Nonlinear Dynamic Analysis of Cracked Micro-Beams Below and at the Onset of Dynamic Pull-In Instability

Document Type: Research Paper

Authors

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

Abstract

In this paper, the effect of the crack on dynamic behavior of cracked micro-beam in the presence of DC and AC loads are investigated. By applying the residual axial stress and fringing field stress, a nonlinear analytical model of cracked micro-beam is presented and crack is modeled by a massless rotational spring. The governing equation of the system is solved using Galerkin procedure and shooting method. The equilibria curve and dynamic response of cracked cantilever and clamped-clamped micro-beam are extracted below and at the onset of the dynamic pull-in instability. The results show that the behavior of cracked micro-beam is different from ordinary cracked beam due to nonlinear effects. For a fixed relative crack location, increasing the crack depth causes increasing in the resonance amplitude and reduction in the resonance frequency below dynamic pull-in instability. Also, in cracked cantilever micro-beams, by approaching the crack to fixed end, the resonance frequency reduces and the resonance amplitude increases. In cracked clamped-clamped micro-beam, trend of variations of resonance frequency and resonance amplitude against the crack location is not regular. At the onset pull-in instability, the presence of the crack causes cyclic-fold bifurcation points to appear at the lower frequency. Therefore, it causes early pull-in phenomenon or unwanted abrupt change at the micro-beam behavior. The achievement of this study is simulation of the response of the faulty low-voltage switch and MEMS resonators for different severity of crack at the onset of dynamic pull-in phenomenon.  

Keywords


[1] Vardan V. M., Vinoy K. J., Jose K. A., 2003, RF MEMS and their Applications, Wiley, New York.
[2] Younis M. I., Nayfeh A. H., 2009, A study of the nonlinear response of a resonant micro-beam to an electric actuation, Nonlinear Dynamic 3(1): 91-117.
[3] Rezazadeh G., Tahmasebi A., Ziaei-rad S., 2009, Nonlinear electrostatic behavior for two elastic parallel fixed-fixed and cantilever micro-beams, Mechatronics 19: 840-846.
[4] Valilou S., Jalilpour M., 2012, Frequency response analysis of a capacitive micro-beam resonator considering residual and axial stresses and temperature changes effects, Journal of Solid Mechanics 4(4): 416-425.
[5] Osterberg P. M., Senturia S. D., 1997, M-TEST: A test chip for MEMS material property measurement using electrostatically actuated test structures, Micro-Electromechanical Systems 6(2): 107-118.
[6] Zhang Y., Zhao Y., 2006, Numerical and analytical study on the pull-in instability of micro-structure under electrostatic loading, Sensor Actuator A 127: 366-380.
[7] Rezazadeh G., Tahmasebi A., Ziaei-rad S., 2009, Nonlinear electrostatic behavior for two elastic parallel fixed-fixed and cantilever micro-beams, Mechatronics 19: 840-846.
[8] Mojahedi M., Moghimi zand M., Ahmadian M.T, 2010, Static pull-in analysis of electrostatically actuated microbeams using homotopy perturbation method, Applied Mathematical Modeling 34: 1032-104.
[9] Wang Y.G., Lin W.H., Feng Z. J., Li X. M., 2012, Characterization of extensional multi-layer microbeams in pull-in phenomenon and vibrations, Mechanical Sciences 54: 225-233.
[10] Mohammad T. F., Ouakad H. M., 2016, Static, eigenvalue problem and bifurcation analysis of MEMS arches actuated by electrostatic fringing-fields, Microsystem Technologies 22: 193-206.
[11] Younis M.I., 2015, Analytical expressions for the electrostatically actuated curled beam problem, Microsystem Technologies 21: 1709-1717.
[12] Mohammad-Alasti B., Rezazadeh G., Abbasgholipour M., 2012, Effect of temperature changes on dynamic pull-in phenomenon in a functionally graded capacitive micro-beam, Journal of Solid Mechanics 4(3): 277-295.
[13] Nayfeh A.H., Younis M.I., Abdel-Rahman E.M., 2007, Dynamic pull-in phenomenon in MEMS resonators, Nonlinear Dynamic 48: 153-163.
[14] Rezazadeh G., Fathalilou M., Sadeghi M., 2011, Pull-in voltage of electrostatically-actuated micro-beams in terms of lumped model pull-in voltage using novel design corrective coefficients, Sensing and Imaging 12: 117-131.
[15] Sedighi H.M., Shirazi K.H., Changizian M., 2015, Effect of the amplitude of vibrations on the pull-in instability of doubled-sided actuated microswitch resonators, Applied Mechanics and Technical Physics 56(2): 304-312.
[16] Muhlstein C., Brown S., 1997, Reliability and fatigue testing of MEMs, Tribology Issues and Opportunities in MEMS 1997: 519-528.
[17] Motallebi A., Fathalilou M., Rezazadeh G., 2012, Effect of the open crack on the pull-in instability of an electrostatically actuated Micro-beam, Acta Mechanica Solidica Sinica 25(6): 627-637.
[18] Zhou H., Zhang W. M., Peng Z. K., Meng G., 2015, Dynamic characteristics of electrostatically actuated micro-beams with slant crack, Mathematical Problems in Engineering 2015: 1-13.
[19] Sourki R., Hoseini S.A.H., 2016, Free vibration analysis of size-dependent cracked microbeam based on the modified couple stress theory, Applied Physics A 122: 1-11.
[20] Younis M.I., Abdel-Rahman E.M., Nayfeh A.H., 2002, Static and dynamic behavior of an electrically excited resonant microbeam, Proceedings of the 43rd Conference on AIAA Structures, Structural Dynamics, and Materials, Denver, Colorado.
[21] Abdel-Rahman E.M., Younis M.I., Nayfeh A.H. 2002, Characterization of the mechanical behavior of an electrically actuated micro-beam, Micromechanical and Microengineering 12: 795-766.
[22] Lin H. P., Chang S. C., Wu J. D., 2002, Beam vibrations with an arbitrary number of cracks, Sound and Vibration 258(5): 987-999.
[23] Younis M.I., 2010, MEMS Linear and Nonlinear Statics and Dynamics, Ph.D. thesis, State University of New York.