Flexoelectric control of beams with atomic force microscope probe excitation

Based on the converse flexoelectric effect, flexoelectric actuator is designed and used to control the dynamic displacement of cantilever beams. First, shell-type stress expression based on double-curvature shell induced by the converse flexoelectric effect is developed, which can be simplified to a flexoelectric-laminated cantilever beam by applying two Lamé parameters and beam radius of curvature. Then, the flexoelectric actuator is designed with a conductive atomic force microscope probe and a flexoelectric layer. An inhomogeneous electric field is generated when the external voltage is applied on the atomic force microscope probe and the flexoelectric layer, which leads to stress in the longitudinal direction of beam and control moment. With the flexoelectric-induced bending moment, displacement induced by the external force and flexoelectric actuator is derived. The displacement is related to many parameters, such as actuation voltage, atomic force microscope probe radius and flexoelectric layer thickness. Cases are studied to optimize the control effect with different parameters. Results show that vibration control effect is enhanced with a higher actuation voltage and a smaller atomic force microscope probe radius for each mode. Besides, the thicker flexoelectric layer enhances the control effect with a larger bending moment arm for each mode. Dynamic vibration is controlled effectively by converse flexoelectric effect.