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Research Papers

Flexoelectric Actuation and Vibration Control of Ring Shells

[+] Author and Article Information
Hornsen Tzou

State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Interdisciplinary Research Institute of
Aeronautics and Astronautics,
College of Aerospace Engineering,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, China
e-mail: hstzou@nuaa.edu.cn

Bolei Deng

StrucTronics and Control Laboratory,
School of Aeronautics and Astronautics,
Zhejiang University,
Hangzhou 310027, China

Huiyu Li

The State Key Laboratory of Fluid Power Transmission and Control,
School of Mechanical Engineering,
Zhejiang University,
Hangzhou 310027, China

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 31, 2015; final manuscript received January 10, 2017; published online April 24, 2017. Editor: I. Y. (Steve) Shen.

J. Vib. Acoust 139(3), 031014 (Apr 24, 2017) (7 pages) Paper No: VIB-15-1198; doi: 10.1115/1.4036097 History: Received May 31, 2015; Revised January 10, 2017

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.

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References

Kogan, S. M. , 1964, “ Piezoelectric Effect During Inhomogeneous Deformation and Acoustic Scattering of Carriers in Crystals,” Sov. Phys. Solid State, 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. Chem. Phys., 98(12), pp. 3076–3079. [CrossRef]
Mindlin, R. D. , 1969, “ Continuum and Lattice Theories of Influence of Electromechanical Coupling on Capacitance of Thin Dielectric Films,” Int. J. Solids Struct., 5(11), pp. 1197–1208. [CrossRef]
Mindlin, R. D. , and Eshel, N. N. , 1968, “ On First Strain-Gradient Theories in Linear Elasticity,” Int. J. Solids Struct., 4(1), pp. 109–124. [CrossRef]
Sahin, E. , and Dost, S. , 1988, “ A Strain-Gradients Theory of Elastic Dielectrics With Spatial-Dispersion,” Int. J. Eng. Sci., 26(12), pp. 1231–1245. [CrossRef]
Cross, L. E. , 2006, “ Flexoelectric Effects: Charge Separation in Insulating Solids Subjected to Elastic Strain Gradients,” J. Mater. Sci., 41(1), pp. 53–63. [CrossRef]
Baskaran, S. , He, X. , and Chen, Q. , 2011, “ Experimental Studies on the Direct Flexoelectric Effect in α-Phase Polyvinylidene Fluoride Films,” Appl. Phys. Lett., 98(24), p. 242901. [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), p. 024112. [CrossRef]
Agronin, A. , Molotskii, M. , Rosenwaks, Y. , Rosenman, G. , Rodriguez, B. J. , Kigon, A. I. , and Gruverman, A. , 2006, “ Dynamics of Ferroelectric Domain Growth in the Field of Atomic Force Microscope,” J. Appl. Phys., 99(10), p. 104102. [CrossRef]
Zubko, P. , Catalan, G. , Buckley, A. , Welche, P. R. L. , and Scott, J. F. , 2007, “ Strain-Gradient-Induced Polarization in SrTiO3 Single Crystals,” Phys. Rev. Lett., 99(16), p. 167601. [CrossRef] [PubMed]
Hu, S. D. , Li, H. , and Tzou, H. S. , 2013, “ Flexoelectric Responses of Circular Rings,” ASME J. Vib. Acoust., 135(2), p. 021003. [CrossRef]
Rao, Z. , Hu, S. D. , and Tzou, H. S. , 2011, “ Diagonal Flexoelectric Sensor on Cylindrical Shell Substructure,” Symposium on Piezoelectricity, Acoustic Waves, and Device Applications (SPAWDA), Shenzhen, China, Dec. 9–11, pp. 106–111.
Tzou, H. S. , and Zhang, X. F. , 2016, “ A Flexoelectric Double-Curvature Nonlinear Shell Energy Harvester,” ASME J. Vib. Acoust., 138(2), p. 031006. [CrossRef]
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]
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.
Soedel, W. , 1993, Vibrations of Shells and Plates, Marcel Dekker, New York.
Tzou, H. S. , Zhong, J. P. , and Natori, M. C. , 1993, “ Sensor Mechanics of Distributed Shell Convolving Sensors Applied to Flexible Rings,” ASME J. Vib. Acoust., 115(1), pp. 40–46. [CrossRef]
Tzou, H. S. , Zhong, J. P. , and Hollkamp, J. J. , 1994, “ Spatially Distributed Orthogonal Piezoelectric Shell Actuators: Theory and Applications,” J. Sound Vib., 177(3), pp. 363–378. [CrossRef]
Tzou, H. S. , 1993, Piezoelectric Shells: Distributed Sensing & Control of Continua, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Abplanalp, M. , 2001, “ Piezoresponse Scanning Force Microscopy of Ferroelectric Domains,” Ph.D. dissertation, Swiss Federal Institute of Technology, Zürich, Switzerland.

Figures

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Fig. 1

Schematic diagram of the elastic ring

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Fig. 2

A ring model of flexoelectric actuation

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Fig. 3

The transverse distribution of the electric field gradient

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Fig. 4

Circumferential distribution of the actuation

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Fig. 5

The distribution of the circumferential loading induced by actuator

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Fig. 6

Distribution of the induced circumferential loading

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Fig. 7

The distribution of the transverse loading induced by actuator

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Fig. 8

Distribution of the induced transverse loading

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Fig. 9

Circumferential distribution of the total induced flexoelectric actuation near the AFM probe

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Fig. 10

Maximal controllable displacement (k = 2–6 ring modes) with flexoelectric patch thickness

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Fig. 11

Maximal controllable displacement (k = 2–6 ring modes) with the radius of AFM probe

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Fig. 12

Maximal controllable displacement (k = 2–6 ring modes) with the ring thickness

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Fig. 13

Maximal controllable displacement (k = 2–6 ring modes) with the ring radius

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