Analytical modeling of a transversely polarized piezoelectric transducer using ABCD transmission parameters

Piezoelectric transducers are part of many devices employed in several applications, such as energy harvesters and sensors. For modeling piezoelectric transducers, one can use numerical methods, such as the finite element method (FEM), or analytical approaches. Among the options for the latter, the two-port network using ABCD parameters emerged as a prominent option since it takes advantage of simple matrix operations. However, this approach is currently only available for transducers polarized in the same direction as their main displacement. Another common polarization is transversal to the direction of its main displacement, which can be found in many sensors for the aircraft industry, rock analysis, as well as biomedical research. Thus, in this paper, the formulation for two-port networks based on ABCD parameters is devised for transversely polarized transducers. New ABCD matrix was derived, allowing the modeling of the d31-mode of vibration. To validate the derived parameters, two different transducers, consisted of PIC144 (hard type) and PIC255 (soft type) materials, were modeled and further compared with finite element simulations and with experiments. Their impedance curves were computed by means of the proposed model and compared with those experimentally obtained with an impedance analyzer and obtained with numerical finite element modeling. Good agreement was observed in the comparisons. In addition, resonance and antiresonance frequency peaks could be correctly modeled for the d31-mode of vibration. Finally, the performance of the analytical model herein proposed was approximately 48.67% faster than FEM; therefore, providing a lightweight method for modeling the transversely polarized transducer.