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NUMERICAL STUDY ON PULL-IN INSTABILITY ANALYSIS OF GEOMETRICALLY NONLINEAR EULER-BERNOULLI MICRO BEAM BASED ON MODIFIED COUPLE STRESS THEORY

Yıl 2012, Cilt: 4 Sayı: 4, 41 - 53, 01.12.2012

Öz

In this paper, the static pull-in instability of beam-type micro-electromechanical systems (MEMS) is theoretically investigated. Two engineering cases including cantilever and double cantilever micro-beam are considered. Considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, a nonlinear sizedependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. By selecting a range of geometric parameters such as beam lengths, width, thickness, gaps and size effect, we identify the static pull-in instability voltage. A MAPLE package is employed to solve the nonlinear differential governing equations to obtain the static pull-in instability voltage of microbeams. The results reveal significant influences of size effect and geometric parameters on the static pull-in instability voltage of MEMS

Kaynakça

  • [1] Khatami, I., Pashai, M.H., Tolou, N., Comparative vibration analysis of a parametrically nonlinear excited oscillator using HPM and numerical method, Mathematical Problems in Engineering, doi:10.1155/2008/956170.
  • [2] Gasparini, A.M., Saetta, A.V., Vitaliani, R.V., on the stability and instability regions of nonconservative continuous system under partially follower forces, Comput. Meth. Appl. Mech. Eng., 124 (1-2), 63-78, 1995.
  • [3] Osterberg, P.M., Senturia, S.D., M-TEST: A test chip for MEMS material property measurements using electrostatically actuated test structures, J. Microelectromech. Syst., 6 (2), 107-118, 1997.
  • [4] Osterberg, P.M., Gupta, R.K., Gilbert, J.R., Senturia, S.D., Quantitative models for the measurement of residual stress, poisson ratio and young’s modulus using electrostatic pullin of beams and diaphragms, Proceedings of the Solid- State Sensor and Actuator Workshop, Hilton Head, SC, 1994.
  • [5] Sadeghian, H., Rezazadeh, G., Osterberg, P., Application of the generalized differential quadrature method to the study of pull-in phenomena of MEMS switches, IEEE/ASME J. Micro Electro Mech. Sys., 16 (6), 1334-1340, 2007.
  • [6] Salekdeh, Y.A., Koochi, A., Beni, Y.T., Abadyan, M., Modeling effect of three nano-scale physical phenomena on instability voltage of multi-layer MEMS/NEMS: Material size dependency, van der waals force and non-classic support conditions, Trends in Applied Sciences Research, 7(1), 1-17, 2012.
  • [7] Batra, R.C., Porfiri, M., Spinello, D., Review of modeling electrostatically actuated microelectromechanical systems, Smart Mater. Struct., 16, R23-R31, 2007.
  • [8] Lin, W.H., Zhao, Y.P., Pull-in instability of micro-switch actuators: Model review, Int. J. Nonlinear Sci. Numer. Simulation, 9 (2), 175-184, 2008.
  • [9] Koiter, W.T., Couple-stresses in the theory of elasticity: I and II. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen Series B, 6717-6744, 1964.
  • [10] Mindlin, R.D., Tiersten, H.F., Effects of couple-stresses in linear elasticity, Archive for Rational Mechanics and Analysis, 11(1), 415-448, 1962.
  • [11] Toupin, R.A., Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis, 11(1), 385–414, 1962.
  • [12] Anthoine, A., Effect of couple-stresses on the elastic bending of beams, International Journal of Solids and Structures, 37, 1003-1018, 2000.
  • [13] Yang, F., Chong, A.C. M., Lam, D.C.C., Tong, P., Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39(10), 2731-2743, 2002.
  • [14] Xia, W., Wang, L., Yin, L., Nonlinear non-classical microscale beams: Static bending, postbuckling and free vibration, International Journal of Engineering Science, 48, 2044- 2053, 2010.
  • [15] Asghari, M., Rahaeifard, M., Kahrobaiyan, M.H., Ahmadian, M.T., on the size-dependent behavior of functionally graded micro-beams, Materials and Design, 32, 1435-1443, 2011.
  • [16] Rong, H., Huang, Q.A., Nie, M., Li, W., An analytical model for pull-in voltage of clamped–clamped multilayer beams, Sens. Actuators A, 116, 15-21, 2004.
  • [17] Yang, F., Chong, A.C.M., Lam, D.C.C., Tong, P., Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39 (10), 2731-2743, 2002.
  • [18] Shengli, K., Shenjie, Z., Zhifeng, N., Kai, W., The size-dependent natural frequency of Bernoulli–Euler micro-beams, Journal of Engineering Science, 46, 427-437, 2008.
  • [19] Ma, H.M., Gao, X.L., Reddy, J.N., A microstructure-dependent Timoshenko beam model based on a modified couple stress theory, Journal of the Mechanics and Physics of Solids, 56, 3379–3391, 2008.
  • [20] Gupta, R.K., Electrostatic pull-in test structure design for in-situ mechanical property measurements of microelectromechanical systems, Ph.D. Disserta-tion, Massachusetts Institute of Technology (MIT), Cambridge, MA., 1997.
  • [21] Zhao, J., Zhou, S., Wanga, B., Wang, X., Nonlinear microbeam model based on strain gradient theory, Applied Mathematical Modelling, 36, 2674-2686, 2012.
Yıl 2012, Cilt: 4 Sayı: 4, 41 - 53, 01.12.2012

