ignored. Hence, continuous dynamic models have been proposed to rectify the mentioned drawbacks. In this method, linear constitutive equations for low voltage applications are usually applied. But, the main challenge in continuous modeling of piezoelectric actuators is the hysteresis nonlinear phenomenon caused by excitation voltages. In this paper, piezoelectric nonlinear constitutive equations have been employed to carry out the continuous dynamic model for two general types of bending actuators i.e. Series and Parallel. In addition, zero dynamic analysis for nonlinear systems has been applied to clarify the effect of higher vibrational modes the actuator dynamic behavior based on the location of Experimental results show the maximum error 1.44 and 1.2% in the identification of first and second modes, respectively, and the maximum error 2.89% in the modeling of actuator nonlinear behavior by two modes. These results validate the efficiency of the proposed dynamic model to express the actuator nonlinear behavior, dynamic analysis, and its superiority over conventional models with one mode.