In the framework of linear piezoelectric ceramics, we study the deformations of a circular infinite hollow cylinder, subjected to a potential difference between the inner and outer surfaces. When the poling direction is perfectly aligned with the cylinder axis, the solution to this problem is a trivial axisymmetric anti-plane state. However, when the poling direction has an offset angle with respect to the cylinder axis, the corresponding behavior becomes more complex, with the anti-plane state coupled to an in-plane, potentially non axisymmetric, deformation. In this work, we show that this structural coupling, due to the poling direction, can be fruitfully exploited to achieve non-standard actuation and sensing properties, like the possibility to generate a torque under axially symmetric electromechanical controls.
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