A 3-D model of the classical Langevin transducer

In this work a 3-D model of the classical Langevin transducer is proposed. The structure analyzed is composed of a piezoceramic disk and two cylinder-shaped loading masses, glued on the two flat faces of the disk. A 3-D matrix model has been used both for the piezoceramic and the loading masses. By cascading these three systems, the transducer is schematized as a six ports system with one electrical and five mechanical ports, corresponding to the three lateral and the two terminal surfaces. The proposed model, which describes both the thickness and the radial modes of each element, is also able to take into account the unwanted lateral vibrations of the structure, to consider the external media and to compute all the transfer functions. Comparisons between computed and experimental results are shown. The frequency spectrum, computed by varying the thickness of the two loading masses, and the transmission transfer function are also shown