Analysis of a plate with a localized piezoelectric patch

We first describe an approach for the modeling of piezoelectric beams and plates that leads to a well-posed system of partial differential equations that retain the coupling between the mechanical system and a potential equation for the electrical components. We then describe how the same approach can be used to analyze a plate with a localized piezoelectric patch. In particular, since the higher order electrical terms have been retained, it is possible to deduce the proper sets of boundary conditions that should apply to an arbitrarily shaped patch