Vibration characteristics of piezoelectric torsional transducers

The vibrational characteristics of Langevin-type torsional transducers, which consist of two piezoelectric torsional disks and two elastic blocks, are studied theoretically and experimentally in this paper. The differential equations of piezoelectric torsional motions are derived in terms of the circumferential displacement and the electric potential. Solutions of the boundary-value problem yield the natural frequencies and mode shapes of the transducers, and the natural frequencies are verified by comparing the numerical results with the experimental ones. The theoretical results enable one to quantitatively predict the effect of the elastic blocks on the reduction of the natural frequencies of a Langevin-type torsional transducer.