Sensitivity of Piezoelectric Stack Actuators

This paper investigates the properties of a mass-attached piezoelectric stack actuator and analyzes its sensitivity, which is defined as the spectrum of the driving force (the output) caused by a single-frequency voltage (the input). The force spectrum is utilized because of the nonlinear hysteresis effect of the piezoelectric stack. The sensitivity analysis shows that the nonlinear dynamics of the actuator can be interpreted as a cascade of two subsystems: a nonlinear hysteresis subsystem and a linear mechanical subsystem. Analytical solutions of the nonlinear differential equations are proposed, which show that the nonlinear transformation can be described by a steady-state mapping of a single-frequency voltage input to a multiple-frequency driving force at the driving frequency and its odd harmonics. The steady-state sensitivity is then determined by the response of the mechanical subsystem to the line spectrum of the driving force. The maximum sensitivity can be achieved by setting the frequency of the input voltage close to the natural frequency of the mechanical subsystem. The analytical model is also validated by a numerical model and experimental results and it may be used for the analysis and design of piezoelectric actuators with different structural configurations.