A generalized approach on bending and stress analysis of beams with piezoelectric material bonded

Abstract

The modeling and analysis of piezoelectric cantilevers are critically important in the design of micro intelligent systems, where piezoelectric beams serve as major components in micro sensors, actuators or energy harvesters. In this paper, we propose an analogy modeling method for the unimorph and bimorph piezoelectric beams, which helps to improve the accuracy of the neutral plane location of piezoelectric beams with different thickness ratios and total thicknesses. In particular, the strains of each layer are obtained by employing the analogy modeling method with the consideration of the transverse strain effect, where the force balance and moment balance equations of the final state of piezoelectric beams are derived under electric fields to reveal the relationship between the external deflection and the internal stress distribution of piezoelectric beams. To verify the effectiveness of the proposed approach, the bending characteristics of unimorph and bimorph piezoelectric beams (PZT-5A) are comprehensively tested under various electric fields, where theoretical values agree well with experiments and simulations. Compared with existing results, the proposed method provides a more general and accurate approach to characterize the properties of deflection and internal stress distribution for piezoelectric beams, which can be better used to study the stress of the adhesive layers, the geometric dimension optimization and the dynamics of piezoelectric beams in micro sensor or actuator applications.