Vibration control with the converse flexoelectric effect on the laminated beams

Flexoelectric material under inhomogeneous electric field can be used as control and actuation systems in engineering applications based on the converse flexoelectric effect. The electric field gradient can be generated by using the atomic force microscope probe placed on the top of flexoelectric layer and coupled with a bottom electrode surface. The induced membrane force and the corresponding control moment in turn influence the dynamic response of the beam. The response of a laminated cantilever beam with initial vibration caused by an external loading is studied. The beam was modelled as a laminated beam to explore the influence of flexoelectric layer stiffness on the dynamic response of the structure. When the flexoelectric layer has higher Young’s modulus and mass density than the elastic layer, with increasing the thickness of the flexoelectric layer, the tip displacement of the laminated beam decreased rapidly. Through case studies, the optimal control positions for each mode of vibration were found to be dependent on the flexoelectric layer properties as well. A displacement-based feedback control was introduced to avoid overactuation caused by open-loop control.