Active shape and vibration control for piezoelectric bonded composite structures using various geometric nonlinearities

This paper deals with simulations of the static and dynamic response, including shape and vibration control, for piezoelectric bonded smart structures using various geometrically nonlinear shell theories based on the first-order shear deformation (FOSD) hypothesis. The nonlinear theories include refined von Kármán nonlinear shell theory (RVK5), moderate rotation shell theory (MRT5), fully geometrically nonlinear shell theory with moderate rotations (LRT5), and fully geometrically nonlinear shell theory with large rotations (LRT56). The structures simulated are mainly comprised of cross-ply or angle-ply laminated thin-walled master structures bonded with isotropic piezoelectric layers or patches that are considered as actuators. Nonlinear finite element (FE) models are constructed for shape and vibration control of structures undergoing large displacements and rotations. Various plates and shells are validated by comparison with those reported in the literature, and then simulated for the current shape and vibration control. A widely used negative proportional velocity feedback control is adopted for the active vibration control. From the simulations, it can be concluded that large rotation theory should be considered for structures undergoing deformations beyond the range of moderate rotations. Additionally, the results show that by applying an appropriate voltage, a desired shape can be achieved, as well as the vibration can be significantly suppressed.