In this work, an approximated 3-D analytical model of the Langevin transducer is proposed. The model, improving the classical 1-D approach describing the thickness extensional mode, allows us to predict also the radial modes of both the piezoelectric ceramic disk and the loading masses; furthermore, it is able to describe the coupling between radial and thickness extensional modes. In order to validate the model, the computed frequency spectrum is compared with that obtained by measurements carried out on 13 manufactured samples of different thicknesses to diameter ratios. The comparison shows that the model predicts with quite good accuracy the resonance frequencies of the two lowest frequency modes, i.e., those of practical interest, all over the explored range. Finally, the coupling effect between thickness and radial modes on the frontal displacement is measured and discussed.
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