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.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Batra, R., Porfiri, M., and Spinello, D., 2007, “Review of Modeling Electrostatically Actuated Microelectromechanical Systems,” Smart Mater. Struct., 16(6), pp. 23–31. [CrossRef]
Legtenberg, R., and Tilmans, H., 1994, “Electrostatically Driven Vacuum-Encapsulated Polysilicon Resonators Part I: Design and Fabrication,” Sens. Actuators, A, 45(1), pp. 57–66. [CrossRef]
Pamidighantam, S., Puers, R., Baert, K., and Tilmans, H., 2002, “Pull-In Voltage Analysis of Electrostatically Actuated Beam Structures With Fixed-Fixed and Fixed-Free End Conditions,” J. Micromech. Microeng., 12, pp. 458–464. [CrossRef]
Zhu, J., 2008, “Pull-In Instability of Two Opposing Microcantilever Arrays With Different Bending Rigidities,” Int. J. Mech. Sci., 50, pp. 55–68. [CrossRef]
Nayfeh, A. H., Younis, M., and Abdel-Rahman, E., 2007, “Dynamic Pull-In Phenomenon in MEMS Resonators,” Nonlinear Dyn., 48, pp. 153–168. [CrossRef]
Chao, P. C.-P., Chiu, C. W., and Liu, T.-H., 2008, “DC Dynamic Pull-In Predictions for a Generalized Clamped-Clamped Micro-Beam Based on a Continuous Model and Bifurcation Analysis,” J. Micromech. Microeng., 18(11), p. 115008. [CrossRef]
Krylov, S., and Maimon, R., 2004, “Pull-In Dynamics of an Elastic Beam Actuated by Continuously Distributed Electrostatic Force,” J. Vibr. Acoust., 126, pp. 332–342. [CrossRef]
Rochus, V., Rixen, D., and Golinval, J., 2005, “Electrostatic Coupling of MEMS Structures: Transient Simulations and Dynamic Pull-In,” Nonlinear Anal. Theory, Methods Appl., 63, pp. 1619–1633. [CrossRef]
Xie, W., Lee, H., and Lim, S., 2003, “Nonlinear Dynamic Analysis of MEMS Switches by Nonlinear Modal Analysis,” Nonlinear Dyn., 31, pp. 243–256. [CrossRef]
Joglekar, M. M., and Pawaskar, D. N., 2011, “Estimation of Oscillation Period/Switching Time for Electrostatically Actuated Micro-Beam Type Switches,” Int. J. Mech. Sci., 53, pp. 116–125. [CrossRef]
Lin, R., and Wang, W., 2006, “Structural Dynamics of Microsystems-Current State of Research and Future Directions,” Mech. Syst. Signal Process., 20(5), pp. 1015–1043. [CrossRef]
Yong, Z., and Espinosa, H. D., 2004, “Reliability of Capacitive RF MEMS Switches at High and Low Temperatures,” Int. J. RF Microwave Comput.-Aided Eng., 14, pp. 317–328. [CrossRef]
Yong, Z., and Espinosa, H. D., 2004, “Effect of Temperature on Capacitive RF MEMS Switch Performance—A Coupled Field Analysis,” J. Micromech. Microeng., 14, pp. 1270–1279. [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, pp. 666–673. [CrossRef]
Feng, C., Zhao, Ya-Pu, and Liu, D. Q., 2007, “Squeeze-Film Effects in MEMS Devices With Perforated Plates for Small Amplitude Vibration,” Microsyst Technol., 13, pp. 625–633. [CrossRef]
Li, W.-L., 2008, “Squeeze Film Effects on Dynamic Performance of MEMS l-Mirrors-Consideration of Gas Rarefaction and Surface Roughness,” Microsyst Technol., 14, pp. 315–324. [CrossRef]
Bao, M., and Yang, H., 2007, “Squeeze Film Air Damping in MEMS,” Sens. Actuators A, 136, pp. 3–27. [CrossRef]
Pandey, A. K., and Pratap, R., 2007, “Effect of Flexural Modes on Squeeze Film Damping in MEMS Cantilever Resonators,” J. Micromech. Microeng., 17, pp. 2475–2484. [CrossRef]
Ali, S. M., Mantell, S. C., and Longmire, E. K., 2011, “Mechanical Performance of Microcantilevers in Liquids,” J. Microelectromech. Syst., 20(2), pp. 441–450. [CrossRef]
