Investigation on the effects of the electrode type and thickness in Langevin ultrasonic transducers based on Euler–Bernoulli beam theory and finite element simulation

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Abstract
Today, ultrasonic transducers are commonly used in various industries. Most of the ultrasonic transducers used in industry are of the longitudinal and piezoelectric type. With the development of the application of these transducers in recent years, the need for small-sized transducers has arisen. In the present research, the vibration behavior of the Langevin transducer with four piezoelectric layers is studied using the simple theory and finite element model. For this purpose, by extracting the governing equations and the corresponding boundary conditions, the characteristic equation of the system is derived, and the effect of various parameters on the natural frequency of the system is studied analytically. Through the finite element simulation analysis of the modal, natural frequencies, frequency response, and vibration mode shapes of the transducer are obtained. Finally, the optimal values are determined to achieve the minimum length for the transducer. The results show that in the case of using aluminum electrode layers, the minimum transducer length of 87.47 mm is achieved with the electrode thickness equivalent to 6 mm. It is about 6% shorter than the corresponding transducer length with a copper electrode. Aluminum electrodes in the Langevin transducer under study achieve the optimal size for the transducer.

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