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Research Papers

Dynamic Flexoelectric Actuation and Vibration Control of Beams

[+] Author and Article Information
Mu Fan

State Key Laboratory of Mechanics and Control
of Mechanical Structures,
Interdisciplinary Research Institute of Aeronautics
and Astronautics,
Nanjing University of Aeronautics
and Astronautics,
Room 217, Building A18, #29 Yu Dao Street,
Nanjing 210016, China
e-mail: mfanz@nuaa.edu.cn

Bolei Deng

StrucTronics and Control Lab,
School of Aeronautics and Astronautics,
Zhejiang University,
Hangzhou 310058, China
e-mail: dengbolei@zju.edu.cn

Hornsen Tzou

Fellow ASME
State Key Laboratory of Mechanics and Control
of Mechanical Structures,
Interdisciplinary Research Institute of Aeronautics
and Astronautics,
Nanjing University of Aeronautics
and Astronautics,
Room 202, Building A18, #29 Yu Dao Street,
Nanjing 210016, China
e-mail: hstzou@nuaa.edu.cn

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 4, 2017; final manuscript received January 5, 2018; published online February 23, 2018. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 140(4), 041005 (Feb 23, 2018) (10 pages) Paper No: VIB-17-1191; doi: 10.1115/1.4039238 History: Received May 04, 2017; Revised January 05, 2018

A flexoelectric cantilever beam actuated by the converse flexoelectric effect is evaluated and its analytical and experimental data are compared in this study. A line-electrode on the top beam surface and a bottom surface electrode are used to generate an electric field gradient in the beam, so that internal stresses can be induced and applied to distributed actuations. The dynamic control effectiveness of the beam is investigated with a mathematical model and is validated by laboratory experiments. Analyses show that the actuation stress induced by the converse flexoelectric effect is in the longitudinal direction and results in a bending control moment to the flexoelectric beam since the stress in the thickness is inhomogeneous. It is found that thinner line-electrode radius and thinner flexoelectric beam lead to larger control effects on the beam. The position of the line-electrode on the top surface of the beam also influences the control effect. When the line-electrode is close to the fixed end, it induces a larger tip displacement than that is close to the free end. Analytical results agree well with laboratory experimental data. This study of flexoelectric actuation and control provides a fundamental understanding of flexoelectric actuation mechanisms.

