Novel reduced order model for electrically actuated microbeam-based MEMS

Sarah Ben Sassi; Fehmi Najar

doi:10.1007/978-3-319-17527-0_51

Novel reduced order model for electrically actuated microbeam-based MEMS

Sarah Ben Sassi
, Fehmi Najar

University of Carthage

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

We present a novel semi-analytical approach to solve nonlinear integral-partial-differential equation related to MEMS microactuators. The proposed approach is based on a reduced-order model of microbeams under the action of electrostatic force. Using Euler-Bernoulli beam theory, we derive the nonlinear equations governing the motion of a doubly clamped microbeam. The formulated model gives good account of nonlinearities such as midplane stretching effects and nonlinear electrostatic force. The dynamic response of the coupled electro-mechanical microsystem is simulated through an innovative approach based on a Galerkin procedure, which allows the use of only one mode in the ROM decomposition. Basis function of the Galerkin decomposition is obtained through the DQM decomposition. The obtained ROM is utilized in combination with the Finite Difference Method to simulate the limit cycle solutions of the microactuator. The novel ROM is applied to study cases provided in the literature and compared with classical Galerkin technique.

Original language	English
Title of host publication	Design and Modeling of Mechanical Systems - II - Proceedings of the 6th Conference on Design and Modeling of Mechanical Systems, CMSM 2015
Editors	Hachmi Ben Daly, Mnaouar Chouchane, Nizar Aifaoui, Mnaouar Chouchane, Tahar Fakhfakh, Fakher Chaari
Publisher	Springer Verlag
Pages	513-520
Number of pages	8
ISBN (Electronic)	9783319175263
DOIs	https://doi.org/10.1007/978-3-319-17527-0_51
State	Published - 2015
Externally published	Yes
Event	6th International Congress on Design and Modeling of Mechanical Systems, CMSM 2015 - Hammamet, Tunisia Duration: 23 Mar 2015 → 25 Mar 2015

Publication series

Name	Lecture Notes in Control and Information Sciences
Volume	789
ISSN (Print)	0170-8643

Conference

Conference	6th International Congress on Design and Modeling of Mechanical Systems, CMSM 2015
Country/Territory	Tunisia
City	Hammamet
Period	23/03/15 → 25/03/15

Keywords

DQM
FDM
Galerkin
Limit-cycle solution
MEMS
Microbeam
Nonlinear dynamics
ROM

Access to Document

10.1007/978-3-319-17527-0_51

Cite this

Sassi, S. B., & Najar, F. (2015). Novel reduced order model for electrically actuated microbeam-based MEMS. In H. B. Daly, M. Chouchane, N. Aifaoui, M. Chouchane, T. Fakhfakh, & F. Chaari (Eds.), Design and Modeling of Mechanical Systems - II - Proceedings of the 6th Conference on Design and Modeling of Mechanical Systems, CMSM 2015 (pp. 513-520). (Lecture Notes in Control and Information Sciences; Vol. 789). Springer Verlag. https://doi.org/10.1007/978-3-319-17527-0_51

Sassi, Sarah Ben ; Najar, Fehmi. / Novel reduced order model for electrically actuated microbeam-based MEMS. Design and Modeling of Mechanical Systems - II - Proceedings of the 6th Conference on Design and Modeling of Mechanical Systems, CMSM 2015. editor / Hachmi Ben Daly ; Mnaouar Chouchane ; Nizar Aifaoui ; Mnaouar Chouchane ; Tahar Fakhfakh ; Fakher Chaari. Springer Verlag, 2015. pp. 513-520 (Lecture Notes in Control and Information Sciences).

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title = "Novel reduced order model for electrically actuated microbeam-based MEMS",

abstract = "We present a novel semi-analytical approach to solve nonlinear integral-partial-differential equation related to MEMS microactuators. The proposed approach is based on a reduced-order model of microbeams under the action of electrostatic force. Using Euler-Bernoulli beam theory, we derive the nonlinear equations governing the motion of a doubly clamped microbeam. The formulated model gives good account of nonlinearities such as midplane stretching effects and nonlinear electrostatic force. The dynamic response of the coupled electro-mechanical microsystem is simulated through an innovative approach based on a Galerkin procedure, which allows the use of only one mode in the ROM decomposition. Basis function of the Galerkin decomposition is obtained through the DQM decomposition. The obtained ROM is utilized in combination with the Finite Difference Method to simulate the limit cycle solutions of the microactuator. The novel ROM is applied to study cases provided in the literature and compared with classical Galerkin technique.",

keywords = "DQM, FDM, Galerkin, Limit-cycle solution, MEMS, Microbeam, Nonlinear dynamics, ROM",

