Research Papers

Stability and Bifurcation Analysis of an Asymmetrically Electrostatically Actuated Microbeam

[+] Author and Article Information
Hadi Madinei

Mechanical Engineering Department,
Urmia University,
Urmia 51818-57561, Iran
e-mail: h.madinei@gmail.com

Ghader Rezazadeh

Mechanical Engineering Department,
Urmia University,
Urmia 51818-57561, Iran
e-mail: g.rezazadeh@urmia.ac.ir

Saber Azizi

Mechanical Engineering Department,
Urmia University of Technology,
Urmia 5716617165, Iran
e-mail: s.azizi@mee.uut.ac.ir

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 29, 2013; final manuscript received September 9, 2014; published online January 12, 2015. Assoc. Editor: Carmen M. Lilley.

J. Comput. Nonlinear Dynam 10(2), 021002 (Mar 01, 2015) (8 pages) Paper No: CND-13-1024; doi: 10.1115/1.4028537 History: Received January 29, 2013; Revised September 09, 2014; Online January 12, 2015

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.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Senturia, S., 2001, Microsystem Design, Kluwer, Norwell, MA.
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. [CrossRef]
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.
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.
Osterberg, P., 1995, Electrostatically Actuated Microelectromechanical Test Structures for Material Property Measurement. Ph.D. thesis, MIT, Cambridge, MA.
Mukherjee, S. R., 1996, “Dynamic Analysis of Micro-Electromechanical System,” Int. J. Numer. Methods Eng.,” 39(24), pp. 4119–4139. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Meirovitz, L., 1967, Analytical Methods in Vibrations, Collier Macmillan, London.
Lee, C. K., and Moon, F. C., 1990, “Modal Sensors/Actuators,” ASME J. Appl. Mech., 57(2), pp.434–441. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Nayfeh, A. H., and Balachandran, B., 1995, Applied Nonlinear Dynamics, Wiley-Interscience, New York.
Rao, S. S., 2007, Mechanical Vibrations, Wiley, New York.


Grahic Jump Location
Fig. 1

Schematic of a clamped microbeam located between four electrodes

Grahic Jump Location
Fig. 2

A equivalent lumped 2-DOF model for new type of electrostatic actuation mechanism

Grahic Jump Location
Fig. 4

Deflection of the microbeam (at x=0.75) versus the applied voltage

Grahic Jump Location
Fig. 5

Deflection of the classically actuated microbeam (at x=0.5) versus the applied voltage

Grahic Jump Location
Fig. 6

Simulation of the microbeam and air gap in Ansys

Grahic Jump Location
Fig. 7

(a) and (b) Deflection of the microbeam simulated by Ansys

Grahic Jump Location
Fig. 8

(a) and (b) Comparing results of the distributed model and Ansys model

Grahic Jump Location
Fig. 3

Deflection of the microbeam (at x=0.25) versus the applied voltage

Grahic Jump Location
Fig. 9

Displacement of x1 versus the applied voltage

Grahic Jump Location
Fig. 10

Comparing results of the lumped model and distributed model

Grahic Jump Location
Fig. 11

Imaginary parts of eigenvalues versus the applied voltage (for branch 1)

Grahic Jump Location
Fig. 12

Real parts of eigenvalues versus the applied voltage (for branch 1)

Grahic Jump Location
Fig. 13

Imaginary parts of eigenvalues versus the applied voltage (for branch 2)

Grahic Jump Location
Fig. 14

Real parts of eigenvalue versus the applied voltage (for branch 2)

Grahic Jump Location
Fig. 15

Imaginary parts of eigenvalue versus the applied voltage (for branch 3)

Grahic Jump Location
Fig. 16

Real parts of eigen-value versus the applied voltage (for branch 3)




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In