Abstract




 
   

IJE TRANSACTIONS C: Aspects Vol. 27, No. 3 (March 2014) 487-498   

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  STABILITY ANALYSIS IN PARAMETRICALLY EXCITED ELECTROSTATIC TORSIONAL MICRO-ACTUATORS
 
B. Abbasnejad, R. Shabani and G. Rezazadeh
 
( Received: June 06, 2013 – Accepted: August 22, 2013 )
 
 

Abstract    This paper addresses the static and dynamic stabilities of a parametrically excited torsional micro-actuator. The system is composed of a rectangular micro-mirror symmetrically suspended between two electrodes and acted upon by a steady (dc ) while simultaneously superimposed to an (ac ) voltage. First, the stability of the system subjected to a quasi-statically applied (dc ) voltage is investigated, where the pull-in instability, equilibrium positions, and bifurcation points of the system are determined. Then by superimposing an (ac) voltage and extracting a Mathieu type governing equation the effects of (ac ) component on the stability of the system is investigated. By varying excitation parameters (steady (dc) voltage and time-dependent amplitude of (ac ) excitation), transition curves and the stability margins of the micro-mirror are demonstrated. Theoretically obtained margins are checked by means of numerical simulations. The results show that superimposing the harmonic (ac ) component could have a stabilizing effect and allow an increase of the steady (dc ) component beyond the pull-in value. The obtained results could be used in design of micro-actuators.

 

Keywords    MEMS, Micro-mirror, Electrostatic actuation, Parametric oscillation, Perturbation method

 

چکیده    در این مقاله پایداری استاتیکی و دینامیکی یک میکرو آینه در شرایط تحریک پارامتریک مورد بررسی قرار گرفته است. سیستم مورد نظر شامل یک میکرو آینه بوده که بصورت متقارن در بین دو الکترود از نوع تحریک الکترو استاتیک قرار گرفته و بصورت همزمان توسط یک ولتاژ ثابت و یک ولتاژ هارمونیک تحریک می گردد. در ابتدا با اعمال ولتاژ ثابت پایداری استاتیکی سیستم مورد بررسی قرار گرفته و ولتاژ ناپایداری، نقاط تعادل و نقاط دوشاخگی سیستم استخراج شده اند. سپس با اضافه کردن ولتاژ متناوب به ولتاژ ثابت معادله حاکم بر سیستم که بفرم معادله ماتیو می باشد استخراج شده و پایداری سیستم مورد بررسی قرار گرفته است. در ادامه با تغییر پارامترهای تحریک سیستم نظیر اندازه ولتاژ ثابت و دامنه ولتاژ تناوبی منحنی های گذر و نواحی پایدار میکرو آینه مشخص گردیده اند. نتایج بدست آمده از روش اغتشاشات برای نقاط خاص بصورت عددی نیز حل شده و پایداری سیستم بصورت موردی بررسی شده است. نتا یج بدست نشان می دهند که با افزودن یک مولفه هارمونیک می توان ولتاژ ناپایداری سیستم را افزایش داده و به مقدار بالاتر از ناپایداری استاتیکی نیز رساند. منحنی هار گذر و نواحی پایدار بدست آمده می توانند در طراحی و ساخت میکرو آینه ها بکار گرفته شوند.

References   

 

1.     Hornbeck, L. J., "128× 128 deformable mirror device", Electron Devices, IEEE Transactions on,  Vol. 30, No. 5, (1983), 539-545.

2.     Muller, R. S. and Lau, K. Y., "Surface-micromachined microoptical elements and systems", Proceedings of the IEEE,  Vol. 86, No. 8, (1998), 1705-1720.

3.     Lin, T.-H., "Implementation and characterization of a flexure-beam micromechanical spatial light modulator", Optical Engineering,  Vol. 33, No. 11, (1994), 3643-3648.

4.     Toshiyoshi, H. and Fujita, H., "Electrostatic micro torsion mirrors for an optical switch matrix", Journal of Microelectromechanical Systems,  Vol. 5, No. 4, (1996), 231-237.

