Mathematical Modeling of Thin Piezoelectric Plates with Electric Field Gradient

Piezoelectric materials are widely used in the design of smart structures. It is thus of major technological interest to provide efficient modelings of such structures. In the case of thin piezoelectric plates, classical studies generally lead to two different models. These two models can be linked to the distinction between sensors and actuators. Here, we extend these results to the second order piezoelectricity, that is to say piezoelectricity with electric field gradient. We recently showed in [1] that three different models have to be taken into account, which broadens the scope of the sensors and actuators field. Second order piezoelectricity being compatible with isotropy (see the introduction below), we also propose a systematic study of the impact of crystalline symmetries on our models and show that a striking effect named ‘structural switch-off’ appears for some specific crystal classes. This paper aims at presenting these results in a simplified but accurate way.