Flexoelectric Actuation and Vibration Control of Ring Shells

The converse flexoelectric effect that the gradient of polarization (or electric field) induces internal stress (or strain) can be utilized to control the vibration of flexible structures. This study focuses on the microscopic actuation behavior and effectiveness of a flexoelectric actuator patch on an elastic ring. An atomic force microscope (AFM) probe is placed on the upper surface of the patch to implement the inhomogeneous electric field inducing stresses inside the actuation patch. The flexoelectric membrane force and bending moment, in turn, actuate the ring vibration and its actuation effect is studied. Actuator’s influence in the transverse and circumferential directions is respectively evaluated. For the transverse direction, the gradient of the electric field decays quickly along the ring thickness, resulting in a nonuniform transverse distribution of the induced stress and such distribution is not influenced by the patch thickness. The flexoelectric induced circumferential membrane force and bending moment resembles the Dirac delta function at the AFM contact point. The influence of the actuator can be regarded as a drastic bending on the ring. To evaluate the actuation effect, dynamic response of controllable displacements of the elastic ring under flexoelectric actuation is analyzed by adjusting the geometric parameters, such as the thickness of flexoelectric patch, AFM probe radius, ring thickness and ring radius. This study represents a thorough understanding of the flexoelectric actuation behavior and serves as a foundation of the flexoelectricity based vibration control.