5.     Dudley, D., Duncan, W. M. and Slaughter, J., "Emerging digital micromirror device (dmd) applications", in Micromachining and Microfabrication, International Society for Optics and Photonics. (2003), 14-25.

6.     Toshiyoshi, H., Piyawattanametha, W., Chan, C.-T. and Wu, M. C., "Linearization of electrostatically actuated surface micromachined 2-d optical scanner", Journal of Microelectromechanical Systems,  Vol. 10, No. 2, (2001), 205-214.

7.     Dickensheets, D. L. and Kino, G. S., "Silicon-micromachined scanning confocal optical microscope", Journal of Microelectromechanical Systems, ,  Vol. 7, No. 1, (1998), 38-47.

8.     Wu, W., Li, D., Sun, W., Hao, Y., Yan, G., and Jin, S., "Fabrication and characterization of torsion-mirror actuators for optical networking applications", Sensors and Actuators A: Physical,  Vol. 108, No. 1, (2003), 175-181.

9.     Lee, K.-N., Shin, D.-S., Lee, Y.-S. and Kim, Y.-K., "Micromirror array for protein micro array fabrication", Journal of Micromechanics and Microengineering,  Vol. 13, No. 3, (2003), 474.

10.   Syms, R. R., "Surface tension powered self-assembly of 3-d micro-optomechanical structures", Journal of Microelectromechanical Systems, Vol. 8, No. 4, (1999), 448-455.

11.   Fischer, M., Giousouf, M., Schaepperle, J., Eichner, D., Weinmann, M., von Munch, W., and Assmus, F., "Electrostatically deflectable polysilicon micro-mirrors dynamic behavior and comparison with the results from fem modeling with ansys", Sens. Actuators A,  Vol. 67, No. 1-3, (1998), 89-95.

12.   Bao, M., Sun, Y., Zhou, J. and Huang, Y., "Squeeze-film air damping of a torsion mirror at a finite tilting angle", Journal of Micromechanics and Microengineering,  Vol. 16, No. 11, (2006), 2330.

13.   Lin, W.-H. and Zhao, Y.-P., "Influence of damping on the dynamical behavior of the electrostatic parallel-plate and torsional actuators with intermolecular forces", Sensors,  Vol. 7, No. 12, (2007), 3012-3026.

14.   Gusso, A. and Delben, G., "Influence of the casimir force on the pull-in parameters of silicon based electrostatic torsional actuators", Sensors and Actuators A: Physical,  Vol. 135, No. 2, (2007), 792-800.

15.   Guo, J.-G. and Zhao, Y.-P., "Influence of van der waals and casimir forces on electrostatic torsional actuators", Journal of Microelectromechanical Systems, Vol. 13, No. 6, (2004), 1027-1035.

16.   Guo, J.-G. and Zhao, Y.-P., "Dynamic stability of electrostatic torsional actuators with van der waals effect", International Journal of Solids and Structures,  Vol. 43, No. 3, (2006), 675-685.

17.   Guo, J.-G., Zhou, L.-J. and Zhao, Y.-P., "Instability analysis of torsional mems/nems actuators under capillary force", Journal of Colloid and Interface Science,  Vol. 331, No. 2, (2009), 458-462.

18.   Lin, W.-H. and Zhao, Y.-P., "Stability and bifurcation behaviour of electrostatic torsional nems varactor influenced by dispersion forces", Journal of Physics D: Applied Physics,  Vol. 40, No. 6, (2007), 1649.

19.   Schenk, H., Dürr, P., Kunze, D., Lakner, H. and Kück, H., "A resonantly excited 2d-micro-scanning-mirror with large deflection", Sensors and Actuators A: Physical,  Vol. 89, No. 1, (2001), 104-111.

