0
Research Papers

Flexoelectric Responses of Circular Rings

[+] Author and Article Information
Shundi Hu

e-mail: shundihu@zju.edu.cn

Hua Li

e-mail: Lhlihua@gmail.com

Hornsen Tzou

e-mail: hstzou@zju.edu.cn
StrucTronics and Control Lab,
School of Aeronautics and Astronautics,
Zhejiang University,
Hangzhou, Zhejiang 310027, P.R.C.

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received April 13, 2011; final manuscript received May 20, 2012; published online February 25, 2013. Assoc. Editor: Wei-Hsin Liao.

J. Vib. Acoust 135(2), 021003 (Feb 25, 2013) (8 pages) Paper No: VIB-11-1075; doi: 10.1115/1.4023044 History: Received April 13, 2011; Revised May 20, 2012

Dynamic sensing is essential to effective closed-loop control of precision structures. In a centrosymmetric crystal subjected to inhomogeneous deformation, when piezoelectricity is absent, only the strain gradient contributes to the polarization known as the “flexoelectricity.” In this study, a flexoelectric layer is laminated on a circular ring shell to monitor the natural modal signal distributions. Due to the strain gradient characteristic, only the bending strain component contributes to the output signal. The total flexoelectric signal consists of two components respectively induced by the transverse modal oscillation and the circumferential modal oscillation. Analog to the signal analysis, the flexoelectric sensitivity is also studied in two forms: a transverse sensitivity induced by the transverse modal oscillation and a transverse sensitivity induced by the circumferential modal oscillation. Analysis data suggest that the transverse modal oscillation dominates the flexoelectric signal generation and its magnitude/distribution shows nearly the same as the total signal. Furthermore, voltage signals and signal sensitivities are evaluated with respect to ring mode, sensor segment size, ring thickness, and ring radius in case studies. The total signal increases with mode numbers and sensor thicknesses, decreases with sensor segment size and ring radii, and remains the same with different ring thicknesses.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Kogan, M. S., 1964, “Piezoelectric Effect During Inhomogeneous Deformation and Acoustic Scattering of Carriers in Crystals,” Sov. Phys. Solid State, 5(10), pp. 2069–2070.
Tagantsev, K., 1986, “Piezoelectricity and Flexoelectricity in Crystalline Dielectrics,” Phys. Rev. B, 34(8), pp. 5883–5889. [CrossRef]
Indenbom, V. L., Loginov, E. B., and Osipov, M. A., 1981, “Flexoelectric Effect and Crystal-Structure,” Kristallografiya, 26(6), pp. 1157–1162.
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]
Maskevich, V. S., and Tolpygo, K. V., 1957, “Investigation of Long-Wavelength Vibrations of Diamond-Type Crystals With an Allowance for Long-Range Forces,” Sov. Phys. JETP, 5, pp. 435–437.
Bursian, E. V., and Trunov, N. N., 1974, “Nonlocal Piezo-Effect,” Fiz. Tverd. Tela, 16(4), pp. 1187–1190.
Marvan, M., and Havránek, A., 1988, “Flexoelectric Effect in Elastomers,” Prog. Colloid Polym. Sci., 78, pp. 33–36. [CrossRef]
Ma, W., and Cross, L. E., 2001, “Observation of the Flexoelectric Effect in Relaxor Pb(Mg1/3Nb2/3)O3 Ceramics,” Appl. Phys. Lett., 78(19), pp. 2920–2921. [CrossRef]
Ma, W. H., and Cross, L. E., 2005, “Flexoelectric Effect in Ceramic Lead Zirconate Titanate,” Appl. Phys. Lett., 86(7), p. 072905. [CrossRef]
Ma, W., and Cross, L. E., 2002, “Flexoelectric Polarization of Barium Strontium Titanate in the Paraelectric State,” Appl. Phys. Lett., 81(18), pp. 3440–3442. [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]
Catalan, G., Sinnamon, L. J., and Gregg, J. M., 2004, “The Effect of Flexoelectricity on the Dielectric Properties of Inhomogeneously Strained Ferroelectric Thin Films,” J. Phys.: Condens. Matter, 16(13), pp. 2253–2264. [CrossRef]
Maranganti, R., Sharma, N. D., and Sharma, P., 2006, “Electromechanical Coupling in Nonpiezoelectric Materials Due to Nanoscale Nonlocal Size Effects: Green's Function Solutions and Embedded Inclusions,” Phys. Rev. B, 74(1), p. 014110. [CrossRef]
Kalinin, S. V., and Meunier, V., 2008, “Electronic Flexoelectricity in Low-Dimensional Systems,” Phys. Rev. B, 77(3), p. 033403. [CrossRef]
Majdoub, M. S., Sharma, P., and Cagin, T., 2008, “Enhanced Size-Dependent Piezoelectricity and Elasticity in Nanostructures Due to the Flexoelectric Effect,” Phys. Rev. B, 77(12), p. 125424. [CrossRef]
Majdoub, M. S., Sharma, P., and Cagin, T., 2008, “Dramatic Enhancement in Energy Harvesting for a Narrow Range of Dimensions in Piezoelectric Nanostructures,” Phys. Rev. B, 78(12), p. 121407. [CrossRef]
Fousek, J., Cross, L. E., and Litvin, D. B., 1999, “Possible Piezoelectric Composites Based on the Flexoelectric Effect,” Mater. Lett., 39(5), pp. 287–291. [CrossRef]
Zhu, W. Y., Fu, J. Y., Li, N., and Cross, L., 2006, “Piezoelectric Composite Based on the Enhanced Flexoelectric Effects,” Appl. Phys. Lett., 89(19), p. 192904. [CrossRef]
Tzou, H. S., Bao, Y., and Venkayya, V. B., 1996, “Study of Segmented Transducers Laminated on Cylindrical Shells, Part 1: Sensor Patches,” J. Sound Vib., 197(2), pp. 207–224. [CrossRef]
Howard, R. V., Chai, W. K., and Tzou, H. S., 2001, “Modal Voltages of Linear and Nonlinear Structures Using Distributed Artificial Neurons,” Mech. Syst. Signal Process., 15(3), pp. 629–640. [CrossRef]
Tzou, H. S., and Chou, C. S., 2001, “Sensors and Actuators,” Encyclopedia of Vibration, S. G.Braun, D. J. Ewins, and S. S. Rao, eds., Academic Press, London, pp. 1134–1144.
Tzou, H. S., Smithmaitrie, P., and Ding, J. H., 2002, “Sensor Electromechanics and Distributed Signal Analysis of Piezo(Electric)–Elastic Spherical Shells,” Mech. Syst. Signal Process., 16(2–3), pp. 185–199. [CrossRef]
Tzou, H. S., and Wang, D. W., 2002, “Micro-Sensing Characteristics and Modal Voltages of Piezoelectric Laminated Linear and Nonlinear Toroidal Shells,” J. Sound Vib., 254(2), pp. 203–218. [CrossRef]
Tzou, H. S., and Ding, J. H., 2004, “Distributed Modal Voltages of Nonlinear Paraboloidal Shells With Distributed Neurons,” ASME J. Vib. Acoust., 126(1), pp. 47–53. [CrossRef]
Tzou, H. S., Chai, W. K., and Wang, D. W., 2003, “Modal Voltages and Micro-Signal Analysis of Conical Shells of Revolution,” J. Sound Vib., 260(4), pp. 589–609. [CrossRef]
Chai, W. K., Smithmaitrie, P., and Tzou, H. S., 2004, “Neural Potentials and Micro-Signals of Nonlinear Deep and Shallow Conical Shells,” Mech. Syst. Signal Process., 18(4), pp. 959–975. [CrossRef]
Yue, H. H., Deng, Z. Q., and Tzou, H. S., 2008, “Spatially Distributed Modal Signals of Free Shallow Membrane Shell Structronic System,” J. Commun. Nonlinear Sci. Numer. Simul., 13(9), pp. 2041–2050. [CrossRef]
Li, H., Chen, Z. B., and Tzou, H. S., 2010, “Torsion and Transverse Sensing of Conical Shells,” Mech. Syst. Signal Process., 24(7), pp. 2235–2249. [CrossRef]
Tzou, H. S., Zhong, J. P., and Natori, M., 1993, “Sensor Mechanics of Distributed Shell Convolving Sensors Applied to Flexible Rings,” ASME J. Vib. Acoust., 115(1), pp. 40–46. [CrossRef]
Soedel, W., 1993, Vibrations of Shells and Plates, M. Dekker, New York.
Tzou, H. S., 1993, Piezoelectric Shells: Distributed Sensing & Control, Kluwer Academic Publishers, Dordrecht, Germany.
Kim, W., and Chung, J., 2002, “Free Non-Linear Vibration of a Rotating Thin Ring With the In-Plane and Out-of-Plane Motions,” J. Sound Vib., 258(1), pp. 167–178. [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]
Lin, Y. S., Chuang, C. C., Chu, C. C., and Tzou, H. S., 2009, “Modal Sensitivities, Spatial Signal Distribution and Average of Segmented Ring Sensors,” Proceedings of the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE2009), San Diego, CA, August 30-September 2, pp. 135–144.
Yang, J. S., Fang, H. Y., and Jiang, Q., 2000, “A Vibrating Piezoelectric Ceramic Shell as a Rotation Sensor,” Smart Mater. Struct., 9(4), pp. 445–451. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Ring with a flexoelectric layer (left) and a segmented sensor patch (right)

