An improved model for the Langevin transducer with numerous piezoelectric ceramics and electrodes

초록

The Langevin transducer, configured with numerous piezoelectric ceramics (PZTs) and electrodes, exhibits a high-power density and can be designed and optimized through dynamic modeling. However, existing modeling approaches face a significant computational challenge, as the dimension of the system matrix increases rapidly with the number of PZTs and electrodes. To address this issue, an improved transfer matrix method (TMM) model is proposed in this paper. First, the transfer equation of the piezoelectric stack (PS), which acts as the vibration excitation source in the Langevin transducer, is derived based on the electromechanical transfer condition. A ternary operation is introduced to combine PZTs and electrodes, resulting in a 3 & times; 3 matrix. Subsequently, by eliminating the state vectors of internal elements such as the PS, the transfer equation of the entire Langevin transducer is obtained, and its overall transfer matrix retains a dimension of 3 & times; 3. A Langevin transducer with 12 PZTs and 13 electrodes is used for validation. The resonant frequencies obtained by the proposed TMM, the finite element method (FEM), and experiment are 32,190 Hz, 31,628 Hz, and 30,824 Hz, respectively. The relative error between the TMM and FEM results is 1.78%, showing good agreement. The error compared with experimental results is 4.43%, demonstrating practical applicability. Besides, compared with the conventional TMM, the proposed TMM reduces both the dimension and the condition number of the system matrix while improving computational accuracy, making it an efficient and practical modeling tool.

키워드