Öz

Kaynakça

  • [1] Khatami, I., Pashai, M.H., Tolou, N., Comparative vibration analysis of a parametrically nonlinear excited oscillator using HPM and numerical method, Mathematical Problems in Engineering, doi:10.1155/2008/956170.
  • [2] Gasparini, A.M., Saetta, A.V., Vitaliani, R.V., on the stability and instability regions of nonconservative continuous system under partially follower forces, Comput. Meth. Appl. Mech. Eng., 124 (1-2), 63-78, 1995.
  • [3] Osterberg, P.M., Senturia, S.D., M-TEST: A test chip for MEMS material property measurements using electrostatically actuated test structures, J. Microelectromech. Syst., 6 (2), 107-118, 1997.
  • [4] Osterberg, P.M., Gupta, R.K., Gilbert, J.R., Senturia, S.D., Quantitative models for the measurement of residual stress, poisson ratio and young’s modulus using electrostatic pullin of beams and diaphragms, Proceedings of the Solid- State Sensor and Actuator Workshop, Hilton Head, SC, 1994.
  • [5] Sadeghian, H., Rezazadeh, G., Osterberg, P., Application of the generalized differential quadrature method to the study of pull-in phenomena of MEMS switches, IEEE/ASME J. Micro Electro Mech. Sys., 16 (6), 1334-1340, 2007.
  • [6] Salekdeh, Y.A., Koochi, A., Beni, Y.T., Abadyan, M., Modeling effect of three nano-scale physical phenomena on instability voltage of multi-layer MEMS/NEMS: Material size dependency, van der waals force and non-classic support conditions, Trends in Applied Sciences Research, 7(1), 1-17, 2012.
  • [7] Batra, R.C., Porfiri, M., Spinello, D., Review of modeling electrostatically actuated microelectromechanical systems, Smart Mater. Struct., 16, R23-R31, 2007.
  • [8] Lin, W.H., Zhao, Y.P., Pull-in instability of micro-switch actuators: Model review, Int. J. Nonlinear Sci. Numer. Simulation, 9 (2), 175-184, 2008.
  • [9] Koiter, W.T., Couple-stresses in the theory of elasticity: I and II. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen Series B, 6717-6744, 1964.
  • [10] Mindlin, R.D., Tiersten, H.F., Effects of couple-stresses in linear elasticity, Archive for Rational Mechanics and Analysis, 11(1), 415-448, 1962.
  • [11] Toupin, R.A., Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis, 11(1), 385–414, 1962.
  • [12] Anthoine, A., Effect of couple-stresses on the elastic bending of beams, International Journal of Solids and Structures, 37, 1003-1018, 2000.
  • [13] Yang, F., Chong, A.C. M., Lam, D.C.C., Tong, P., Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39(10), 2731-2743, 2002.
  • [14] Xia, W., Wang, L., Yin, L., Nonlinear non-classical microscale beams: Static bending, postbuckling and free vibration, International Journal of Engineering Science, 48, 2044- 2053, 2010.
  • [15] Asghari, M., Rahaeifard, M., Kahrobaiyan, M.H., Ahmadian, M.T., on the size-dependent behavior of functionally graded micro-beams, Materials and Design, 32, 1435-1443, 2011.
  • [16] Rong, H., Huang, Q.A., Nie, M., Li, W., An analytical model for pull-in voltage of clamped–clamped multilayer beams, Sens. Actuators A, 116, 15-21, 2004.
  • [17] Yang, F., Chong, A.C.M., Lam, D.C.C., Tong, P., Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39 (10), 2731-2743, 2002.
  • [18] Shengli, K., Shenjie, Z., Zhifeng, N., Kai, W., The size-dependent natural frequency of Bernoulli–Euler micro-beams, Journal of Engineering Science, 46, 427-437, 2008.
  • [19] Ma, H.M., Gao, X.L., Reddy, J.N., A microstructure-dependent Timoshenko beam model based on a modified couple stress theory, Journal of the Mechanics and Physics of Solids, 56, 3379–3391, 2008.
  • [20] Gupta, R.K., Electrostatic pull-in test structure design for in-situ mechanical property measurements of microelectromechanical systems, Ph.D. Disserta-tion, Massachusetts Institute of Technology (MIT), Cambridge, MA., 1997.
  • [21] Zhao, J., Zhou, S., Wanga, B., Wang, X., Nonlinear microbeam model based on strain gradient theory, Applied Mathematical Modelling, 36, 2674-2686, 2012.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Diğer ID JA66BB47CG
Bölüm Makaleler
Yazarlar

