A phenomenological model for pre-stressed piezoelectric ceramic stack actuators

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