This paper deals with the study of bifurcational behavior of a capacitive microbeam actuated by asymmetrically located electrodes in the upper and lower sides of the microbeam. A distributed and a modified two degree of freedom (DOF) mass–spring model have been implemented for the analysis of the microbeam behavior. Fixed or equilibrium points of the microbeam have been obtained and have been shown that with variation of the applied voltage as a control parameter the number of equilibrium points is changed. The stability of the fixed points has been investigated by Jacobian matrix of system in the two DOF mass–spring model. Pull-in or critical values of the applied voltage leading to qualitative changes in the microbeam behavior have been obtained and has been shown that the proposed model has a tendency to a static instability by undergoing a pitchfork bifurcation whereas classic capacitive microbeams cease to have stability by undergoing to a saddle node bifurcation.
Issue Section:
Research Papers
References
1.
Zhang
, Y.
, and Zhao
, Y. P.
, 2006
, “Numerical and Analytical Study on Pull-In Instability of Micro-Structure Under Electro-Static Loading
,” Sens. Actuators A
, 127
(2
), pp. 366
–380
.10.1016/j.sna.2005.12.0452.
Nabian
, A.
, Rezazadeh
, G.
, Haddad-derafshi
, M.
, and Tahmasebi
, A.
, 2008
, “Mechanical Behavior of a Circular Micro Plate Subjected to Uniform Hydrostatic and Non-Uniform Electrostatic Pressure
,” J. Microsys. Technol.
, 14
(2
), pp. 235
–240
.10.1007/s00542-007-0425-y3.
Ouakad
, H. M.
, and Younis
, M. I.
, 2010
, “The Dynamic Behavior of MEMS Arch Resonators Actuated Electrically
,” Int. J. Non-Linear Mech.
45
(7
), pp.704
–713
.10.1016/j.ijnonlinmec.2010.04.0054.
Saif
, M. T. A.
, Alaca
, B. E.
, and Sehitoglu
, H.
, 1999
, “Analytical Modeling of Electrostatic Membrane Actuator for Micro Pumps
,” J. Microelectromech. Syst.
, 8
(3), pp.335
–345
.10.1109/84.7886385.
Senturia
, S.
, 2001
, Microsystem Design
, Kluwer
, Norwell, MA
.6.
Abdel-Rahman
, E. M.
, Younis
, M. I.
, and Nayfeh
, A. H.
, 2002
, “Characterization of the Mechanical Behavior of an Electrically Actuated Micro-Beam
,” J. Micromech. Microeng.
, 12
(6
), pp. 795
–766
.10.1088/0960-1317/12/6/3067.
Nathanson
, H. C.
, Newell
, W. E.
, Wickstrom
, R. A.
, and Davis
, J. R.
, 1967, “The Resonant Gate Transistor,” IEEE Trans Elect Devices, 14
, pp. 117–133.8.
Taylor
, G. I.
, 1968, “The Coalescence of Closely Spaced Drops When They Are at Different Electric Potentials,” Proc. Roy. Soc A. 306
, pp. 423–434.9.
Osterberg
, P.
, 1995
, Electrostatically Actuated Microelectromechanical Test Structures for Material Property Measurement. Ph.D. thesis, MIT
, Cambridge, MA
.10.
Mukherjee
, S. R.
, 1996
, “Dynamic Analysis of Micro-Electromechanical System
,” Int. J. Numer. Methods Eng.
,” 39
(24
), pp. 4119
–4139
.10.1002/(SICI)1097-0207(19961230)39:24<4119::AID-NME42>3.0.CO;2-411.
Nemirovsky
, Y.
, and Bochobza-Degani
, O.
, 2001
, “A Methodology and Model for the Pull-In Parameters of Electrostatic Actuators
,” J. Microelectromech. Syst.
, 10
(4
), pp. 601
–615
.10.1109/84.96738412.
Krylov
, S.
, and Maimon
, R.
, 2003
, “Pull-in Dynamics of an Elastic Beam Actuated By Distributed Electrostatic Force
,” ASME
Paper No. DETC/VIB-48518, pp.1779
–1787
.10.1115/DETC2003/VIB-4851813.
Chowdhury
, S.
, Ahmadi
, M.
, and Miller
, W. C.
, 2005
, “A Closed-Form Model for the Pull-in Voltage of Electrostatically Actuated Cantilever Beams
,” J. Micromech. Microeng.
, 15
(4
), pp. 756
–763
.10.1088/0960-1317/15/4/01214.
Batra
, R. C.
, Porfirib
, M.
, and Spinello
, D.
, 2008
, “Vibrations of Narrow Micro-Beams Predeformed by an Electric Field
,” J. Sound Vib.
