Flexoelectric Responses of Circular Rings

Abstract

Dynamic sensing is essential to effective closed-loop control of precision structures. In a centrosymmetric crystal subjected to inhomogeneous deformation, when piezoelectricity is absent, only the strain gradient contributes to the polarization known as the “flexoelectricity.” In this study, a flexoelectric layer is laminated on a circular ring shell to monitor the natural modal signal distributions. Due to the strain gradient characteristic, only the bending strain component contributes to the output signal. The total flexoelectric signal consists of two components respectively induced by the transverse modal oscillation and the circumferential modal oscillation. Analog to the signal analysis, the flexoelectric sensitivity is also studied in two forms: a transverse sensitivity induced by the transverse modal oscillation and a transverse sensitivity induced by the circumferential modal oscillation. Analysis data suggest that the transverse modal oscillation dominates the flexoelectric signal generation and its magnitude/distribution shows nearly the same as the total signal. Furthermore, voltage signals and signal sensitivities are evaluated with respect to ring mode, sensor segment size, ring thickness, and ring radius in case studies. The total signal increases with mode numbers and sensor thicknesses, decreases with sensor segment size and ring radii, and remains the same with different ring thicknesses.