Shape modeling and validation of stress-biased piezoelectric actuators

Piezoelectric composites with a characteristic initial curvature and accompanying residual stresses are capable of enhanced performance, relative to flat actuators. This paper utilizes Rayleigh-Ritz techniques with revisions regarding the effective in-plane resultant force and the effective bending moment. The Rayleigh-Ritz technique is based on the assumption that the stable geometric configuration developed in the actuator after manufacturing is the configuration that minimizes the total potential energy. This energy is a function of the displacement field which can be approximated by either a four-term model or a 23-term model. In this case, Thunder((R)), a composite of steel, polyimide adhesive, PZT, and aluminum is constructed with varying geometries so that three-dimensional surface topology maps are measured. Numerically, the four-coefficient model produces results that are not comparable to experimental data. The 23-coefficient model generally shows good agreement with the data for all studied actuators. In the case of actuators with a length to width ratio of one, simulations are close to experimental results. In the case of length to width ratios different to unity, the model accurately predicts the devices' shape. It is further demonstrated that the curvature of the devices seems to follow the rolling direction of the stainless steel layer, challenging the isotropy assumption.