A 2D equivalent circuit of piezoelectric ceramic ring for transducer design

In this paper a 2D equivalent circuit of longitudinally polarized piezoelectric ceramic rings is established, which is obtained as an approximated analytical solution of 3D constitutive equations in the hypothesis of axial symmetry when the shearing stress and torsion are ignored. The mechanical part of the equivalent circuit can be divided into two branches; one branch characterizes the longitudinal extensional vibration, the other represents the radial vibration. The two branches, which are coupled to an electrical port by two transformers separately, mechanically couple to each other by some mechanical impedance at the same time. Similar circuit is also presented when piezoelectric disk is concerned. Based on this model it is able to compute all the relations between the input applied voltage and the output forces and velocities on every external surface analytically. Compared with the 1D equivalent circuits, the 2D equivalent circuit gives a more comprehensive predicts of the thickness and radial modes with sufficient accuracy when the ring or disk is thin. When the ring or disk is so thick that the 1D theory is not validated, an effective predict of the coupled vibration can also be presented. Comparisons with the experimental results show this model is rather accuracy in frequency calculation.