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References

Soedel, W. , 2004, Vibrations of Shells and Plates—Revised and Expanded, 3rd ed., Marcel Dekker, New York.
Qatu, M.-S. K. , 2004, Vibration of Laminated Shells and Plates, Elsevier, San Diego, CA.
Tzou, H. S. , and Ye, R. , 1994, “ Piezothermoelasticity and Precision Control of Piezoelectric Systems: Theory and Finite Element Analysis,” ASME J. Vib. Acoust., 116(4), pp. 489–495. [CrossRef]
Tzou, H. , and Hollkamp, J. , 1999, “ Collocated Independent Modal Control With Self-Sensing Orthogonal Piezoelectric Actuators—Theory and Experiment,” Smart Mater. Struct., 3(3), pp. 277–284. [CrossRef]
Bao, Y. , Tzou, H. S. , and Venkayya, V. B. , 1998, “ Analysis of Non-Linear Piezothermoelastic Laminated Beams With Electric and Temperature Effects,” J. Sound Vib., 209(3), pp. 505–518. [CrossRef]
Wang, D. W. , Tzou, H. S. , and Lee, H. J. , 2004, “ Control of Nonlinear Electro/Elastic Beam and Plate Systems (Finite Element Formulation and Analysis),” ASME J. Vib. Acoust., 126(1), pp. 63–70. [CrossRef]
Tzou, H. S. , and Ye, R. , 1996, “ Analysis of Piezoelastic Structures With Laminated Piezoelectric Triangle Shell Elements,” AIAA J., 34(1), pp. 110–115. [CrossRef]
Bergamini, A. , Delpero, T. , De, S. L. , Di, L. L. , Ruzzene, M. , and Ermanni, P. , 2014, “ Phononic Crystal With Adaptive Connectivity,” Adv. Mater., 26(9), pp. 1343–1347. [CrossRef] [PubMed]
Tzou, H. S. , and Gadre, M. , 1989, “ Theoretical Analysis of a Multi-Layered Thin Shell Coupled With Piezoelectric Shell Actuators for Distributed Vibration Controls,” J. Sound Vib., 132(3), pp. 433–450. [CrossRef]
Yan, X. , Huang, W. , Ryung Kwon, S. , Yang, S. , Jiang, X. , and Yuan, F. G. , 2013, “ A Sensor for the Direct Measurement of Curvature Based on Flexoelectricity,” Smart Mater. Struct., 22(8), pp. 1–8. [CrossRef]
Huang, W. , Kwon, S. R. , Zhang, S. , Yuan, F. G. , and Jiang, X. , 2014, “ A Trapezoidal Flexoelectric Accelerometer,” J. Intell. Mater. Syst. Struct., 25(3), pp. 271–277. [CrossRef]
Kwon, S. R. , Zhang, S. , Yuan, F. G. , and Jiang, X. , 2014, “ A New Type of Microphone Using Flexoelectric Barium Strontium Titanate,” Proc. SPIE, 9062, pp. 2978–2982.
Hu, S. D. , Li, H. , and Tzou, H. S. , 2015, “ Distributed Flexoelectric Structural Sensing: Theory and Experiment,” J. Sound Vib., 348, pp. 126–136. [CrossRef]
Fu, J. Y. , Zhu, W. , Li, N. , and Smith, N. B. , 2007, “ Gradient Scaling Phenomenon in Microsize Flexoelectric Piezoelectric Composites,” Appl. Phys. Lett., 91(18), p. 182910. [CrossRef]
Kogan, S. M. , 1964, “ Piezoelectric Effect During Inhomogeneous Deformation and Acoustic Scattering of Carriers in Crystals,” Sov. Phys.-Solid States, 5(10), pp. 2069–2070.
Tagantsev, A. K. , 1986, “ Piezoelectricity and Flexoelectricity in Crystalline Dielectrics,” Phys. Rev. B, 34(8), pp. 5883–5889. [CrossRef]
Todorov, A. T. , Petrov, A. G. , and Fendler, J. H. , 1994, “ First Observation of the Converse Flexoelectric Effect in Bilayer Lipid Membranes,” J. Phys. Chem., 98(12), pp. 3076–3079. [CrossRef]
Baskaran, S. , Thiruvannamalai, S. , Heo, H. , Lee, H. J. , Francis, S. M. , Ramachandran, N. , and Fu, J. Y. , 2010, “ Converse Piezoelectric Responses in Nonpiezoelectric Materials Implemented Via Asymmetric Configurations of Electrodes,” J. Appl. Phys., 108(6), p. 064114. [CrossRef]
Fu, J. Y. , Zhu, W. , Li, N. , and Cross, L. E. , 2006, “ Experimental Studies of the Converse Flexoelectric Effect Induced by Inhomogeneous Electric Field in a Barium Strontium Titanate Composition,” J. Appl. Phys., 100(2), pp. 6394–6401. [CrossRef]
Shen, Z. , and Chen, W. , 2012, “ Converse Flexoelectric Effect in Comb Electrode Piezoelectric Microbeam,” Phys. Lett. A, 376(19), pp. 1661–1663. [CrossRef]
Hu, S. D. , Li, H. , and Tzou, H. S. , 2011, “Static Nano-Control of Cantilever Beams Using the Inverse Flexoelectric Effect,” ASME Paper No. IMECE2011-65123.
Griffiths, D. J. , 1999, Introduction to Electrodynamics, 3rd ed., Prentice Hall, Upper Saddle River, NJ.
Hu, S. D. , Li, H. , and Tzou, H. S. , 2014, “ Comparison of Flexoelectric and Piezoelectric Dynamic Signal Responses on Flexible Rings,” J. Intell. Mater. Syst. Struct., 25(7), pp. 832–844. [CrossRef]
Tzou, H. S. , 1993, Piezoelectric Shells: Distributed Sensing and Control, Kluwer Academic Publishers, London. [CrossRef]
Tzou, H. , Deng, B. , and Huiyu, L. I. , 2017, “ Flexoelectric Actuation and Vibration Control of Ring Shells,” ASME J. Vib. Acoust., 139(3), p. 031014. [CrossRef]

Figures

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Fig. 1

Schematic diagram of flexoelectric beam model

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Fig. 2

Solution of the two-dimensional electric field problem with the method of images

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Fig. 4

Spatial distribution of induced longitudinal normal stress

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Fig. 3

Spatial distribution of the potential field and the electric field

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Fig. 11

Experimental setup for evaluating flexoelectric actuation effect

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Fig. 12

Measured and predicted data of tip displacements with (a) R = 150 μm, (b) R = 200 μm, and (c) R = 250 μm

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Fig. 5

Longitudinal distribution of the induced moment under different line-electrode radius

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Fig. 6

Longitude distribution of the induced moment under different beam thickness

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Fig. 7

Tip displacement with the line-electrode location under different line-electrode radius

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Fig. 8

Tip displacement with the line-electrode location under different beam thickness

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Fig. 9

Tip displacement with the line-electrode location under (a) mode 1, (b) mode 2, and (c) mode 3

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Fig. 10

The flexoelectric beam and its eight line-electrodes

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