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Deflection control during dynamic deformations of a rectangular plate using piezoceramic elements

Formulation of the Problem We consider a 0.3 m x 0.3 m x 1.8 mm aluminum plate simply supported on two opposite edges with PZTs affixed to its top and bottom surfaces as shown in Fig. 1. The technique developed herein is valid for plates of other dimensions, materials, and support conditions. The PZT element at the centroid of the plate is used as a sensor and the other PZT elements are used as actuators. We employ the first-order shear deformation theory to study elastic deformations of the plate and the PZTs. The PZTs are assumed to be perfectly bonded to the plate surfaces through adhesives of negligible thicknesses, and displacements and surface tractions across the interfaces between the PZTs and the plate are taken to be continuous. Whereas the plate material is modeled by Hooke's law and is taken to be isotropic, the PZTs are transversely isotropic with electroelastic response given by