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Modeling of MEMS Resonator Piezoelectric Disc Partially Covered with Electrodes

Received: 31 August 2016     Accepted: 26 September 2016     Published: 19 October 2016
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Abstract

The Legendre polynomial method has been extended to the modeling of MEMS resonator disc partially covered with electrodes. The disc has been divided into two areas: one with electrodes and the other without electrodes. For each area, The Maxwell equations and the piezoelectric constitutive equations of motion are studied and solved to yield a frequency response and electrical behavior of the MEMS resonator applying a semi analytical method based on a Legendre polynomials series and trigonometric functions. However, the method allows incorporating the boundary conditions directly into the governing equations by assuming position-dependent of elastic constants, mass density and delta functions. The alternating electrical source is described by specific terms which are also introduced into the equation of motion. The formalism has been developed which allows for both harmonic and modal analyses. In order to validate our polynomial approach, numerical results are presented such as resonant and anti-resonant frequencies, electric input admittance, electromechanical coupling coefficient and field profiles of fully and partially metallized PZT5A resonator discs. The results obtained were compared with those obtained by an approximated analytical method. The developed software proves to be very efficient to retrieve the contour modes of all orders.

Published in American Journal of Mechanics and Applications (Volume 4, Issue 1)
DOI 10.11648/j.ajma.20160401.11
Page(s) 1-9
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), 2016. Published by Science Publishing Group

Keywords

MEMS Resonators, Legendre Polynomial Approach, Centralized Metallization, Piezoelectric Resonator Disc, Electrical Admittance, Resonant, Anti-resonant Frequencies

References
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[5] D. W. Greve, J. J. Neumann, I. J. Oppenheim, S. P. Pessiki, D. Ozevin, Robust capacitive MEMS ultrasonics transducers for liquid immersion, IEEE Symp. Ultrason. Vol.1, pp. 581–584, 2003.
[6] D. K. Agrawal, P. Thiruvenkatanathan, J. Yan, A. A. Seshia, Electrically coupled MEMS oscillators, in: Joint Conf. IEEE Int. Freq. Control Eur. Freq. Time Forum (FCS), pp. 1-5, 2011.
[7] H. F. Tiersten, Linear piezoelectric plate vibration, Plenum, New York, 1969.
[8] IEEE Standard on Piezoelectricity, ANSI-IEEE Std. 176, IEEE New York, 1987.
[9] E. P Eer Nisse, “Variational Method for Electroelastic Vibration Analysis,” IEEE Trans. Sonics. Ultra. Vol. 14 (4), pp. 153–160, 1967.
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[12] H. A Kunkel, S. Locke, and B. Pikeroen, “Finite-Element Analysis of Vibrational Modes in Piezoelectric Ceramics Disks,” IEEE. Trans. Ultrason. Ferr. Freq. Cont, Vol. 37 (4), pp. 316–328, 1990.
[13] N. Guo, P. Cawley and D. Hitchings, “The Finite Element Analysis of the Vibration Characteristics of Piezoelectric Disks,” J Sound. Vib., Vol. 159 (1), pp. 115-138, 1992.
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[15] J. E. Lefebvre, V. Zhang, J. Gazalet, T. Gryba and V. Sadaune, “Acoustic Waves Propagation in Continuous Functionally Graded Plates: An Extension of the Legendre Polynomial Approach” IEEE. Trans. Ultrason. Ferr. Freq. Cont, Vol. 48 (5), pp. 1332-1340, 2001.
[16] J. Yu, J. E. Lefebvre and L. Elmaimouni, Toroidal wave in multilayered spherical curved plates, Journal of Sound and Vibration, Vol. 332 (11), pp. 2816-2830, 2013.
[17] L. Elmaimouni, J. E. Lefebvre, F. E. Ratolojanahary, A. Raherison, T. Gryba and J. Carlier, “Modal analysis and harmonic response of resonators: an extension of a mapped orthogonal functions technique” Wave Motion, Vol. 48 (1), pp. 93-104, 2011.
[18] L. Elmaimouni, J. E. Lefebvre, F. E. Ratolojanahary, A. Raherison, T. Gryba and J. Carlier, “Modal analysis and harmonic response of resonators: an extension of a mapped orthogonal functions technique” Wave Motion, Vol. 48 (1), pp. 93-104 (2011).
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[20] P. M. Rabotovao, F. E. Ratolojanahary, J. E. Lefebvre, A. Raherison, L. Elmaimouni, T. Gryba, and J. G. Yu, “Modeling of high contrast partially electroded resonators by means of a polynomial approach”, J. Applied Physics, Vol. 114 (12), pp. 124502, 2013.
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Cite This Article
  • APA Style

    Ismail Naciri, Lahoucine Elmaimouni, Jean-Etienne Lefebvre, Faniry Emilson Ratolojanahary, Mohamed Rguiti, et al. (2016). Modeling of MEMS Resonator Piezoelectric Disc Partially Covered with Electrodes. American Journal of Mechanics and Applications, 4(1), 1-9. https://doi.org/10.11648/j.ajma.20160401.11

