Static Nano-Control of Cantilever Beams Using the Inverse Flexoelectric Effect

Abstract

Flexoelectricity, an electromechanical coupling effect, exhibits two opposite electromechanical properties. One is the direct flexoelectric effect that mechanical strain gradient induces an electric polarization (or electric field); the other is the inverse flexoelectric effect that polarization (or electric field) gradient induces internal stress (or strain). The later can serve as an actuation mechanism to control the static deformation of flexible structures. This study focuses on an application of the inverse flexoelectric effect to the static displacement control of a cantilever beam. The flexoelectric layer is covered with an electrode layer on the bottom surface and an AFM probe tip on the top surface in order to generate an inhomogeneous electric field when powered. The control force induced by the inverse flexoelectric effect is evaluated and its spatial distribution resembles a Dirac delta function. Therefore, a “buckling” characteristic happens at the contact point of the beam under the inverse flexoelectric control. The deflection results of the cantilever beam with respect to the AFM probe tip radius indicate that a smaller AFM probe tip achieves a more effective control effect. To evaluate the control effectiveness, the flexoelectric deflections are also compared with those resulting from the converse piezoelectric effect. It is evident that the inverse flexoelectric effect provides much better localized static deflection control of.flexible beams.

Flexoelectric Actuation and Vibration Control of Ring Shells

“…The bending control moment plays a dominant role in the transverse actuation, because the transverse deformation can be considered as a drastic bending resembling a Dirac delta function at the AFM probe's contact point, shown in Fig.8. Note that this sharp bending has been describled as the "buckling" characteristic in an earlier research on staitic deformation control of the cantilever beam based on AFM probe [16]. When the ring actuated by the flexoelectric actuator driven by an AFM probe, a transverse deformation is induced as illustrated above.…”

“…where * 0  is the AFM probe location. In this study, the net electric field in the  direction is almost zero [16], thus only the transverse electric field is considered here. The transverse electric field can be obtained by differentiating the potential expression in the opposite transverse direction.…”

“…(18) can be used to describe the electric field for the whole plane. The circumferential stress induced by the electric field can be derived from the general converse flexoelectric equations [16] and expressed as…”

“…With the explicit expression of the membrane force and bending moment induced by the flexoelectric actuator, the flexoelectric actuation response of the ring can be obtained by the expression of transverse displacement, i.e., Eq. (16). Based on the formulations of the flexoelectric actuated vibration, microscopic actuation behaviors and specific modal control characteristics are analyzed and evaluated in case studies.…”

“…The signal analysis and dynamic responses of the flexoelectric materials have been reported recently and their applications on rings and cylindrical shells were studied [12][13][14][15]. Static flexoelectric actuation effects of a cantilever beam using the AFM probe were also evaluated [16].…”