Analytical modeling of curved piezoelectric, Langevin-type, vibrating transducers using transfer matrices

• Differential equations for a curved piezoelectric transducer are given.
• A transfer matrix based approach is proposed for solving the equations.
• Same problem is solved with finite element method and using the model.
• The results given by the model are compared to the measurements.

This paper describes a relatively general method based on a transfer matrices approach, for modeling piezoelectric Langevin-type transducers presenting a curved geometry. The obtained equations are simple enough to be solved for a vast number of configurations and be easily implemented in a program. The paper explains how they were obtained and how they can be solved using a method involving transfer matrices. The model was also employed to simulate a real transducer and a good agreement was found between calculated and measured data. Also the results given by model were compared with those obtained with FEM software ANSYS, again the model proved to work well.