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    ACS Style

    Ismail Naciri; Lahoucine Elmaimouni; Jean-Etienne Lefebvre; Faniry Emilson Ratolojanahary; Mohamed Rguiti, et al. Modeling of MEMS Resonator Piezoelectric Disc Partially Covered with Electrodes. Am. J. Mech. Appl. 2016, 4(1), 1-9. doi: 10.11648/j.ajma.20160401.11

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    AMA Style

    Ismail Naciri, Lahoucine Elmaimouni, Jean-Etienne Lefebvre, Faniry Emilson Ratolojanahary, Mohamed Rguiti, et al. Modeling of MEMS Resonator Piezoelectric Disc Partially Covered with Electrodes. Am J Mech Appl. 2016;4(1):1-9. doi: 10.11648/j.ajma.20160401.11

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  • @article{10.11648/j.ajma.20160401.11,
      author = {Ismail Naciri and Lahoucine Elmaimouni and Jean-Etienne Lefebvre and Faniry Emilson Ratolojanahary and Mohamed Rguiti and Tadeusz Gryba},
      title = {Modeling of MEMS Resonator Piezoelectric Disc Partially Covered with Electrodes},
      journal = {American Journal of Mechanics and Applications},
      volume = {4},
      number = {1},
      pages = {1-9},
      doi = {10.11648/j.ajma.20160401.11},
      url = {https://doi.org/10.11648/j.ajma.20160401.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajma.20160401.11},
      abstract = {The Legendre polynomial method has been extended to the modeling of MEMS resonator disc partially covered with electrodes. The disc has been divided into two areas: one with electrodes and the other without electrodes. For each area, The Maxwell equations and the piezoelectric constitutive equations of motion are studied and solved to yield a frequency response and electrical behavior of the MEMS resonator applying a semi analytical method based on a Legendre polynomials series and trigonometric functions. However, the method allows incorporating the boundary conditions directly into the governing equations by assuming position-dependent of elastic constants, mass density and delta functions. The alternating electrical source is described by specific terms which are also introduced into the equation of motion. The formalism has been developed which allows for both harmonic and modal analyses. In order to validate our polynomial approach, numerical results are presented such as resonant and anti-resonant frequencies, electric input admittance, electromechanical coupling coefficient and field profiles of fully and partially metallized PZT5A resonator discs. The results obtained were compared with those obtained by an approximated analytical method. The developed software proves to be very efficient to retrieve the contour modes of all orders.},
     year = {2016}
    }
    

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  • TY  - JOUR
    T1  - Modeling of MEMS Resonator Piezoelectric Disc Partially Covered with Electrodes
    AU  - Ismail Naciri
    AU  - Lahoucine Elmaimouni
    AU  - Jean-Etienne Lefebvre
    AU  - Faniry Emilson Ratolojanahary
    AU  - Mohamed Rguiti
    AU  - Tadeusz Gryba
    Y1  - 2016/10/19
    PY  - 2016
    N1  - https://doi.org/10.11648/j.ajma.20160401.11
    DO  - 10.11648/j.ajma.20160401.11
    T2  - American Journal of Mechanics and Applications
    JF  - American Journal of Mechanics and Applications
    JO  - American Journal of Mechanics and Applications
    SP  - 1
    EP  - 9
    PB  - Science Publishing Group
    SN  - 2376-6131
    UR  - https://doi.org/10.11648/j.ajma.20160401.11
    AB  - The Legendre polynomial method has been extended to the modeling of MEMS resonator disc partially covered with electrodes. The disc has been divided into two areas: one with electrodes and the other without electrodes. For each area, The Maxwell equations and the piezoelectric constitutive equations of motion are studied and solved to yield a frequency response and electrical behavior of the MEMS resonator applying a semi analytical method based on a Legendre polynomials series and trigonometric functions. However, the method allows incorporating the boundary conditions directly into the governing equations by assuming position-dependent of elastic constants, mass density and delta functions. The alternating electrical source is described by specific terms which are also introduced into the equation of motion. The formalism has been developed which allows for both harmonic and modal analyses. In order to validate our polynomial approach, numerical results are presented such as resonant and anti-resonant frequencies, electric input admittance, electromechanical coupling coefficient and field profiles of fully and partially metallized PZT5A resonator discs. The results obtained were compared with those obtained by an approximated analytical method. The developed software proves to be very efficient to retrieve the contour modes of all orders.
    VL  - 4
    IS  - 1
    ER  - 

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Author Information
  • Laboratoire Sciences Ingénierie et Energie, Energie Renouvelable, Microsystèmes Acoustique et Micanique, Polydisciplinary Faculty of Ouarzazate, Ibn Zohr University, Morocco

  • Laboratoire Sciences Ingénierie et Energie, Energie Renouvelable, Microsystèmes Acoustique et Micanique, Polydisciplinary Faculty of Ouarzazate, Ibn Zohr University, Morocco

  • The Institute of Electronics, Microelectronics and Nanotechnology, Opto-Acousto-Electronic Department, University of Valenciennes, France

  • Laboratory of applied Physics, Fianarantsoa University, Madagascar

  • Laboratoire des Matériaux Céramiques et procédés Associés, Université de Valenciennes, Maubeuge, France

  • The Institute of Electronics, Microelectronics and Nanotechnology, Opto-Acousto-Electronic Department, University of Valenciennes, France

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