An Investigation of the Effects of Crack on the Zone of Pull-in Suppression in MicroElectromechanical Systems Using High-Frequency Excitation

Document Type : Research Article

Authors

Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran

Abstract

In this paper, the pull-in phenomenon is suppressed using a range of values of amplitude
and frequency of high-frequency voltage excitations in the post pull-in condition of the cracked microelectromechanical systems. These specified ranges are named as stable zones. It is investigated the effects of the crack parameters (depth and location) on changes of these zones, in the post pull-in condition. It is shown that these zones have different areas for different crack parameters. The cracked micro-beam is
modeled as a single-degree-of-freedom systems consist of mass-spring-damper and the motion equation
of the cracked micro-beam is extracted. The method of direct partition of motion is used to split the fast
and slow dynamics. By means of slow dynamic part, the effects of the crack on the averaged position of
vibration of cracked micro-beam are investigated versus voltage amplitude and frequency of the highfrequency AC. By approaching the crack to the fixed end or increasing the depth of crack, the stability
zone reduced. Therefore, the pull-in instability can be suppressed in the lower range of amplitude and
frequency. This method can be used in sensors’ health-monitoring and one can predict the parameters of
the crack using this method.

Highlights

[1] C.L. Goldsmith, Z. Yao, S. Eshelman, D. Denniston, Performance of low-loss RF MEMS capacitive switches, IEEE Microwave and Guided Wave Letters, 8 (1998) 269–271.

[2] E.K. Chan, K. Garikipati, W.R. Dutton, Characteristics of contact electromechanics through capacitance-voltage measurements and simulations, Microelectromechanical systems, 8 (1999) 208–217.

[3] M.K. Andrews, G.C. Tunner, P.D. Hariss, I.M. Hariss, A resonant pressure sensor based on a squeezed film of gas, Sensors and Actuators A: Physical, 36(3) (1993) 219- 226.

[4] F. Ayela, T. Fournier, An experimental study of anharmonic micromachined silicon resonator, Measurement Science and Technology, 9(11) (1998) 1821-1830.

[5] V.M. Vardan, K.J. Vinoy, K.A. Jose, RF MEMS and their applications, Wiley, New York, 2003.

[6] M.I. Younis, A.H. Nayfeh, A study of the nonlinear response of a resonant micro-beam to an electric actuation, Nonlinear Dynamic, 3(1) (2003) 91-117.

[7] G. Rezazadeh, A. Tahmasebi, S. and Ziaei-rad, Nonlinear electrostatic behavior for two elastic parallel fixed-fixed and cantilever micro-beams, Mechatronics, 19 (2009) 840-846.

[8] P.M. Osterberg, S.D. Senturia, M-TESt: A Test Chip for MEMS Material Property Measurement Using Electrostatically Actuated Test Structures, Microelectromechanical system, 6(2) (1997) 107-118.

[9] M.I. Younis, MEMS linear and nonlinear statics and dynamics, 2010.

[10] X.L. Jia, J. Yang, S. Kitipornchai, C.W. Lim, Pull-in instability and free vibration of electrically actuated poly-SIGE graded micro-beams with a curved ground electrode, Applied Mathematical Modelling, 36(5) (2012) 1875-1884.

[11] Y. Zhang, Y. Zhao, Numerical and analytical study on the pull-in instability of micro-structure under electrostatic loading, Sensors and Actuators A: Physical, 127(2) (2006) 366-380.

[12] M. Mojahedi, M. Moghimi zand, M.T. Ahmadian, Static pull-in analysis of electrostatically actuated microbeams using homotopy perturbation method, Applied Mathematical Modelling, 34(4) (2010) 1032-1041.

[13] A.H. Nayfeh, M.I. Younis, E.M. Abdel-Rahman, Dynamic pull-in phenomenon in MEMS resonators, Nonlinear Dynamics, 48(1) (2007) 153-163.

[14] M. Sadeghi, M. Fathalilou, G. Rezazadeh, Study of the size dependent behavior of a micro-beam subjected to a nonlinear electrostatic pressure, Modares Mechanical Engineering, 14 (2014) 137-144.

[15] F. Lakrad, M. Belhaq, Suppression of pull-in instability in MEMS using a high-frequency actuation, Communications in Nonlinear Science and Numerical Simulation, 15(11) (2010) 3640-3646.

[16] F. Lakrad, M. Belhaq, Suppression of pull-in in a microstructure actuated by mechanical shocks and electrostatic forces, International Journal of Non-Linear Mechanics, 46(2) (2011) 407-414.

[17] C. Muhlstein, S. Brown, Reliability and Fatigue Testing of MEMS, Klewer Academic Publications, 1997.

[18] A. Motallebi, M. Fathalilou, G. Rezazadeh, Effect of the open crack on the pull-in instability of an electrostatically actuated Micro-beam, Acta Mechanica Solida Sinica, 25(6) (2012) 627-637.

[19] H. Zhou, W.M. Zhang, Z.K. Peng, G. Meng, Dynamic characteristics of electrostatically actuated micro-beams with slant crack, Mathematical Problems in Engineering, 2015 (2015).

[20] M.I. Younis, R. Miles, D. Jordy, Investigation of the response of microstructures under the combined effect of mechanical shock and electrostatic forces, micromechanical and microengineering, 16(11) (2011) 2463-2474.

