Equivalent homogeneous model of D31-mode longitudinal piezoelectric transducers

This article focuses on modelling of D31-mode longitudinal piezoelectric transducers. A simple equivalent one-dimensional homogeneous model of D31-mode longitudinal piezoelectric transducers is proposed in this article. Homogeneous properties of the model are derived by a simple analytical mixing method based on the operation principle of D31-mode longitudinal piezoelectric transducers. Compared with other models in the literature, the proposed homogeneous model can consider passive layers in D31-mode longitudinal piezoelectric transducers for more accurate predictions in either static or dynamic behaviour. The proposed model is validated by a three-dimensional finite element model. Besides, based on the homogeneous model and borrowing the network theory, an exact equivalent circuit is formulated. A more straightforward form of the equivalent circuit can further facilitate analysis and modelling of D31-mode longitudinal piezoelectric transducers. Also, the proposed homogeneous model is wrapped into a transfer matrix form. The formulated transfer matrix of D31-mode longitudinal piezoelectric transducers can be used with the transfer matrix method to facilitate the calculations, when D31-mode longitudinal piezoelectric transducers are connected with numerous mediums in the operation direction. The effectiveness of the equivalent circuit and the transfer matrix is also verified.