Equivalent circuit for analyzing the transmitting characteristics of multimode Tonpilz transducer

Multimode Tonpilz transducers operate at longitudinal and flexural vibration modes simultaneously. Consequently, they have wider bandwidths than conventional single-mode transducers. Generally, the performance of Tonpilz transducers is analyzed using the finite element method (FEM), whereas the equivalent circuit method (ECM) has proven to be a fast and efficient alternative to the FEM. However, the ECM for analyzing the acoustic characteristics of multimode Tonpilz transducers has not yet been developed. To address this issue, an equivalent circuit for the multimode Tonpilz transducer is developed herein. The proposed ECM encompasses the flexural characteristics of the Tonpilz head mass, which is impossible with conventional equivalent circuits. Furthermore, a prototype of the multimode Tonpilz transducer was fabricated to verify the validity of the developed ECM. Additionally, the accuracy and compliance of the ECM were confirmed by comparing the measured performance of the transducer with that from the equivalent circuit analysis.