Based on the converse flexoelectric effect, flexoelectric actuator is designed and used to control the dynamic displacement of cantilever beams. First, shell-type stress expression based on double-curvature shell induced by the converse flexoelectric effect is developed, which can be simplified to a flexoelectric-laminated cantilever beam by applying two Lamé parameters and beam radius of curvature. Then, the flexoelectric actuator is designed with a conductive atomic force microscope probe and a flexoelectric layer. An inhomogeneous electric field is generated when the external voltage is applied on the atomic force microscope probe and the flexoelectric layer, which leads to stress in the longitudinal direction of beam and control moment. With the flexoelectric-induced bending moment, displacement induced by the external force and flexoelectric actuator is derived. The displacement is related to many parameters, such as actuation voltage, atomic force microscope probe radius and flexoelectric layer thickness. Cases are studied to optimize the control effect with different parameters. Results show that vibration control effect is enhanced with a higher actuation voltage and a smaller atomic force microscope probe radius for each mode. Besides, the thicker flexoelectric layer enhances the control effect with a larger bending moment arm for each mode. Dynamic vibration is controlled effectively by converse flexoelectric effect.
FuJYZhuWYLiN, et al.Gradient scaling phenomenon in microsize flexoelectric piezoelectric composites. Appl Phys Lett2007; 91: 182910–182910.
2.
TagantsevAK. Piezoelectricity and flexoelectricity in crystalline dielectrics. Phys Rev B1986; 34: 5883–5889.
3.
WangBGuYZhangS, et al.Flexoelectricity in solids: Progress, challenges, and perspectives. Prog Mater Sci2019; 106: 100570–100570.
4.
MaWHCrossLE. Flexoelectricity of barium titanate. Appl Phys Lett2006; 88: 232902–232902.
5.
MajdoubMSSharmaPCaginT. Enhanced size-dependent piezoelectricity and elasticity in nanostructures due to the flexoelectric effect. Phys Rev B2008; 77: 125424–125424.
6.
ZhuJChenTShuL, et al.Flexoelectric fatigue in (K,Na,Li)(Nb,Sb)O3 ceramics. Appl Phys Lett2018; 113: 182901–182901.
7.
SuSHuangHLiuY, et al.Wrinkling of flexoelectric nano-film/substrate systems. J Phys D: Appl Phys2018; 51: 075309–075309.
8.
SamaniMSEBeniYT. Size dependent thermo-mechanical buckling of the flexoelectric nanobeam. Mater Res Express2018; 5(8): 085018–085018.
9.
ZengSWangBLWangKF. Static stability analysis of nanoscale piezoelectric shells with flexoelectric effect based on couple stress theory. Microsyst Technol2018; 24: 2957–2967.
10.
HamdiaKMGhasemiHZhuangXY, et al.Sensitivity and uncertainty analysis for flexoelectric nanostructures. Comput Method Appl M2018; 337: 95–109.
11.
GhasemiHParkHSRabczukT. A multi-material level set-based topology optimization of flexoelectric composites. Comput Method Appl M2018; 332: 47–62.
12.
GhasemiHParkHSRabczukT. A level-set based IGA formulation for topology optimization of flexoelectric materials. Comput Method Appl M2017; 313: 239–258.
13.
YanXHuangWBKwonSR, et al.A sensor for the direct measurement of curvature based on flexoelectricity. Smart Mater Struct2013; 22: 085016–085016.
14.
HuangWBKwonSRZhangSJ, et al.A trapezoidal flexoelectric accelerometer. J Intell Mater Syst Struct2014; 25: 271–277.
15.
KwonSRHuangWBZhangSJ, et al.Study on a flexoelectric microphone using barium strontium titanate. J Micromech Microeng2016; 26: 045001–045001.
16.
LiuKZhangSWuT, et al.Experimental decoupling of cylindrical flexoelectric coefficients. Appl Phys Lett2018; 113: 102902–102902.
17.
LiHHuKMTzouHS. Distributed flexoelectric modal signals on circular cylindrical shells. Proc IMechE, Part C: J Mech Eng Sci2018; 232: 952–961.
