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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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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