Inaba, S., AkaishiK., Mori, T., and Hane, K., 1993, “Analysis of the Resonance Characteristics of a Cantilever Vibrated Phototherrnally in a Liquid,” J. Appl. Phys., 73(6), pp. 2654–2658. [CrossRef]
Lindholm, U. S., Kana, D. D., Chu, W. H., and Abramson, H. N., 1965, “Elastic Vibration Characteristics of Cantilever Plates in Water,” J. Ship Res., 9, pp. 11–22.
Minami, H., 1998, “Added Mass of a Membrane Vibrating at Finite Amplitude,” J. Fluids Struct.12, pp. 919–932. [CrossRef]
Meyerhoff, W. K., 1970, “Added Masses of Thin Rectangular Plates Calculated From Potential Theory,” J. Ship Res., 14, pp. 100–111.
Ergin, A., and Ugurlu, B., 2003, “Linear Vibration Analysis of Cantilever Plates Partially Submerged in Fluid,” J. Fluids Struct., 17, pp. 927–939. [CrossRef]
Sinha, J. K., Sandeep, S., and Rama, R. A., 2003, “Added Mass and Damping of Submerged Perforated Plates,” J. Sound Vib., 260, pp. 549–564. [CrossRef]
Yadykin, Y., Tenetov, V., and Levin, D., 2003, “The Added Mass of a Flexible Plate Oscillating in a Fluid,” J. Fluids Struct., 17, pp. 115–123. [CrossRef]
Gorman, D. G., Trendafilova, I., Mulholland, A. J., and Horáček, J., 2007, “Analytical Modelling and Extraction of the Modal Behaviour of a Cantilever Beam in Fluid Interaction,” J. Sound Vib., 308, pp. 231–245. [CrossRef]
Rezazadeh, G., Fathalilou, M., Shabani, R., Tarverdilou, S., and Talebian, S., 2009, “Dynamic Characteristics and Forced Response of an Electrostatically-Actuated Micro-Beam Subjected to Fluid Loading,” Microsyst. Technol., 15, pp. 1355–1363. [CrossRef]
Sader, J. E., 1998, “Frequency Response of Cantilever Beams Immersed in Viscous Fluids With Applications to the Atomic Force Microscope,” J. Appl. Phys., 84(1), pp. 64–76. [CrossRef]
Harrison, C., Tavernier, E., Vancauwenberghe, O., Donzier, E., Hsud, K., Goodwin, A., Marty, F., and Mercier, B., 2007, “On the Response of a Resonating Plate in a Liquid Near a Solid Wall,” Sens. Actuators, A, 134, pp. 414–426. [CrossRef]
Chon, J. W. M., Mulvaney, P., and Sader, J. E., 2000, “Experimental Validation of Theoretical Models for the Frequency Response of Atomic Force Microscope Cantilever Beams Immersed in Fluids,” J. Appl. Phys., 87(8), pp. 3978–3988. [CrossRef]
Naik, T., Longmire, E. K., and Mantell, S. C., 2003, “Dynamic Response of a Cantilever in Liquid Near a Solid Wall,” Sens. Actuators, A, 102, pp. 240–254. [CrossRef]
Krylov, S., 2007, “Lyapunov Exponents as a Criterion for the Dynamic Pull-In Instability of Electrostatically Actuated Microstructures,” Int. J. Non-Linear Mech., 42, pp. 626–642. [CrossRef]
Hu, Y. C., Chang, C. M., and Huang, S. C., 2004, “Some Design Considerations on the Electrostatically Actuated Microstructures,” Sens. Actuators, A, 112, pp. 155–161. [CrossRef]
Chaterjee, S., and Pohit, G., 2009, “A Large Deflection Model for the Pull-In Analysis of Electrostatically Actuated Microcantilever Beams,” J. Sound Vib., 322, pp. 969–986. [CrossRef]
Meirovitch, L., 1997, Principles and Techniques of Vibrations, Prentice-Hall, Englewood Cliffs, NJ.


Grahic Jump Location
Fig. 1

Schematics diagram of the coupled system

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
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

Grahic Jump Location
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




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