[21] S.D. Senturia, Microsystem design, Kluwer, Boston, 2001.

[22] S. Pamidighantam, R. Puers, K. Baert, H. Tilmans, Pull-in voltage analysis of electrostatically actuated beam structures with fixed–fixed and fixed–free end conditions, Micromechanics and Microengineering, 12(4) (2002) 458-464.

[23] J.J. Thomson, Vibrations and Sability: Advanced Theory, Analysis, and Tools, second ed., Springer, Berlin- Heidelberg, 2003

Keywords

References

[1] C.L. Goldsmith, Z. Yao, S. Eshelman, D. Denniston, Performance of low-loss RF MEMS capacitive switches, IEEE Microwave and Guided Wave Letters, 8 (1998) 269–271.
[2] E.K. Chan, K. Garikipati, W.R. Dutton, Characteristics of contact electromechanics through capacitance-voltage measurements and simulations, Microelectromechanical systems, 8 (1999) 208–217.
[3] M.K. Andrews, G.C. Tunner, P.D. Hariss, I.M. Hariss, A resonant pressure sensor based on a squeezed film of gas, Sensors and Actuators A: Physical, 36(3) (1993) 219- 226.
[4] F. Ayela, T. Fournier, An experimental study of anharmonic micromachined silicon resonator, Measurement Science and Technology, 9(11) (1998) 1821-1830.
[5] V.M. Vardan, K.J. Vinoy, K.A. Jose, RF MEMS and their applications, Wiley, New York, 2003.
[6] M.I. Younis, A.H. Nayfeh, A study of the nonlinear response of a resonant micro-beam to an electric actuation, Nonlinear Dynamic, 3(1) (2003) 91-117.
[7] G. Rezazadeh, A. Tahmasebi, S. and Ziaei-rad, Nonlinear electrostatic behavior for two elastic parallel fixed-fixed and cantilever micro-beams, Mechatronics, 19 (2009) 840-846.
[8] P.M. Osterberg, S.D. Senturia, M-TESt: A Test Chip for MEMS Material Property Measurement Using Electrostatically Actuated Test Structures, Microelectromechanical system, 6(2) (1997) 107-118.
[9] M.I. Younis, MEMS linear and nonlinear statics and dynamics, 2010.
[10] X.L. Jia, J. Yang, S. Kitipornchai, C.W. Lim, Pull-in instability and free vibration of electrically actuated poly-SIGE graded micro-beams with a curved ground electrode, Applied Mathematical Modelling, 36(5) (2012) 1875-1884.
[11] Y. Zhang, Y. Zhao, Numerical and analytical study on the pull-in instability of micro-structure under electrostatic loading, Sensors and Actuators A: Physical, 127(2) (2006) 366-380.
[12] M. Mojahedi, M. Moghimi zand, M.T. Ahmadian, Static pull-in analysis of electrostatically actuated microbeams using homotopy perturbation method, Applied Mathematical Modelling, 34(4) (2010) 1032-1041.
[13] A.H. Nayfeh, M.I. Younis, E.M. Abdel-Rahman, Dynamic pull-in phenomenon in MEMS resonators, Nonlinear Dynamics, 48(1) (2007) 153-163.
[14] M. Sadeghi, M. Fathalilou, G. Rezazadeh, Study of the size dependent behavior of a micro-beam subjected to a nonlinear electrostatic pressure, Modares Mechanical Engineering, 14 (2014) 137-144.
[15] F. Lakrad, M. Belhaq, Suppression of pull-in instability in MEMS using a high-frequency actuation, Communications in Nonlinear Science and Numerical Simulation, 15(11) (2010) 3640-3646.
[16] F. Lakrad, M. Belhaq, Suppression of pull-in in a microstructure actuated by mechanical shocks and electrostatic forces, International Journal of Non-Linear Mechanics, 46(2) (2011) 407-414.
[17] C. Muhlstein, S. Brown, Reliability and Fatigue Testing of MEMS, Klewer Academic Publications, 1997.
[18] A. Motallebi, M. Fathalilou, G. Rezazadeh, Effect of the open crack on the pull-in instability of an electrostatically actuated Micro-beam, Acta Mechanica Solida Sinica, 25(6) (2012) 627-637.
[19] H. Zhou, W.M. Zhang, Z.K. Peng, G. Meng, Dynamic characteristics of electrostatically actuated micro-beams with slant crack, Mathematical Problems in Engineering, 2015 (2015).
[20] M.I. Younis, R. Miles, D. Jordy, Investigation of the response of microstructures under the combined effect of mechanical shock and electrostatic forces, micromechanical and microengineering, 16(11) (2011) 2463-2474.
[21] S.D. Senturia, Microsystem design, Kluwer, Boston, 2001.
[22] S. Pamidighantam, R. Puers, K. Baert, H. Tilmans, Pull-in voltage analysis of electrostatically actuated beam structures with fixed–fixed and fixed–free end conditions, Micromechanics and Microengineering, 12(4) (2002) 458-464.
[23] J.J. Thomson, Vibrations and Sability: Advanced Theory, Analysis, and Tools, second ed., Springer, Berlin- Heidelberg, 2003
AUT Journal of Mechanical Engineering
Volume 1, Issue 1
June 2017
Pages 99-108

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