An analytical investigation of static models of piezoelectric patches attached to beams and plates

Abstract

On the basis of the deformation compatibility of piezoelectric patches and a beam or plate, equations for determining their interaction force are given. Their solutions show that the interaction force arises from structural deformation and the electric field imposed on the piezoelectric patches as well, and demonstrate that deformation of the beam and the plate may be caused by imposing an electric field on the piezoelectric patches, while the deformation may also lead to the variation of the static capacitance of the piezoelectric patches. Therefore, it is possible to retrieve information about the deformation of the beam and plate from the change of the static capacitance of patches which simultaneously take the role of actuators. However, their sensitivity to deformation is dependent on the area of the interface of the patches and the beam or plates; meanwhile it is also affected by the piezoelectric anisotropy of the patches when the patches are bonded to a plate. As an application, the static models are then used to investigate the feasibility of using piezoelectric patches to actively adjust the shape of the beam and plate, and the imposed voltage required for the shape control of beams and plates is predicted.