Modeling of MEMS Resonator Piezoelectric Disc Partially Covered with Electrodes

Ismail Naciri; Lahoucine Elmaimouni; Jean-Etienne Lefebvre; Faniry Emilson Ratolojanahary; Mohamed Rguiti; Tadeusz Gryba

doi:doi:10.11648/j.ajma.20160401.11

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Modeling of MEMS Resonator Piezoelectric Disc Partially Covered with Electrodes

Ismail Naciri, Lahoucine Elmaimouni, Jean-Etienne Lefebvre, Faniry Emilson Ratolojanahary, Mohamed Rguiti, Tadeusz Gryba

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.

DOI	10.11648/j.ajma.20160401.11
Published in	American Journal of Mechanics and Applications (Volume 4, Issue 1, November 2016)
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), 2024. 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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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

Ismail Naciri

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

Laboratoire Sciences Ingénierie et Energie, Energie Renouvelable, Microsystèmes Acoustique et Micanique, Polydisciplinary Faculty of Ouarzazate, Ibn Zohr University, Morocco
Jean-Etienne Lefebvre

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

Laboratory of applied Physics, Fianarantsoa University, Madagascar
Mohamed Rguiti

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

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

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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}
}

Copy | Download

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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