AB. Special Case of a Tangentially Polarized Piezoelectric Segmented Ring

The objective is to model a tangentially polarized piezoelectric segmented ring (Fig. 1) with a two-dimensional mesh such as wouldbe used if the structure were axisymmetric. This objective corresponds to theneed to reduce the problem size when dealing with radiation problems.  Thesuggested method of solution is as follows:

Notes

Since the potential degree-of-freedom is actually a scalar,the difference between radial and tangential poling is simply a mechanicaltransformation of ratio d/e.

This way of dealing with a tangentially polarized ring canbe used only if the displacement field of the real structure is nearlyaxisymmetrical.  It is, for example, impossible to obtain circumferential modesusing this method.

Fig. 1: Segmented free-flooded ring