Acta Mechanica Solida Sinica

, Volume 25, Issue 6, pp 627–637 | Cite as

Effect of the Open Crack on the Pull-In Instability of an Electrostatically Actuated Micro-Beam

  • Asadollah Motallebi
  • Mohammad Fathalilou
  • Ghader Rezazadeh
Article

Abstract

In this paper, the effects of the open crack on the static and dynamic pull-in voltages of an electrostatically actuated fixed-fixed and cantilever micro-beam are investigated. By presenting a mathematical modeling, the governing static and dynamic equations are solved by SSLM and Galerkin-based Reduced Order Model, respectively. Then, each single-side open crack in the micro-beam is modeled by a massless rotational spring and the cracked mode shapes and corresponding natural frequencies are calculated by considering the boundary and patching conditions and using transfer matrix methods. Finally, the effects of the crack depth ratio, crack position and crack number on the pull-in voltage of the micro-beams are studied. It is shown that beside the residual stresses created in the machining process, the crack(s) can be initiated, growth and consequently change the pull-in voltage of the system by decreasing the natural frequencies. The results show that the crack position is effective beside the crack depth ratio in decreasing the pull-in voltage. Also it is shown that in the fixed-fixed micro-beam there are several points for the crack location in which, the pull-in voltage is extremum.