18.
HuSDLiHTzouHS. Distributed flexoelectric structural sensing: Theory and experiment. J Sound Vib2015; 348: 126–136.
19.
HuSDLiHTzouHS. Comparison of flexoelectric and piezoelectric dynamic signal responses on flexible rings. J Intell Mater Syst Struct2014; 25: 832–844.
20.
LiHHuSDTzouHS. Modal signal analysis of conical shells with flexoelectric sensors. J Intell Mater Syst Struct2015; 26: 1551–1563.
21.
ZhangXFTzouH. Theoretical and experimental studies of a piezoelectric ring energy harvester. J Intell Mater Syst Struct2019; 30: 998–1009.
22.
TzouHSZhangXF. A flexoelectric double-curvature nonlinear shell energy harvester. J Vib Acoust2016; 138: 031006–031006.
23.
YanZ. Modeling of a nanoscale flexoelectric energy harvester with surface effects. Physica E2017; 88: 125–132.
24.
LinXSuYChenB, et al.Effects of tip mass on performance of cantilever beam flexoelectric energy harvesters. J Xiamen Univ Nat Sci2019; 58: 87–95.
25.
SuYLinXHuangR, et al.Analytical electromechanical modeling of nanoscale flexoelectric energy harvesting. Appl Sci2019; 9(11): 2273–2273.
26.
ShenZYChenW. Converse flexoelectric effect in comb electrode piezoelectric microbeam. Phys Lett A2012; 376: 1661–1663.
27.
FuJYZhuWYLiN, et al.Experimental studies of the converse flexoelectric effect induced by inhomogeneous electric field in a barium strontium titanate composition. J Appl Phys2006; 100: 024112–024112.
28.
BaskaranSThiruvannamalaiSHeoH, et al.Converse piezoelectric responses in nonpiezoelectric materials implemented via asymmetric configurations of electrodes. J Appl Phys2010; 108: 064116–064116.
29.
MaWH. A study of flexoelectric coupling associated internal electric field and stress in thin film ferroelectrics. Phys Status Solidi B Basic Res2008; 245: 761–768.
30.
TzouHDengBLLiHY. Flexoelectric actuation and vibration control of ring shells. J Vib Acoust2017; 139: 7–7.
31.
FanMTzouH. Vibration control with the converse flexoelectric effect on the laminated beams. J Intell Mater Syst Struct2019; 30: 2556–2566.
32.
FanMDengBLTzouHS. Dynamic flexoelectric actuation and vibration control of beams. J Vib Acoust2018; 140: 041005–041005.
33.
Zhang XF, Li H and Tzou HS. Vibration control of a cantilever beam by metal-core flexoelectric and piezoelectric fibers. In: ASME 2014 international mechanical engineering congress & exposition, IMECE2014, Montreal, Quebec, Canada, 14–20 November 2014, paper No. IMECE2014-37772, p. V04BTA063.
34.
MaWHCrossLE. Observation of the flexoelectric effect in relaxor ceramics. Appl Phys Lett2001; 78: 2920–2921.
35.
AgroninAMolotskiiMRosenwaksY, et al.Dynamics of ferroelectric domain growth in the field of atomic force microscope. J Appl Phys2006; 99: 104102–104102.
36.
Abplanalp M. Piezoresponse scanning force microscopy of ferroelectric domains. PhD Thesis, Swiss Federal Institute of Technology, Switzerland, 2001.
37.
TzouHS. Piezoelectric shells: Sensing, energy harvesting and distributed control, Dordrecht: Springer, 2019.
38.
SoedelW. Vibrations of shells and plates, New York: Dekker, 1993.
39.
YueHHSunGLDengZQ, et al.Distributed shell control with a new multi-DOF photostrictive actuator design. J Sound Vib2010; 329: 3647–3659.
40.
BaskaranSHeXTWangY, et al.Strain gradient induced electric polarization in a-phase polyvinylidene fluoride films under bending conditions. J Appl Phys2012; 111: 014109–014109.
