A phenomenological model for pre-stressed piezoelectric ceramic stack actuators

Abstract

In order to characterize the hysteretic characteristics between the output displacement andapplied voltage of pre-stressed piezoelectric ceramic stack actuators (PCSAs), this paperconsiders that a linear force and a hysteretic force will be generated by a linearextension and a hysteretic extension, respectively, due to the applied voltage to apre-stressed PCSA and the total force will result in the forced vibration of thesingle-degree-of-freedom (DOF) system composed of the mass of the pre-stressed PCSAand the equivalent spring and damper of the pre-stressed mechanism, which lets the PCSAbe pre-stressed to endure enough tension. On this basis, the phenomenological modelto characterize the hysteretic behavior of the pre-stressed PCSA is put forwardby using the Bouc–Wen hysteresis operator to model the hysteretic extension.The parameter identification method in a least-squares sense is established byidentifying the parameters for the linear and hysteretic components separatelywith the step and periodic responses of the pre-stressed PCSA, respectively. Theperformance of the proposed phenomenological model with the corresponding parameteridentification method is experimentally verified by the established experimental set-up.The research results show that the phenomenological model for the pre-stressedPCSA with the corresponding parameter identification method can accuratelyportray the hysteretic characteristics of the pre-stressed PCSA. In addition, thephenomenological model for PCSAs can be deduced from the phenomenological model forpre-stressed PCSAs by removing the terms related to the pre-stressed mechanisms.