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.

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Grahic Jump Location
Fig. 1

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

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. 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. 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. 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)




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