An improved small-deflection electromechanical model for piezoelectric bending beam actuators and energy harvesters

The analytical model presented in this paper describes the energy conversion mechanism of a piezoelectric beam (bimorph) under small-deflection static and vibrating conditions. The model provides an improved approach to design and analyze the performance of piezoelectric actuators and energy harvesters (sensors). Conventional models assume a linear voltage distribution over the piezoelectric beam thickness, which is shown here to be invalid. The proposed modeling method improves accuracy by using a quadratic voltage distribution. The equivalent capacitance of a beam shows a 40% discrepancy between a conventional model and the proposed model for PZT5A material. This inaccuracy level is not negligible, especially when the design of micro- power electrical energy harvesting is concerned. The method solves simultaneously the solid mechanics and Maxwell's equations with the constitutive equations for piezoelectric materials. The paper also proposes a phasor- based procedure for measuring the damping of a piezoelectric beam. An experimental setup is developed to verify the validity of the model. The experimental results confirm the accuracy of the improved model and also reveal limitations in using models for small deflections.