Grahic Jump Location
Fig. 2

Maximum voltages (n = 2–6 ring modes) versus sensor segment size (upper-left: (ϕs)3: the transverse signal, upper-right: (ϕs)ψ: the circumferential signal, bottom: ϕs: the total signal)

Grahic Jump Location
Fig. 3

Maximum voltages (n = 2–6 ring modes) versus ring thickness (upper-left: (ϕs)3, upper-right: (ϕs)ψ, bottom: ϕs)

Grahic Jump Location
Fig. 4

Maximum voltages (n = 2–6 ring modes) versus sensor thickness (upper-left: (ϕs)3, upper-right: (ϕs)ψ, bottom: ϕs)

Grahic Jump Location
Fig. 5

Maximum voltages (n = 2–6 ring modes) versus neutral surface ring radius (upper-left: (ϕs)3, upper-right: (ϕs)ψ, bottom: ϕs)

Grahic Jump Location
Fig. 6

Sensitivities (n = 2–6 ring modes) versus ring thickness (left: transverse sensitivity Stt defined by the circumferential modal oscillation and right: transverse sensitivity Sct defined by the transverse modal oscillation)

Grahic Jump Location
Fig. 7

Sensitivities (n = 2–6 ring modes) versus sensor thickness (left: Stt, right: Sct)

Grahic Jump Location
Fig. 8

Sensitivities (n = 2–6 ring modes) versus ring radius (left: Stt, right: Sct)

Grahic Jump Location
Fig. 9

Sensitivities (n = 2–6 ring modes) with various segment sizes (left: Stt, right: Sct)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In