, 309
(3
), pp. 600
–612
.10.1016/j.jsv.2007.07.03015.
Sadeghian
, H.
, and Rezazadeh
, G.
, 2009
, “Comparison of Generalized Differential Quadrature and Galerkin Methods for the Analysis of Micro-Electro-Mechanical Coupled Systems
,” Commun. Nonlinear Sci. Numer. Simul.
, 14
(6
), pp. 2807
–2816
.10.1016/j.cnsns.2008.07.01616.
Talebian
, S.
, Rezazadeh
, G.
, Fathalilou
, M.
, and Toosi
, B.
, 2010
, “Effect of Temperature on Pull-In Voltage and Natural Frequency of an Electrostatically Actuated Microplate
,” Mechatronics
, 20
(6
), pp. 666
–673
.10.1016/j.mechatronics.2010.07.00917.
Saeedivahdat
, A.
, Abdolkarimzadeh
, F.
, Feyzi
, A.
, Rezazadeh
, G.
, and Tarverdilo
, S.
, 2010
, “Effect of Thermal Stresses on Stability and Frequency Response of a Capacitive Microphone
,” Microelectron. J.
, 41
(12
), pp. 865
–873
.10.1016/j.mejo.2010.07.01318.
Meirovitz
, L.
, 1967
, Analytical Methods in Vibrations
, Collier Macmillan
, London
.19.
Lee
, C. K.
, and Moon
, F. C.
, 1990
, “Modal Sensors/Actuators
,” ASME J. Appl. Mech.
, 57
(2
), pp.434
–441
.10.1115/1.289200820.
Park
, A.
, Elwens
, O. M.
, and Fluitman
, H. J.
, 1992
, “Selective Mode Excitation and Detection of Micromachined Resonators
,” J. Microelectromechan. Syst.
, 1
(4
), pp.179
–186
.10.1109/JMEMS.1992.75250921.
Dominguez-Pumar
, M.
, Blokhina
, E.
, Pons-Nin
, J.
, Feely
, O.
, and Sanchez-Rojas
, J. L.
, 2010
, “Activation of Different MEMS Resonant Modes With Pulsed Digital Oscillators
,” Sensoren und Messsysteme
, pp. 316
–322
.10.1117/12.85306922.
Mohammadi
, S.
, Eftekhar
, A.
, Pourabolghasem
, R.
, and Adibi
, A.
, 2011
, “Simultaneous High-Q Confinement and Selective Direct Piezoelectric Excitation of Flexural and Extensional Lateral Vibrations in a Silicon Phononic Crystal Slab Resonator
,” Sens. Actuators A
, 167
(2
), pp. 524
–530
.10.1016/j.sna.2011.03.01423.
Gil
, M.
, Manzaneque
, T.
, Hernando-García
, J.
, Ababneh
, A.
, Seidel
, H.
, and Sánchez-Rojas
, J. L.
, 2012
, “Selective Modal Excitation in Coupled Piezoelectric Microcantilevers
,” Microsyst. Technol.
, 18
(7, 8
), pp. 917
–924
.10.1007/s00542-011-1411-y24.
Rezazadeh
, G.
, Madinei
, H.
, and Shabani
, R.
, 2012
, “Study of Parametric Oscillation of an Electrostatically Actuated Microbeam Using Variational Iteration Method
,” Appl. Math. Model
, 36
(1
), pp. 430
–443
.10.1016/j.apm.2011.07.02625.
Mobki
, H.
, Rezazadeh
, G.
, Sadeghi
, M.
, Vakili-Tahami
, F.
, and Seyyed-Fakhrabadi
, M. M.
, 2013
, “A Comprehensive Study of Stability in an Electro-Statically Actuated Micro-Beam
,” Int. J. Non-Linear Mech.
, 48
, pp. 78
–85
.10.1016/j.ijnonlinmec.2012.08.00226.
Rezazadeh
, G.
, Fathalilou
, M.
, and Sadeghi
, M.
, 2011
, “Pull-in Voltage of Electrostatically-Actuated Microbeams in Terms of Lumped Model Pull-in Voltage Using Novel Design Corrective Coefficients
,” Sens. Imaging J.
, 12
(3
), pp. 117
–131
.10.1007/s11220-011-0065-227.
Nayfeh
, A. H.
, and Balachandran
, B.
, 1995
, Applied Nonlinear Dynamics
, Wiley-Interscience
, New York
.28.
Rao
, S. S.
, 2007
, Mechanical Vibrations
, Wiley
, New York
.Copyright © 2015 by ASME
You do not currently have access to this content.