Y. Tadi Beni Bu kişi benim

M. Heidari Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2012
Yayımlandığı Sayı Yıl 2012 Cilt: 4 Sayı: 4

Kaynak Göster

APA Beni, Y. T., & Heidari, M. (2012). NUMERICAL STUDY ON PULL-IN INSTABILITY ANALYSIS OF GEOMETRICALLY NONLINEAR EULER-BERNOULLI MICRO BEAM BASED ON MODIFIED COUPLE STRESS THEORY. International Journal of Engineering and Applied Sciences, 4(4), 41-53.
AMA Beni YT, Heidari M. NUMERICAL STUDY ON PULL-IN INSTABILITY ANALYSIS OF GEOMETRICALLY NONLINEAR EULER-BERNOULLI MICRO BEAM BASED ON MODIFIED COUPLE STRESS THEORY. IJEAS. Aralık 2012;4(4):41-53.
Chicago Beni, Y. Tadi, ve M. Heidari. “NUMERICAL STUDY ON PULL-IN INSTABILITY ANALYSIS OF GEOMETRICALLY NONLINEAR EULER-BERNOULLI MICRO BEAM BASED ON MODIFIED COUPLE STRESS THEORY”. International Journal of Engineering and Applied Sciences 4, sy. 4 (Aralık 2012): 41-53.
EndNote Beni YT, Heidari M (01 Aralık 2012) NUMERICAL STUDY ON PULL-IN INSTABILITY ANALYSIS OF GEOMETRICALLY NONLINEAR EULER-BERNOULLI MICRO BEAM BASED ON MODIFIED COUPLE STRESS THEORY. International Journal of Engineering and Applied Sciences 4 4 41–53.
IEEE Y. T. Beni ve M. Heidari, “NUMERICAL STUDY ON PULL-IN INSTABILITY ANALYSIS OF GEOMETRICALLY NONLINEAR EULER-BERNOULLI MICRO BEAM BASED ON MODIFIED COUPLE STRESS THEORY”, IJEAS, c. 4, sy. 4, ss. 41–53, 2012.
ISNAD Beni, Y. Tadi - Heidari, M. “NUMERICAL STUDY ON PULL-IN INSTABILITY ANALYSIS OF GEOMETRICALLY NONLINEAR EULER-BERNOULLI MICRO BEAM BASED ON MODIFIED COUPLE STRESS THEORY”. International Journal of Engineering and Applied Sciences 4/4 (Aralık 2012), 41-53.
JAMA Beni YT, Heidari M. NUMERICAL STUDY ON PULL-IN INSTABILITY ANALYSIS OF GEOMETRICALLY NONLINEAR EULER-BERNOULLI MICRO BEAM BASED ON MODIFIED COUPLE STRESS THEORY. IJEAS. 2012;4:41–53.
MLA Beni, Y. Tadi ve M. Heidari. “NUMERICAL STUDY ON PULL-IN INSTABILITY ANALYSIS OF GEOMETRICALLY NONLINEAR EULER-BERNOULLI MICRO BEAM BASED ON MODIFIED COUPLE STRESS THEORY”. International Journal of Engineering and Applied Sciences, c. 4, sy. 4, 2012, ss. 41-53.
Vancouver Beni YT, Heidari M. NUMERICAL STUDY ON PULL-IN INSTABILITY ANALYSIS OF GEOMETRICALLY NONLINEAR EULER-BERNOULLI MICRO BEAM BASED ON MODIFIED COUPLE STRESS THEORY. IJEAS. 2012;4(4):41-53.

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