Models of elastic plates with piezoelectric inclusions part I: Models without homogenization

In this paper, we present models of elastic plates, dielectric plates and elastic plates with piezoelectric inclusions. Single layer plate models and multilayered plate models are presented. They are studied in view of the active controlled structures design. Various sorts of boundary conditions for the piezoelectric cells are considered. They represent different ways of controlling the structure: voltage, current, or voltage/current control. The derivation of these models is based on asymptotic methods.