Study on the Radial Vibration of a Thin Annular Vibrator with Multi-Radial Slots

Liu Shiqing; Ma Leilei; Liu Yifeng; Li Dan; Chen Zhaojiang

doi:doi:10.11648/j.ajasr.20190501.11

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Study on the Radial Vibration of a Thin Annular Vibrator with Multi-Radial Slots

Liu Shiqing, Ma Leilei, Liu Yifeng, Li Dan, Chen Zhaojiang

Published in American Journal of Applied Scientific Research (Volume 5, Issue 1)

Received: 31 December 2018 Accepted: 21 January 2019 Published: 28 March 2019

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Abstract

The radial vibration of a thin annular vibrator with multiple radial slots is studied. Based on the electro-mechanical analogy, the equivalent circuit and the frequency equation of the slotting thin annular vibrator in radial vibration are derived. By numerical simulations, the influences of the radius ratio of the thin annular vibrator on its displacement amplitude amplification factor and the first- and the second-order resonance frequency have been investigated. The analysis results manifest that the first-order amplitude amplification factor and the resonance frequency of the ring increase with the increases of the radius ratio, and the situation is the opposite for the relation between the second-order amplitude amplification factor and the radius ratio. The Finite Element Method (FEM) is employed for the simulation of the radial vibration of the thin annular vibrator. The FEM results are in good agreement with the analytical solution.

Published in	American Journal of Applied Scientific Research (Volume 5, Issue 1)
DOI	10.11648/j.ajasr.20190501.11
Page(s)	1-5
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Thin Annular Vibrator, Multiple Radial Slots, Radial Vibration, Resonance Frequency, The Amplitude Amplification Factor, FEM Simulation

References

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[2]	N A Shvetsova, D I Makarev, I A Shvetsov, et al. New Techniques and Designs of Focusing Piezoelectric Transducers for Ultrasonic Diagnostics and Therapy [J]. Bulletin of the Russian Academy of Sciences: Physics, 2018, 82 (3): 251-256.
[3]	PI Jun. Longitudinal torsional vibration conversion of ring chute transmission rod [J]. Chinese Journal of Mechanical Engineering, 2008, 44 (5): 242-248.
[4]	J Tsujino, T ueoka, K Otoda, et al. One-dimensional longitudinal torsional vibration converter with multiple diagonally slitted parts [J]. Ultrasonics, 2000, 38 (8): 72-76.
[5]	LIN Dzon-mou. Equivalent circuit of a vibrating system magnetostrictive transducer-concentrator-sample. Procesdings of vibration problems (Poland), 1963, 4: 175-184.
[6]	K Siegert, J Uner. Superimposing ultrasonic waves on the dies in tube and wire drawing [J]. Journal of Engineering Material and Technology, 2001, 123 (4): 517-523.
[7]	D H Xiang, X T Zhi, G X Yue, B Zhao, Q T Fan. Experimental Study on Ultrasonic Vibration Dressing Wheel [J]. Advanced Materials Research, 2010, 135: 260-264.
[8]	KANG Jae-Hoon. Three-dimensional vibration analysis of thick, circular and annular plates with nonlinear thickness variation [J]. Computers and Structures, 2003, 81: 1663-1675.
[9]	LIU Shiqing, YANG Xianli, LI Luhua. Radial vibration of a slit-type annular ultrasonic concentrator [J]. Chinese Journal of Acoustics, 2015, 34 (2): 153-165.
[10]	LIN Shuyu. Radial vibration and equivalent circuit of thin elastic circular rings [J]. ACTA ACUSTICA, 2003, 28 (2): 102-106.
[11]	LIN Shuyu. Coupled vibration of isotropic metal hollow cylinders with lager geometrical dimensions [J]. Journal of Sound and Vibration, 2007, 305 (1-2): 308-316.

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APA Style

Liu Shiqing, Ma Leilei, Liu Yifeng, Li Dan, Chen Zhaojiang. (2019). Study on the Radial Vibration of a Thin Annular Vibrator with Multi-Radial Slots. American Journal of Applied Scientific Research, 5(1), 1-5. https://doi.org/10.11648/j.ajasr.20190501.11

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ACS Style

Liu Shiqing; Ma Leilei; Liu Yifeng; Li Dan; Chen Zhaojiang. Study on the Radial Vibration of a Thin Annular Vibrator with Multi-Radial Slots. Am. J. Appl. Sci. Res. 2019, 5(1), 1-5. doi: 10.11648/j.ajasr.20190501.11

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AMA Style

Liu Shiqing, Ma Leilei, Liu Yifeng, Li Dan, Chen Zhaojiang. Study on the Radial Vibration of a Thin Annular Vibrator with Multi-Radial Slots. Am J Appl Sci Res. 2019;5(1):1-5. doi: 10.11648/j.ajasr.20190501.11

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@article{10.11648/j.ajasr.20190501.11,
  author = {Liu Shiqing and Ma Leilei and Liu Yifeng and Li Dan and Chen Zhaojiang},
  title = {Study on the Radial Vibration of a Thin Annular Vibrator with Multi-Radial Slots},
  journal = {American Journal of Applied Scientific Research},
  volume = {5},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ajasr.20190501.11},
  url = {https://doi.org/10.11648/j.ajasr.20190501.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajasr.20190501.11},
  abstract = {The radial vibration of a thin annular vibrator with multiple radial slots is studied. Based on the electro-mechanical analogy, the equivalent circuit and the frequency equation of the slotting thin annular vibrator in radial vibration are derived. By numerical simulations, the influences of the radius ratio of the thin annular vibrator on its displacement amplitude amplification factor and the first- and the second-order resonance frequency have been investigated. The analysis results manifest that the first-order amplitude amplification factor and the resonance frequency of the ring increase with the increases of the radius ratio, and the situation is the opposite for the relation between the second-order amplitude amplification factor and the radius ratio. The Finite Element Method (FEM) is employed for the simulation of the radial vibration of the thin annular vibrator. The FEM results are in good agreement with the analytical solution.},
 year = {2019}
}

