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.

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Fig. 1

Schematic of a clamped microbeam located between four electrodes

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Fig. 2

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

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Fig. 3

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

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Fig. 4

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

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Fig. 5

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

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Fig. 6

Simulation of the microbeam and air gap in Ansys

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Fig. 7

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

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Fig. 8

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

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Fig. 16

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

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Fig. 9

Displacement of x1 versus the applied voltage

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Fig. 10

Comparing results of the lumped model and distributed model

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Fig. 11

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

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Fig. 12

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

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Fig. 13

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

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Fig. 14

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

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Fig. 15

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




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