The electric polarization induced by the strain gradient is the direct flexoelectric effect; the mechanical stress/strain induced by the electric field gradient is the converse flexoelectric effect. Accordingly, flexoelectric sensors and actuators are respectively designed to monitor the structural dynamic behavior and to control the structural vibration. In this study, a line-electrode induced flexoelectric actuation is designed to control the plate vibrations. A flexoelectric layer laminated on the thin plate is used as a distributed actuator. The bottom surface of the flexoelectric actuator is a common electrode and the top surface is driven by a conductive line to generate an inhomogeneous electric field. Based on the converse flexoelectric effect, the electric filed gradient induces mechanical stresses in the flexoelectric layer resulting in induced bending moments to the plate structure. With the control moment imposed on the plate, flexoelectric vibration control of the plate is evaluated in this study. The objective of this study is to explore the modal control effects of the plate by the conductive line excitation. For a plate with two opposite sides simply supported and the other two are free (SS-F-SS-F), vibration control response of the plate is studied when the conductive line locates parallel to the y width direction. Then, independent modal control effects (i.e., the induced or controllable displacements by the flexoelectric actuator) are evaluated for the modes (1,1), (1,2), (1,3), (2,1) and (3,1) with different line actuation locations. Control effects of the conductive line location to various plate modes are explored and results show that the optimal conductive line location differs for different plate modes. When the FF width decreases to far less than the SS length, the SS-F-SS-F plate is degraded to a simply supported beam. Then, control effects for modes (1,1), (2,1) and (3,1) with different conductive line locations are discussed. The results are compared with the control effect derived directly by the simply supported beam theory. Thus, this study suggests that plate vibration can be controlled by the line-electrode induced converse flexoelectric effect. Conductive line locations are critical to control of various plate modes.

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