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

2011 ◽  
Author(s):  
S. D. Hu ◽  
H. Li ◽  
H. S. Tzou
Keyword(s):  
Electric Field ◽  
Cantilever Beam ◽  
Mechanical Strain ◽  
Effective Control ◽  
Bottom Surface ◽  
Control Force ◽  
Dirac Delta ◽  
Flexoelectric Effect ◽  
Afm Probe ◽  
Converse Piezoelectric Effect

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

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Hornsen Tzou ◽  
Bolei Deng ◽  
Huiyu Li
Keyword(s):  
Electric Field ◽  
Electric Field Gradient ◽  
Field Gradient ◽  
Design Parameters ◽  
Internal Stresses ◽  
Control Force ◽  
Elastic Ring ◽  
Dirac Delta ◽  
Control Moment ◽  
Afm Probe

The converse flexoelectric effect, i.e., the polarization (or electric field) gradient-induced internal stress (or strain), can be utilized to actuate and control flexible structures. This study focuses on the microscopic actuation behavior and effectiveness of a flexoelectric actuator patch laminated on an elastic ring shell. An atomic force microscope (AFM) probe is placed on the upper surface of the flexoelectric patch to induce an inhomogeneous electric field resulting in internal stresses of the actuator patch. The flexoelectric stress-induced membrane control force and bending control moment regulate the ring vibration and their actuation mechanics, i.e., transverse and circumferential control actions, are, respectively, studied. For the transverse direction, the electric field gradient quickly decays along the ring thickness, resulting in a nonuniform transverse distribution of the induced stress, and this distribution profile is not influenced by the actuator thickness. The flexoelectric-induced circumferential membrane control force and bending control moment resemble the Dirac delta functions at the AFM contact point. The flexoelectric actuation can be regarded as a localized drastic bending to the ring. To evaluate the actuation effect, dynamic responses and controllable displacements of the elastic ring with flexoelectric actuations are analyzed with respect to design parameters, such as the flexoelectric patch thickness, AFM probe radius, ring thickness, and ring radius.

Sensing Signal and Energy Generation Analysis on a Flexoelectric Beam

2012 ◽  
Author(s):  
S. D. Hu ◽  
H. Li ◽  
H. S. Tzou
Keyword(s):  
Cantilever Beam ◽  
Coupling Effect ◽  
Mechanical Strain ◽  
Electric Energy ◽  
Energy Generation ◽  
Electric Polarization ◽  
Ambient Vibration ◽  
Electric Voltage ◽  
Flexoelectric Effect ◽  
Fourth Mode

Flexoelectricity is known as an electromechanical gradient coupling effect. The direct flexoelectric effect that can convert mechanical strain gradient into electric polarization (or electric field) plays an important role in charge generation in the situation when piezoelectricity is absent. This study focuses on the application of the direct flexoelectric effect based on a flexoelectric cantilever beam to investigate its effectiveness of sensing signal and energy generation. The dielectric cantilever beam is deposited with electrodes both on top and bottom surfaces to generate an electric voltage. The sensing mechanism of flexo-piezo-electric effect is analyzed and the expression of sensing signal is derived. Results show that the output sensing signal is only contributed by the flexoelectric effect while the piezoelectric effect is eliminated due to the symmetric bending strains through the beam thickness. The spatial distribution of sensing signal when the fully covered electrode is uniformly segmented to 10 patches is evaluated as an illustration, and the flexoelectric sensitivity of about 0.15V/mm for the first mode and 4V/mm for the fourth mode is achieved. The optimal sensing position is dependent of the electrode size and the vibration mode and in general, it locates where the difference between the slopes at two ends of the electrode patch reaches maximum. Based on the flexoelectric voltage, the energy generation power is also conducted when the flexoelectric cantilever beam is treated as distributed energy harvesters. As a result, the maximal power of RMS is about 1.5×10−8W/mm for the first mode and increases to about 0.6mW/mm for the fourth mode. It provides an alternative way to harvest electric energy from the ambient vibration without using piezoelectricity.

