Finite element three-dimensional analysis of the vibrational behaviour of the Langevin-type transducer

The vibrational behaviour of the Langevin transducer is usually analysed using 1D Mason model which is valid when the lateral dimensions of the transducer are smaller than a quarter wavelength at the fundamental longitudinal resonance. In this work a 3D finite element analysis of the Langevin transducer's behaviour operating in the underwater sonar range of frequencies (30-140 kHz) is presented. Several samples with total length greater, comparable to, and smaller than the diameter of the transducer are analysed. For each sample, the resonance frequencies in the observed frequency range are computed and compared with those obtained experimentally from the measurements carried out using several in-house built prototypes. For the most important aspect ratios the resonance displacement distributions are presented and discussed. The results obtained permit to gain insight into the coupling phenomenon between thickness-extensional and radial modes and suggest that in practical applications transducers with diameters comparable to or greater than total length of the active stack can also be used. The trade-off between the efficiency and power handling ability for different designs is also discussed.