Flexoelectric Vibration Control of Plates by Line Electrodes

2016 ◽  
Author(s):  
X. F. Zhang ◽  
H. Y. Li ◽  
H. S. Tzou
Keyword(s):  
Electric Field ◽  
Vibration Control ◽  
Bottom Surface ◽  
Modal Control ◽  
Sensors And Actuators ◽  
Structural Dynamic ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Flexoelectric Effect ◽  
Conductive Line

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.

Vibration Control of a Cantilever Beam by Metal-Core Flexoelectric and Piezoelectric Fibers

2014 ◽  
Author(s):  
X. F. Zhang ◽  
H. Li ◽  
H. S. Tzou
Keyword(s):  
Electric Field ◽  
Electric Field Gradient ◽  
Vibration Control ◽  
Field Gradient ◽  
Cantilever Beam ◽  
Electromechanical Coupling ◽  
Control Effect ◽  
Metal Core ◽  
Flexoelectric Effect ◽  
Piezoelectric Fiber

Flexoelectric effect occurs in the solid crystalline dielectrics of symmetry or centro-symmetric crystals, which shows the electromechanical coupling of the polarization response and the strain gradient or the stress and the electric field gradient. Thus, a generic stress expression induced by the converse flexoelectric effect is established first in this study. The generic stress expression is simplified to a cantilever beam to evaluate the vibration control effect due to the converse flexoelectric effect. Flexoelectric fiber embedded with a metal core is placed into the cantilever beam to generate inhomogeneous electric field. When the flexoelectric fiber is actuated with the applied voltage, stress induced by the actuator is obtained with the electric field gradient, which results in a control bending moment to the beam. Static displacement control of the cantilever beam is established and the control effect is related to the fiber location and size of the flexoelectric fiber and the metal core. Cases show that the control effect is enhanced when the flexoelectric fiber is far away from the neural surface of the beam. Besides, the control effect can enhance with thinner fiber thickness. Since the piezoelectricity is similar to the flexoelectricity, comparison of the vibration control induced by the piezoelectric fiber is also discussed. The results show that the control effect of the flexoelectric fiber is more effective than the piezoelectric fiber in the cantilever beam.

Independent Modal Control of Beams With Spatially Distributed Orthogonal Photostrictive Actuators

2012 ◽  
Author(s):  
Jing Jiang ◽  
Hong-Hao Yue ◽  
Wen-Xiu Cheng ◽  
Zong-Quan Deng ◽  
Horn-Sen Tzou
Keyword(s):  
Light Intensity ◽  
Time History ◽  
High Energy ◽  
Modal Control ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Electrode Shape ◽  
Intensity Control ◽  
Spatially Distributed ◽  
Photostrictive Actuators

High-energy light regulated photostrictive actuators provide a new wireless and non-contact precision actuation mechanism. For PLZT actuators with 0–3 polarization, the electrode shape can be designed to achieve desired modal control effects. In this paper, the photonic control of flexible shells using shaped photostrictive actuators is investigated. Spatially distributed and shaped 0–3 polarized PLZT actuators are selected to achieve independent control of various natural modes of a simply supported beam. Constitutive equations which define the time history response of photo-induced strain for 0–3 polarized PLZT actuator are presented. Based on experimental observation and theoretical analysis, the relationships of saturated photovoltage and time constant with actuator thickness and light intensity are formulated. Based on the orthogonality of the mode shape function, distributed orthogonal modal actuators designed for a simply supported beam are proposed. In order to realize the actuator shape design, paired spatially shaped photostrictive actuators are segmented and respectively placed on the top and bottom surfaces of the beam and the light direction of each segment actuator is regulated. Their control effectiveness with constant light intensity control is evaluated and the time history analysis is presented.

Comparison of Flexoelectric and Piezoelectric Actuating of Beams

2020 ◽  
Author(s):  
Mu Fan
Keyword(s):  
Electric Field ◽  
Electric Field Gradient ◽  
Vibration Control ◽  
Case Studies ◽  
Field Gradient ◽  
Patch Size ◽  
Flexoelectric Effect ◽  
Control Moment ◽  
Modal Force ◽  
Afm Probe

Abstract The flexoelectric and piezoelectric effect on the actuating of a cantilever beam are compared in this study to explore how the size-dependent effect could affect the application of the flexoelectric effect. An AFM (atomic force microscopy) probe is used to generate the electric field in the flexoelectric patch, significant electric field gradient is induced. The electric field, distribution of control moment, induced modal force and the vibration control efficiency in terms of transverse displacements are analyzed in case studies. Analytical results show that the control moment of flexoelectric effect highly concentrates at the location of the AFM probe due to the inhomogeneous electric field, which shrink the effect area of flexoelectric patch size. The distribution of the flexoelectric control moment is an impulse function and the distribution of the piezoelectric control moment is a step function, which results to the flexoelectric modal force strongly affected by the electric field gradient while the piezoelectric modal force highly depends on the patch size. For the flexoelectric actuating, decreasing the AFM probe radius can increase the electric field gradient and induce larger modal force. The thickness effect of flexoelectric patch depends on the electric field gradient and the control moment arm, and in the current study, increasing the patch size, the induced flexoelectric modal force increases slightly. Case studies on vibration control show that both the flexoelectric actuating and piezoelectric actuating could generate larger transverse tip displacement with increasing the patch size. This study proves that the flexoelectric actuating can provide effectively actuating and control effect to engineering structures when the size decreases.

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