Investigation on the Uniform-Electrical-Field Assumption for Modelling Multi-layer Piezoelectric Actuators

A multi-layer piezoelectric actuator (PEA) is a 1-D thickness-mode piezoelectric transducer commonly used for producing extremely small displacements. The previous paper of the authors demonstrates that the complex electromechanical coupled behaviors of PEA can be described by a simple distribute-parameter model with a critical assumption that the electrical field is uniform across each piezo layer in PEA. Besides PEA, this assumption is also widely used in modelling other thickness-mode piezoelectric transducers in literature. However, the rationale and criteria of such an important assumption is lacking. This paper unveiled the rationale and the criteria from the IEEE standard piezoelectric constitutive relations. The finding is that the assumption is effective, when thickness of a piezo layer is far less than the overall length of the thickness-mode piezoelectric transducer along the thickness direction. Besides, to further quantify the criteria of the assumption to effectively model PEA, the simple distributed-parameter PEA model, which is based on the uniform-electrical-field assumption, was compared with a FEA model, which simulates a real scenario of PEA with no uniform electrical-field simplification. The simulation results demonstrate the finding that when a PEA is stacked by more than around 10 piezo layers, this assumption is effective for modelling the PEA.