Analytical and Experimental Studies of Flexoelectric Beam Control

2016 ◽  
Author(s):  
Xufang Zhang ◽  
Huiyu Li ◽  
Hornsen Tzou
Keyword(s):  
Electric Field ◽  
Design Parameters ◽  
Analytical Prediction ◽  
Probe Radius ◽  
Flexoelectric Effect ◽  
Control Moment ◽  
Probe Location ◽  
Afm Probe ◽  
Fixed End ◽  
Tip Displacement

Flexoelectricity includes two effects: the direct flexoelectric effect and the converse flexoelectric effect, which can be respectively applied to flexoelectric sensors and actuators to monitor structural dynamic behaviors or to control structural vibrations. This study focuses on the converse flexoelectric effect and its application to dynamic control of cantilever beams analytically and experimentally. In the mathematical model, a conductive atomic force microscope (AFM) probe with an external voltage is used to generate an inhomogeneous electric field driving the flexoelectric beam. The electric field gradient leads to an actuation stress in the longitudinal direction due to the converse flexoelectric effect. The actuation stress results in a bending control moment to the flexoelectric beam since the stress in the thickness is inhomogeneous. In order to evaluate the actuation effect of the flexoelectric actuator, the flexoelectric induced tip displacement is evaluated when the mechanical force is assumed zero. With the induced control moment, vibration control of the cantilever beam is discussed and the control effect is evaluated. Flexoelectric control effects with different design parameters, such as AFM probe location, AFM probe radius and flexoelectric beam thickness, are evaluated. Analytical results show that the optimal AFM probe location for all beam modes is close to the fixed end. Besides, thinner AFM probe radius and thinner flexoelectric beam enhance the control effects. Laboratory experiments are also conducted with different probe locations to validate the analytical predictions. Experimental results show that the induced tip displacement decreases when the input location moves away from the fixed end, which is consistent with the analytical prediction. The studies provide design guidelines of flexoelectric actuations in engineering applications.

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.

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.

Cantilever Beam Design for Projectile Internal Moving Mass Systems

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Jonathan Rogers ◽  
Mark Costello
Keyword(s):  
Cantilever Beam ◽  
Damping Ratio ◽  
Effective Control ◽  
Moving Mass ◽  
Control Mechanisms ◽  
Control Force ◽  
Internal Mass ◽  
Mass System ◽  
Electromagnetic Actuators ◽  
Beam Design

Internal masses that undergo controlled translation within a projectile have been shown to be effective control mechanisms for smart weapons. However, internal mass oscillation must occur at the projectile roll frequency to generate sufficient control force. This can lead to high power requirements and place a heavy burden on designers attempting to allocate volume within the projectile for internal mass actuators and power supplies. The work reported here outlines a conceptual design for an internal translating mass system using a cantilever beam and electromagnetic actuators. The cantilever beam acts as the moving mass, vibrating at the projectile roll frequency to generate control force. First, a dynamic model is developed to describe the system. Then the natural frequency, damping ratio, and length of the beam are varied to study their affects on force required and total battery size. Trade studies also examine the effect on force required and total battery size of a roll-rate feedback system that actively changes beam elastic properties. Results show that, with proper sizing and specifications, the cantilever beam control mechanism requires relatively small batteries and low actuator control forces with minimum actuator complexity and space requirements.

Flexoelectric Actuation and Vibration Control of Ring Shells

2015 ◽  
Author(s):  
Bolei Deng ◽  
Huiyu Li ◽  
Hornsen Tzou
Keyword(s):  
Electric Field ◽  
Vibration Control ◽  
Contact Point ◽  
Flexible Structures ◽  
Bending Moment ◽  
Delta Function ◽  
Elastic Ring ◽  
Dirac Delta ◽  
Probe Radius ◽  
Afm Probe

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.

Relative stabilities of various fully functionalized graphene polymorphs under mechanical strain and electric field

2019 ◽  
Vol 463 ◽  
pp. 1051-1057 ◽  
Author(s):  
Konstantin S. Grishakov ◽  
Konstantin P. Katin ◽  
Vladimir S. Prudkovskiy ◽  
Mikhail M. Maslov
Keyword(s):  
Electric Field ◽  
Mechanical Strain ◽  
Functionalized Graphene ◽  
Relative Stabilities
Sign in / Sign up

Export Citation Format

Share Document