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Research Papers

Stability Analysis and Transient Response of Electrostatically Actuated Microbeam Interacting With Bounded Compressible Fluids

[+] Author and Article Information
R. Shabani

e-mail: r.shabani@urmia.ac.ir
Mechanical Engineering Department,
Urmia University,
Urmia, Iran

S. Tariverdilo

Civil Engineering Department,
Urmia University,
Urmia, Iran

G. Rezazadeh

Mechanical Engineering Department,
Urmia University,
Urmia, Iran

1Corresponding author.

Manuscript received December 19, 2011; final manuscript received June 13, 2012; accepted manuscript posted July 16, 2012; published online November 19, 2012. Assoc. Editor: Chad Landis.

J. Appl. Mech 80(1), 011024 (Nov 19, 2012) (7 pages) Paper No: JAM-11-1483; doi: 10.1115/1.4007141 History: Received December 19, 2011; Revised June 13, 2012; Accepted July 16, 2012

This paper studies the stability and transient response of electrostatically excited microbeam interacting with bounded compressible fluid. At first, employing Fourier-Bessel series, the related eigenvalue problem of the coupled system is solved. Investigating the change in the free vibration properties of the system, a parametric study is done, accounting for changing physical properties and geometric dimensions of the bounded fluid. Then, considering the step response of the coupled system, pull-in time and voltage and also attraction zones of the microbeam are derived. It is shown that, beside the electrical property of the contained fluid, its inertial property could also change the transient response significantly. Fluid added mass by increasing the period of the free vibration response in stable condition also changes the pull-in time. In addition, it is found that the attraction zones of stable fixed points vary for different contained fluids that could change the sensitivity of the microbeam to uncertainty in the initial condition.

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Figures

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Fig. 1

Schematics diagram of the coupled system

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Fig. 2

Variations of two first natural frequencies of the microbeam as function of different fluid densities

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Fig. 3

Variations of the resonant natural frequency of the microbeam versus the operating fluids depth

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Fig. 4

Step responses of the microbeam interacting with different fluids due to v = 5 V; (a) time histories, (b) phase plane

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Fig. 5

Pull-in conditions of the microbeam interacting with different fluids (pull-in voltages for vacuum, butane, carbon tetrachloride, benzene, and phenol are 24.99, 21.09, 16.71, 16.45, and 12.03, respectively); (a) time histories, (b) phase plane

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Fig. 6

Step response of the microbeam interacting with different fluids for nondimensional input voltage V¯=7.6; (a) time histories, (b) phase plane

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Fig. 7

Pull-in responses of the microbeam interacting with different fluids, where the nondimensional pull-in voltage is V¯=7.66; (a) time histories, (b) phase plane

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Fig. 8

Effects of the different fluids on the stability of the microbeam, where the nondimensional input voltage is V¯=7.66 and an uncertainty is in the initial conditions; (a) time histories related to initial condition of point A* (w∧(l2,0)=0.3, ∧·w(l2,0)=0.44), (b) phase plane

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