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TY  - JOUR
T1  - Study on the Radial Vibration of a Thin Annular Vibrator with Multi-Radial Slots
AU  - Liu Shiqing
AU  - Ma Leilei
AU  - Liu Yifeng
AU  - Li Dan
AU  - Chen Zhaojiang
Y1  - 2019/03/28
PY  - 2019
N1  - https://doi.org/10.11648/j.ajasr.20190501.11
DO  - 10.11648/j.ajasr.20190501.11
T2  - American Journal of Applied Scientific Research
JF  - American Journal of Applied Scientific Research
JO  - American Journal of Applied Scientific Research
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2471-9730
UR  - https://doi.org/10.11648/j.ajasr.20190501.11
AB  - The radial vibration of a thin annular vibrator with multiple radial slots is studied. Based on the electro-mechanical analogy, the equivalent circuit and the frequency equation of the slotting thin annular vibrator in radial vibration are derived. By numerical simulations, the influences of the radius ratio of the thin annular vibrator on its displacement amplitude amplification factor and the first- and the second-order resonance frequency have been investigated. The analysis results manifest that the first-order amplitude amplification factor and the resonance frequency of the ring increase with the increases of the radius ratio, and the situation is the opposite for the relation between the second-order amplitude amplification factor and the radius ratio. The Finite Element Method (FEM) is employed for the simulation of the radial vibration of the thin annular vibrator. The FEM results are in good agreement with the analytical solution.
VL  - 5
IS  - 1
ER  -

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Author Information

Liu Shiqing

College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, China
Ma Leilei

College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, China
Liu Yifeng

Institute of Acoustics, Chinese Academy of Sciences, Beijing, China
Li Dan

College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, China
Chen Zhaojiang

College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, China

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Plain Text BibTeX RIS

APA Style

Liu Shiqing, Ma Leilei, Liu Yifeng, Li Dan, Chen Zhaojiang. (2019). Study on the Radial Vibration of a Thin Annular Vibrator with Multi-Radial Slots. American Journal of Applied Scientific Research, 5(1), 1-5. https://doi.org/10.11648/j.ajasr.20190501.11

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ACS Style

Liu Shiqing; Ma Leilei; Liu Yifeng; Li Dan; Chen Zhaojiang. Study on the Radial Vibration of a Thin Annular Vibrator with Multi-Radial Slots. Am. J. Appl. Sci. Res. 2019, 5(1), 1-5. doi: 10.11648/j.ajasr.20190501.11

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AMA Style

Liu Shiqing, Ma Leilei, Liu Yifeng, Li Dan, Chen Zhaojiang. Study on the Radial Vibration of a Thin Annular Vibrator with Multi-Radial Slots. Am J Appl Sci Res. 2019;5(1):1-5. doi: 10.11648/j.ajasr.20190501.11

Copy | Download

@article{10.11648/j.ajasr.20190501.11,
  author = {Liu Shiqing and Ma Leilei and Liu Yifeng and Li Dan and Chen Zhaojiang},
  title = {Study on the Radial Vibration of a Thin Annular Vibrator with Multi-Radial Slots},
  journal = {American Journal of Applied Scientific Research},
  volume = {5},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ajasr.20190501.11},
  url = {https://doi.org/10.11648/j.ajasr.20190501.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajasr.20190501.11},
  abstract = {The radial vibration of a thin annular vibrator with multiple radial slots is studied. Based on the electro-mechanical analogy, the equivalent circuit and the frequency equation of the slotting thin annular vibrator in radial vibration are derived. By numerical simulations, the influences of the radius ratio of the thin annular vibrator on its displacement amplitude amplification factor and the first- and the second-order resonance frequency have been investigated. The analysis results manifest that the first-order amplitude amplification factor and the resonance frequency of the ring increase with the increases of the radius ratio, and the situation is the opposite for the relation between the second-order amplitude amplification factor and the radius ratio. The Finite Element Method (FEM) is employed for the simulation of the radial vibration of the thin annular vibrator. The FEM results are in good agreement with the analytical solution.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Study on the Radial Vibration of a Thin Annular Vibrator with Multi-Radial Slots
AU  - Liu Shiqing
AU  - Ma Leilei
AU  - Liu Yifeng
AU  - Li Dan
AU  - Chen Zhaojiang
Y1  - 2019/03/28
PY  - 2019
N1  - https://doi.org/10.11648/j.ajasr.20190501.11
DO  - 10.11648/j.ajasr.20190501.11
T2  - American Journal of Applied Scientific Research
JF  - American Journal of Applied Scientific Research
JO  - American Journal of Applied Scientific Research
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2471-9730
UR  - https://doi.org/10.11648/j.ajasr.20190501.11
AB  - The radial vibration of a thin annular vibrator with multiple radial slots is studied. Based on the electro-mechanical analogy, the equivalent circuit and the frequency equation of the slotting thin annular vibrator in radial vibration are derived. By numerical simulations, the influences of the radius ratio of the thin annular vibrator on its displacement amplitude amplification factor and the first- and the second-order resonance frequency have been investigated. The analysis results manifest that the first-order amplitude amplification factor and the resonance frequency of the ring increase with the increases of the radius ratio, and the situation is the opposite for the relation between the second-order amplitude amplification factor and the radius ratio. The Finite Element Method (FEM) is employed for the simulation of the radial vibration of the thin annular vibrator. The FEM results are in good agreement with the analytical solution.
VL  - 5
IS  - 1
ER  -

Copy | Download