Key words

MEMS open crack electrostatic pull-in instability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Basso, M., Giarre, L., Dahleh, M. and Mezic, I., Numerical analysis of complex dynamics in atomic force microscopes. In: Proceedings of the IEEE International Conference on Control Applications, Trieste, Italy, 1998: 1026–1030.Google Scholar
  2. [2]
    Fritz, J., Baller, M.K., Lang, H.P., Rothuizen, H., Vettiger, P., Meyer, E., Gntherodt, H.J., Gerber, C. and Gimzewski, J.K., Translating bio-molecular recognition into nanomechanics. Science, 2000, 288: 316–318.CrossRefGoogle Scholar
  3. [3]
    Sidles, J.A., Noninductive detection of single proton-magnetic resonance. Applied Physics Letter, 1991, 58, 24: 2854–2856.CrossRefGoogle Scholar
  4. [4]
    Rezazadeh, G., Fathalilou, M. and Shabani, R., Static and dynamic stabilities of a micro-beam actuated by a piezoelectric voltage. Microsystem Technologies, 2009, 15: 1785–1791.CrossRefGoogle Scholar
  5. [5]
    Senturia, S., Microsystem Design. Norwell, MA: Kluwer, 2001.Google Scholar
  6. [6]
    Sadeghian, H., Rezazadeh, G. and Osterberg, P.M., Application of the generalized differential quadrature method to the study of pull-in phenomena of MEMS switches. Journal of Microelectromechanical Systems, 2007, 16: 1334–1340.CrossRefGoogle Scholar
  7. [7]
    Osterberg, P.M. and Senturia, S.D., M-TEST: a test chip for MEMS material property measurement using electrostatically actuated test structures. Journal of Microelectromechanical Systems, 1997, 6: 107–118.CrossRefGoogle Scholar
  8. [8]
    Abdel-Rahman, E.M., Younis, M.I. and Nayfeh, A.H., Characterization of the mechanical behavior of an electrically actuated micro-beam. Journal of Micromechanics and Microengineering, 2002, 12: 759–766.CrossRefGoogle Scholar
  9. [9]
    Fathalilou, M., Motallebi, A., Rezazadeh, G., Yagubizade, H., Shirazi, K. and Alizadeh, Y., Mechanical behavior of an electrostatically actuated micro-beam under mechanical shock. Journal of Solid Mechanics, 2009: 45–57.Google Scholar
  10. [10]
    Younis, M.I., Abdel-Rahman, E.M. and Nayfeh, A., A reduced-order model for electrically actuated micro-beam-based MEMS. Journal of Microelectromechanical systems, 2003, 12, 5: 672–680.CrossRefGoogle Scholar
  11. [11]
    Younis, M.I., Miles, R. and Jordy, D., Investigation of the response of microstructures under the combined effect of mechanical shock and electrostatic forces. Journal of Micromechanics and Microengineering, 2006, 16: 2463–2474.CrossRefGoogle Scholar
  12. [12]
    Hung, E.S. and Senturia, S.D., Generating efficient dynamical models for Microelectromechanical systems from a few finite-element simulation runs. Journal of Microelectromechanical Systems, 1999, 8: 280–289.CrossRefGoogle Scholar
  13. [13]
    Varvani-Farahani, A., Silicon MEMS components: a fatigue life assessment approach. Microsystems Technologies, 2005, 11: 129–134.CrossRefGoogle Scholar
  14. [14]
    Hill, M.J. and Rowcliffe, D.J., Deformation of silicon at low temperatures. Journal of Materials Science, 1974, 9: 1569–1576.CrossRefGoogle Scholar
  15. [15]
    Muhlstein, C.L., Brown, S.B. and Ritchie, R.O., High-cycle fatigue and durability of polycrystalline silicon films in ambient air. Sensors and Actuators, 2001a, A94: 177–178.CrossRefGoogle Scholar
  16. [16]
    Ando, T., Shikida, M. and Sato, K., Tensile-mode fatigue testing of silicon films as structural materials for MEMS. Sensors and Actuators, 2001, A93: 70–75.CrossRefGoogle Scholar
  17. [17]
    Muhlstein, C.L., Brown, S.B. and Ritchie, R.O., High-cycle fatigue of single crystal silicon thin films. Journal of Microelectromechanical systems, 2001b, 10: 593–600.Google Scholar
  18. [18]
    Zhang, G.P. and Wang, Z.G., Fatigue of small-scale metal materials: from micro to nano-scale. In: Sih, G.C. (ed.), Multi-scale Fatigue Crack Initiation and Propagation of Engineering Materials: Structural Integrity and Microstructural Worthiness, 275–326.Google Scholar
  19. [19]
    Rezaee, M. and Hassannejad, R., Free vibration analysis of simply supported beam with breathing crack using perturbation method. Acta Mechanica Solida Sinica, 2010, 23(5): 459–470.CrossRefGoogle Scholar
  20. [20]
    Chondros, T.G., Dimarogonas, A.D. and Yao, J., Vibration of a beam with a breathing crack. Journal of Sound and Vibration, 2001, 239(1): 57–67.CrossRefGoogle Scholar
  21. [21]
    Lin, H.P., Chang, S.C. and Wu, J.D., Beam vibrations with an arbitrary number of cracks. Journal of Sound and Vibration, 2002, 258, 5: 987–999.CrossRefGoogle Scholar
  22. [22]
    Chondros, T.G., Dimarogonas, A.D. and Yao, J., A continuous cracked beam vibration theory. Journal of Sound and Vibration, 1998, 215: 17–34.CrossRefGoogle Scholar
  23. [23]
    Shen, M.H. and Pierre, C., Natural modes of Bernolli-Euler beams with symmetric cracks. Journal of Sound and Vibration, 1990, 138: 115–134.CrossRefGoogle Scholar
  24. [24]
    Boltezar, M., Strancar, B. and Kuhelj, A., Identification of transverse crack location in flexural vibrations of free-free beam. Journal of Sound and Vibration, 1998, 211: 739–734.CrossRefGoogle Scholar
  25. [25]
    Liu, C.T., Monitoring microstructural evolution, crack formation, and damage characteristics near crack tip in a highly filled elastomer using digital radiography X-ray techniques. Experimental Mechanics, 2007, 47: 79–85.CrossRefGoogle Scholar
  26. [26]
    Chung, C.K., Fang, Y.J., Cheng, C.M., Hong, Y.Z. and Wang, C.M., Effect of seed layer stress on the fabrication of monolithic MEMS microstructure. Microsystems Technologies, 2007, 13: 299–304.CrossRefGoogle Scholar
  27. [27]
    Lin, M.T., Tong, C.J and Shiu, K.S., Monotonic and fatigue testing of freestanding submicron thin beams application for MEMS. Microsystems Technologies, 2008, 14: 1041–1048.CrossRefGoogle Scholar
  28. [28]
    Son, D., Kim, J.J, Kim, J.Y. and Kwon, D., Tensile properties and fatigue crack growth in LIGA nickel MEMS structures. Materials Science and Engineering A, 2005, 406: 274–278.CrossRefGoogle Scholar
  29. [29]
    Rezazadeh, G., Fathalilou, M., Shabani, R., Tarverdilou, S. and Talebian, S., Dynamic characteristics and forced response of an electrostatically actuated micro-beam subjected to fluid loading. Journal of Microsystem Technologies, 2009, 15, 9: 1355–1363.CrossRefGoogle Scholar
  30. [30]
    Osterberg, P., Electrostatically Actuated Microelectromechanical Test Structures for Material Property Measurement. Ph.D. Thesis, MIT, Cambridge, 1995.Google Scholar
  31. [31]
    Younis, M.I., Miles, R. and Jordy, D., Investigation of the response of microstructures under the combined effect of mechanical shock and electrostatic forces. Journal of Micromechanics and Microengineering, 2006, 16: 2463–2474.CrossRefGoogle Scholar
  32. [32]
    Ananthasuresh, G.K., Gupta, R.K. and Senturia, S.D., An approach to macromodeling of MEMS for non-linear dynamic simulation. In: Proceeding of ASME International Conference of Mechanical Engineering Congress and Exposition (MEMS), Atlanta, GA, 1996, 401–407.Google Scholar
  33. [33]
    Krylov, S., and Maimon, R., Pull-in dynamics of an elastic beam actuated by distributed electrostatic force. In: Proceedings of 19th Biennial Conference in Mechanical Vibration and Noise (VIB), Chicago, IL, 2003, DETC2003/VIB-48518, 2003.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2012

Authors and Affiliations

  • Asadollah Motallebi
    • 1
  • Mohammad Fathalilou
    • 1
  • Ghader Rezazadeh
    • 2
  1. 1.Mech. Eng. Dept.Islamic Azad University, Khoy BranchKhoyIran
  2. 2.Mech. Eng. Dept.Urmia UniversityUrmiaIran

Personalised recommendations