author = "Sassi, \{Sarah Ben\} and Fehmi Najar",

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Sassi, SB & Najar, F 2015, Novel reduced order model for electrically actuated microbeam-based MEMS. in HB Daly, M Chouchane, N Aifaoui, M Chouchane, T Fakhfakh & F Chaari (eds), Design and Modeling of Mechanical Systems - II - Proceedings of the 6th Conference on Design and Modeling of Mechanical Systems, CMSM 2015. Lecture Notes in Control and Information Sciences, vol. 789, Springer Verlag, pp. 513-520, 6th International Congress on Design and Modeling of Mechanical Systems, CMSM 2015, Hammamet, Tunisia, 23/03/15. https://doi.org/10.1007/978-3-319-17527-0_51

Novel reduced order model for electrically actuated microbeam-based MEMS. / Sassi, Sarah Ben; Najar, Fehmi.
Design and Modeling of Mechanical Systems - II - Proceedings of the 6th Conference on Design and Modeling of Mechanical Systems, CMSM 2015. ed. / Hachmi Ben Daly; Mnaouar Chouchane; Nizar Aifaoui; Mnaouar Chouchane; Tahar Fakhfakh; Fakher Chaari. Springer Verlag, 2015. p. 513-520 (Lecture Notes in Control and Information Sciences; Vol. 789).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Novel reduced order model for electrically actuated microbeam-based MEMS

AU - Sassi, Sarah Ben

AU - Najar, Fehmi

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2015.

PY - 2015

Y1 - 2015

N2 - We present a novel semi-analytical approach to solve nonlinear integral-partial-differential equation related to MEMS microactuators. The proposed approach is based on a reduced-order model of microbeams under the action of electrostatic force. Using Euler-Bernoulli beam theory, we derive the nonlinear equations governing the motion of a doubly clamped microbeam. The formulated model gives good account of nonlinearities such as midplane stretching effects and nonlinear electrostatic force. The dynamic response of the coupled electro-mechanical microsystem is simulated through an innovative approach based on a Galerkin procedure, which allows the use of only one mode in the ROM decomposition. Basis function of the Galerkin decomposition is obtained through the DQM decomposition. The obtained ROM is utilized in combination with the Finite Difference Method to simulate the limit cycle solutions of the microactuator. The novel ROM is applied to study cases provided in the literature and compared with classical Galerkin technique.

AB - We present a novel semi-analytical approach to solve nonlinear integral-partial-differential equation related to MEMS microactuators. The proposed approach is based on a reduced-order model of microbeams under the action of electrostatic force. Using Euler-Bernoulli beam theory, we derive the nonlinear equations governing the motion of a doubly clamped microbeam. The formulated model gives good account of nonlinearities such as midplane stretching effects and nonlinear electrostatic force. The dynamic response of the coupled electro-mechanical microsystem is simulated through an innovative approach based on a Galerkin procedure, which allows the use of only one mode in the ROM decomposition. Basis function of the Galerkin decomposition is obtained through the DQM decomposition. The obtained ROM is utilized in combination with the Finite Difference Method to simulate the limit cycle solutions of the microactuator. The novel ROM is applied to study cases provided in the literature and compared with classical Galerkin technique.

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KW - FDM

KW - Galerkin

KW - Limit-cycle solution

KW - MEMS

KW - Microbeam

KW - Nonlinear dynamics

KW - ROM

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M3 - Conference contribution

AN - SCOPUS:84926330697

T3 - Lecture Notes in Control and Information Sciences

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EP - 520

BT - Design and Modeling of Mechanical Systems - II - Proceedings of the 6th Conference on Design and Modeling of Mechanical Systems, CMSM 2015

A2 - Daly, Hachmi Ben

A2 - Chouchane, Mnaouar

A2 - Aifaoui, Nizar

A2 - Chouchane, Mnaouar

A2 - Fakhfakh, Tahar

A2 - Chaari, Fakher

PB - Springer Verlag

T2 - 6th International Congress on Design and Modeling of Mechanical Systems, CMSM 2015

Y2 - 23 March 2015 through 25 March 2015

ER -

Sassi SB, Najar F. Novel reduced order model for electrically actuated microbeam-based MEMS. In Daly HB, Chouchane M, Aifaoui N, Chouchane M, Fakhfakh T, Chaari F, editors, Design and Modeling of Mechanical Systems - II - Proceedings of the 6th Conference on Design and Modeling of Mechanical Systems, CMSM 2015. Springer Verlag. 2015. p. 513-520. (Lecture Notes in Control and Information Sciences). doi: 10.1007/978-3-319-17527-0_51

Novel reduced order model for electrically actuated microbeam-based MEMS

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