20.   Ping Zhao, J., Ling Chen, H., Ming Huang, J. and Qun Liu, A., "A study of dynamic characteristics and simulation of mems torsional micromirrors", Sensors and Actuators A: Physical,  Vol. 120, No. 1, (2005), 199-210.

21.   Pandey, A. K. and Pratap, R., "A semi-analytical model for squeeze-film damping including rarefaction in a mems torsion mirror with complex geometry", Journal of Micromechanics and Microengineering,  Vol. 18, No. 10, (2008), 105003.

22.   Shabani, R., Tariverdilo, S., Rezazadeh, G. and Agdam, A., "Nonlinear vibrations and chaos in electrostatic torsional actuators", Nonlinear Analysis: Real World Applications,  Vol. 12, No. 6, (2011), 3572-3584.

23.   Azizi, S., Rezazadeh, G., Ghazavi, M.-R. and Khadem, S. E., "Stabilizing the pull-in instability of an electro-statically actuated micro-beam using piezoelectric actuation", Applied Mathematical Modelling,  Vol. 35, No. 10, (2011), 4796-4815.

24.   Krylov, S., Harari, I. and Cohen, Y., "Stabilization of electrostatically actuated microstructures using parametric excitation", Journal of Micromechanics and Microengineering,  Vol. 15, No. 6, (2005), 1188.

25.   Rezazadeh, G., Madinei, H. and Shabani, R., "Study of parametric oscillation of an electrostatically actuated microbeam using variational iteration method", Applied Mathematical Modelling,  Vol. 36, No. 1, (2012), 430-443.

26.   Rhoads, J. F., Shaw, S. W. and Turner, K. L., "The nonlinear response of resonant microbeam systems with purely-parametric electrostatic actuation", Journal of Micromechanics and Microengineering,  Vol. 16, No. 5, (2006), 890.

27.   Nayfeh, A. and Mook, D., "Nonlinear oscillations. 1979", John Willey and Sons, New York,  Vol., No.

28.   Şimşek, M., "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nuclear Engineering and Design,  Vol. 240, No. 4, (2010), 697-705.

29.   Yang, F., Chong, A., Lam, D. and Tong, P., "Couple stress based strain gradient theory for elasticity", International Journal of Solids and Structures,  Vol. 39, No. 10, (2002), 2731-2743.

30.   Sadeghian, H., Goosen, H., Bossche, A., Thijsse, B. and van Keulen, F., "On the size-dependent elasticity of silicon nanocantilevers: Impact of defects", Journal of Physics D: Applied Physics,  Vol. 44, No. 7, (2011), 072001.

31.   Sadeghian, H., Yang, C., Goosen, J., Van Der Drift, E., Bossche, A., French, P., and Van Keulen, F., "Characterizing size-dependent effective elastic modulus of silicon nanocantilevers using electrostatic pull-in instability", Applied Physics Letters,  Vol. 94, No. 22, (2009), 221903-221903-3.

32.   Li, X., Ono, T., Wang, Y. and Esashi, M., "Ultrathin single-crystalline-silicon cantilever resonators: Fabrication technology and significant specimen size effect on young’s modulus", Applied Physics Letters,  Vol. 83, No. 15, (2003), 3081-3083.

33.   Namazu, T., Isono, Y. and Tanaka, T., "Evaluation of size effect on mechanical properties of single crystal silicon by nanoscale bending test using afm", Microelectromechanical Systems, Journal of,  Vol. 9, No. 4, (2000), 450-459.

34.   Gordon, M. J., Baron, T., Dhalluin, F., Gentile, P. and Ferret, P., "Size effects in mechanical deformation and fracture of cantilevered silicon nanowires", Nano Letters,  Vol. 9, No. 2, (2009), 525-529.

35.           Sadeghian, H., Yang, C.-K., Goosen, J. F., Bossche, A., Staufer, U., French, P. J., and van Keulen, F., "Effects of size and defects on the elasticity of silicon nanocantilevers", Journal of Micromechanics and Microengineering,  Vol. 20, No. 6, (2010), 064012.   





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