3D finite element analysis of the Langevin transducer

In this paper, a 3-D finite element analysis of the vibrational behaviour of the Langevin transducer and of the dependence of its performances on the length to diameter ratio is presented. Several transducers with total length greater than, comparable to, and smaller than the diameter have been simulated, and the frequency spectrum is drawn in order to identify the regions where coupling between thickness and radial modes exists, and to highlight the limit of the classical 1-D theory. Performances of transducers with any length to diameter ratio, but all working at the same frequency (153 kHz), are evaluated by comparing the product between the output mean displacement and the area of the radiating surface. Results have shown that Langevin transducers with comparable longitudinal and lateral dimensions have performances comparable to or even better than transducers with total length much greater than diameter.