Identification and modeling of frequency-dependent piezoelectric coefficient d 33 of piezoelectric stack actuators via sinusoidal excitation tests

One of the most important material parameters of the piezoelectric material, piezoelectric coefficient d 33 , may change with various parameters. Although many groups have investigated how d 33 of a piezoelectric film or plate changes with related parameters, very few studies investigated frequency-dependent d 33 of a piezoelectric stack actuator (PSA) which consists of multiple layers. The value for d 33 of a PSA, which can be expressed as d 33(PSA) , actually incorporates the intrinsic piezoelectric effect of the material (i.e., d 33 of a piezoelectric film or plate), structural boundary conditions, the influence of bonding layers, inertial effects and the overall dynamic response of the system. This paper investigates dynamic responses of PSAs based on two different theoretical methods, in order to identify the values for frequency-dependent d 33(PSA) by the indirect method, distinguish between linear superposition and nonlinear superposition of multiple layers, and finally explore a unified prediction model suitable for a range of working conditions. As a result, the power function model can be regarded as the unified prediction model for frequency-dependent d 33(PSA) , which can be used as a theoretical reference for quickly predicting the dynamic responses of PSAs.