Effect of self-induced electric displacement field on the response of a piezo-bimorph actuator at high electric field

Abstract

This paper analytically illustrates the response of a piezoelectric bimorph actuator considering the effect of self-induced electric displacement field. In the analysis, we have considered response of the actuator at high electric field. The self-induced electric displacement field exists inside the piezoelectric actuator during its bending. This effect was not considered in the earlier modeling, which typically followed stress-strain based approaches, instead of following the extended Hamilton's principle for electromechanical systems driven by constant voltage source. This electric displacement field affects the tip deflection of a piezoelectric actuator. The new derivation based on Hamilton's principle also shows that a piezo-bimorph's short circuit stiffness, which was considered independent of the piezoelectric coupling coefficient in earlier literature, actually depends on the piezoelectric coupling coefficient. A piezoelectric material of high piezoelectric coupling coefficient can produce a significant self-induced electric displacement field, which can significantly impact the tip deflection and the stiffness of a piezoelectric bimorph actuator. The analytical results are validated with the experimental results, published in earlier literature.