Skip to main content
SpringerLink
Log in

Dynamic response of a torsional micromirror to electrostatic force and mechanical shock

  • Technical Paper
  • Published:
Microsystem Technologies Aims and scope Submit manuscript

Abstract

In this paper dynamic characteristics of a capacitive torsional micromirror under electrostatic forces and mechanical shocks have been investigated. A 2DOF model considering the torsion and bending stiffness of the micromirror structure has been presented. A set of nonlinear equations have been derived and solved by Runge–Kutta method. The Static pull-in voltage has been calculated by frequency analyzing method, and the dynamic pull-in voltage of the micromirror imposed to a step DC voltage has been derived for different damping ratios. It has been shown that by increasing the damping ratio the dynamic pull-in voltage converges to static one. The effects of linear and torsional shock forces on the mechanical behavior of the electrostatically deflected and undeflected micromirror have been studied. The results have shown that the combined effect of a shock load and an electrostatic actuation makes the instability threshold much lower than the threshold predicted, considering the effect of shock force or electrostatic actuation alone. It has been shown that the torsional shock force has negligible influence on dynamic response of the micromirror in comparison with the linear one. The results have been calculated for linear shocks with different durations, amplitudes, and input times.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Ananthasuresh GK, Gupta RK, Senturia SD (1996) An approach to macromodeling of MEMS for nonlinear dynamic simulation. In: Proceedings of ASME international conference of mechanical engineering congress and exposition (MEMS), vol 40. Atlanta, GA, pp 1–7

  • Brown TG (2003) Harsh military environments and microelectromechanical (MEMS) devices. Proc IEEE Sens 2(7):53–60

    Google Scholar 

  • Coster JD, Tilmans HCM, van Beek JT, Rijks TGSM, Puers R (2004) The influence of mechanical shock on the operation of electrostatically driven RF-MEMS switches. J Micromech Microeng 14(S):49–54

    Article  Google Scholar 

  • Dickensheets DL, Kino GS (1998) Silicon-micromachined scanning confocal optical microscope. J Microelectromech Syst 7:38–47. doi:10.1109/84.661382

    Article  Google Scholar 

  • Guo JG, Zhao Ya-Pu (2004) Influence of van der Waals and Casimir forces on electrostatic torsional actuators. J Microelectromech Syst 13(6):1027–1035. doi:10.1109/JMEMS.2004.838390

    Article  MathSciNet  Google Scholar 

  • Hornbeck LJ (1983) 128 128 deformable mirror devices. IEEE Trans Electron Dev ED-30(5):539–545. doi:10.1109/T-ED.1983.21163

    Google Scholar 

  • Hornbeck LJ (1989) Deformable-mirror spatial light modulators spatial light modulators and applications III. SPIE Crit 1150:86–102

    Google Scholar 

  • Huang JM, Liu AQ, Deng ZL, Zhang QX, Ahn J, Asundi A (2004) An approach to the coupling effect between torsion and bending for electrostatic torsional micromirrors. Sens Actuators A 115:159–167. doi:10.1016/j.sna.2004.04.032

    Article  Google Scholar 

  • Jaecklin VP, Linder C, De Rooij NF, Moret JM, Vuilleumier R (1993) Optical microshutters and torsional micromirror for light modulator arrays. In: Proceedings of the IEEE Micro Electro Mech. Systems Workshop, Fort Lauderdale, FL, USA, pp 124–127

  • Krylov S, Maimon R (2003) Pull-in dynamics of an elastic beam actuated by distributed electrostatic force. In: Proceedings of the 19th biennial conference in mechanical vibration and noise (VIB), (Chicago, IL) DETC/VIB-48518

  • Lin T-H (1994) Implementation and characterization of a flexure-beam micromechanical spatial light modulator. Opt Eng 33(11):3643–3648. doi:10.1117/12.181578

    Article  Google Scholar 

  • Lin W-H, Zhao Y-P (2005) Nonlinear behavior for nanoscale electrostatic actuators with Casimir force. J Chaos Solitons Fractals 23(5):1777–1785

    MATH  Google Scholar 

  • Muller RS, Lau KY (1998) Surface-micromachined microoptical elements and systems. Proc IEEE 86(8):1705–1720. doi:10.1109/5.704276

    Article  Google Scholar 

  • Petersen KE (1980) Silicon torsional scanning mirror. IBM J Res Dev 24(5):631–637

    Article  Google Scholar 

  • Rezazadeh Gh, Tahmasebi AA, Zubtsov M (2006) Application of piezoelectric layers in electrostatic mem actuators: controlling of pull-in voltage. J Microsyst Technol 12(12):1163–1170

    Article  Google Scholar 

  • Rezazadeh Gh, Khatami F, Tahmasebi AA (2007) Investigation of the torsion and bending effects on static stability of electrostatic torsional micromirrors. J. Microsyst Technol 13:715–722. doi:10.1007/s00542-006-0362-1

    Article  Google Scholar 

  • Shi F, Ramesh P, Mukherjee A (1996) Dynamic analysis of micro-electromechanical systems. Int J Numer Methods Eng 39:4119–4139. doi:10.1002/(SICI)1097-0207(19961230)39:24<4119::AID-NME42>3.0.CO;2-4

    Article  MATH  Google Scholar 

  • Timoshenko SP, Goodier JN (1970) Theory of elasticity, 3rd edn. McGraw-Hill, New York

    MATH  Google Scholar 

  • Toshiyoshi H, Fujita H (1996) Electrostatic micro torsion mirrors for an optical switch matrix. J Microelectromech Syst 5:231–237. doi:10.1109/84.546402

    Article  Google Scholar 

  • Van Kessel PF, Hornbeck LJ, Meier RE, Douglass MR (1998) MEMS-based projection display. Proc IEEE 86(8):1687–1704. doi:10.1109/5.704274

    Article  Google Scholar 

  • Wagner U, Franz J, Schweiker M, Bernhard W, Muller-Fiedler R, Michel B, Paul O (2001) Mechanical reliability of MEMS-structures under shock load. Microelectron Reliab 41(16):57–62

    Google Scholar 

  • Younis MI, Miles R, Jordy D (2006) Investigation of the response of microstructures under the combined effect of mechanical shock and electrostatic forces. J Micromech Microeng 16:2463–2474. doi:10.1088/0960-1317/16/11/030

    Article  Google Scholar 

  • Yu H, Chen H (2006) Development of a novel micromirror based on surface micromachining technology. J Sens Actuators 125(A):458–462

    Article  Google Scholar 

  • Zavracky PM, Majumder S, McGruer NE (1997) Micromechanical switches fabricated using nickel surface micromaching. J Microelectromech Syst 6:3–9. doi:10.1109/84.557524

    Article  Google Scholar 

  • Zhao JP, Chen HL, Huang JM, Liu AQ (2005) A study of dynamic characteristics and simulation of MEMS torsional micromirrors. Sens Actuators 120(A):199–210

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering, Urmia University, Nazloo Road, Urmia, Iran

    Faraz Khatami & Ghader Rezazadeh

Authors
  1. Faraz Khatami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ghader Rezazadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ghader Rezazadeh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khatami, F., Rezazadeh, G. Dynamic response of a torsional micromirror to electrostatic force and mechanical shock. Microsyst Technol 15, 535–545 (2009). https://doi.org/10.1007/s00542-008-0738-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00542-008-0738-5

Keywords

Search

Navigation