Abstract
Oscillating microplates attached to microbeams is the main part of many microresonators and micro-electro-mechanical systems (MEMS). The sque-eze-film phenomena appears when the microplate is vibrating in a viscose medium. The phenomena can potentially change the design point and performance of the micro-system, although its effects on MEMS dynamic are considered secondary compared to main mechanical and electrical forces. In this investigation, we model the squeeze-film phenomena and present two nonlinear mathematical functions to define and model the restoring and damping behaviors of squeeze-film phenomena. Accepting an analytical approach, we present the mathematical modeling of microresonator dynamic and develop effective equations to be utilized to study the electrically actuated microresonators. Then employing the averaging perturbation method, we determine the frequency response of the microbeam and examine the effects of parameters on the resonator’s dynamics. The nonlinear model for MEMS includes the initial deflection due to polarization voltage, mid-plane stretching, and axial loads, as well as the nonlinear displacement coupling of the actuating electric force. The main purpose of this chapter is to present an applied model to simulate the squeeze-film phenomena, and introduce their design parameters.
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References
Abdel-Rahman EA, Nayfeh AH, Younis MI (2004) Finite amplitude motions of beam resonators and their stability. J Comput Theoret Nanosci 1(4):385–391
Abdel-Rahman EM, Younis MI, Nayfeh AH (2002) Characterization of the mechanicsl behavior of an electrically actuated microbeam. J Micromech Microeng 12:759–766
Andrews M, Harris I, Turner G (1993) A comparison of squeeze-film theory with measurements on a microstructure. Sensors Actuators A 36:79–87
Andrews MK, Harris PD (1995) Damping and gas viscosity measurements using a microstructure. Sensors Actuators A 49:103–108
Bao M, Yang H, Sun Y, French PJ (2003) Modified Reynolds equation and analytical analysis of squeeze-film air damping of perforated structures. J Micromech Microeng 13:795–800
Blech JJ (1983) On isothermal squeeze-films. J Lubric Technol 105:615–620
Burgdorfer A (1959) The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated bearing. J Basic Eng 81:94–99
Chen J, Kang SM (2000) An algorithm for automatic model reduction of nonlinear MEMS devices. Proceedings of IEEE International Symposium Circuits and Systems, 28–31 May 2000, pp 445–448
Chen J, Kang S, Zou J, Liu C, Schutt-Ainé JE (2004) Reduced-order modeling of weakly nonlinear MEMS devices with Taylor-series expansion and Arnoldi approach. J Microelectromech Syst 13(3):441–451
Chen Y, White J (2000) A quadratic method for nonlinear model order reduction. Proceedings of the International Symposium on Modeling and Simulation of Microsystem Conference, March 2000
Christopherson J, Jazar GN (2005) Optimization of classical hydraulic engine mounts based on RMS method. J Shock Vibr 12(12):119–147
Darling RB, Hivick C, Xu J (1998) Compact analytical modeling of squeeze-film damping with arbitrary venting conditions using a green’s function approach. Sensors Actuators A 70:32–41
Esmailzadeh E, Mehri B, Reza NJ (1997) Existence of periodic solution for equation of motion of simple beams with harmonically variable length. J Vibr Acoustics 119:485–488
Fedder GK (1994) Simulation Micromech Syst Ph.D. dissertation, University of California at Berkeley
Golnaraghi MF, Jazar RN (2001) Development and analysis of a simplified nonlinear model of a hydraulic engine mount. J Vibr Control 7(4):495–526
Griffin WS, Richardson HH, Yamanami S (1966) A study of fluid squeeze-film damping. ASME J Basic Eng D 88, 451–456.
Gupta A, Denton JP, McNally H, Bashar R (2003) NovelFabrication method for surface micromachined thin single-crystal silicon cantilever beams. J Microelectromech Syst 12(2):185
Gupta RK, Senturia SD (1997) Pull-in time dynamics as a measure of absolute pressure. Proceedings of the tenth annual international workshop on micro electro mechanical systems, New York, NY, pp 290–294
Harmany Z (2003) Effects of vacuum pressure on the response characteristics on MEMS cantilever structures. NSF EE REU PENN STATE Ann Res J I:54–64
Houlihan R, Kraft M (2005) Modeling squeeze-film effects in a MEMS accelerometer with a levitated proof mass. J Micromech Microeng 15:893–902
Hung ES, Senturia SD (1999) Generating efficient dynamical models for microelectromechanical systems from a few finite element simulation runs. J Microelectromech Syst 8:280–289
Jazar RN, Golnaraghi MF (2002) Nonlinear modeling, experimental verification, and theoretical analysis of a hydraulic engine mount. J Vibr Control 8(1):87–116
Khaled ARA, Vafai K, Yang M, Zhang X, Ozkan CS (2003) Analysis, control and augmentation of microcantilever deflections in bio-sensing systems. Sensors Actuators B 7092:1–13
Langlois WE (1962) Isothermal squeeze-films. Q Appl Math 20:131–150
Lyshevski SE (2001) Nano- and microelectromechanical systems, fundamentals of nano- and microengineering. CRC Press, Boca Raton, Florida
Madou MJ (2002) Fundamentals of microfabrication: the science of miniaturization, 2nd edn. CRC Press, Boca Raton, FL
Mahmoudian N, Aagaah MR, Jazar RN, Mahinfalah M (2004) Dynamics of a micro electro mechanical system (MEMS). International conference on MEMS, NANO, and smart systems, Banff, Alberta - Canada, 25–27 August 2004
Malatkar P (2003) Nonlinear vibrations of cantilever beams and plates. Ph.D. Thesis in Mechanical Engineering, Virginia Polytechnic Institute and State University
Mukherjee T, Fedder GK, Blanton RD (1999) Hierarchical design and test of integrated microsystems. IEEE Design Test 16:18–27
Najar F, Choura S, El-Borgi S, Abdel-Rahman EM, Nayfeh AH (2005) Modeling and design of variable-geometry electrostatic microactuators. J Micromech Microeng 15(3):419–429
Nayfeh AH, Mook DT (1979) Nonlinear oscillations. Wiley, New York
Nayfeh AH, Younis MI (2004a) Modeling and simulations of thermoelastic damping in microplates. J Micromech Microeng 14:1711–1717
Nayfeh AH and Younis MI (2004b) A new approach to the modeling and simulation of flexible microstructures under the effect of squeeze-film damping. J Micromech Microeng 14:170–181
Nayfeh AH, Younis MI, Abdel-Rahman EA (2005) Reduced-order modeling of MEMS. Third MIT conference on computational fluid and solid mechanics, Cambridge, MA, 14–17 June 2005
Pan F, Kubby J, Peeters E, Tan A, Mukherjee S (1998) Squeeze film damping effect on the dynamic response of a MEMS torsion mirror. J Micromech Microeng 8(3i):200–208
Rewienski MJ (2003) A trajectory piecewise-linear approach to model order reduction of nonlinear dynamical systems. Ph.D. thesis, Department of Electrical Engineering, Massachusetts Institute of Technology
Shi F, Ramesh P, Mukherjee S (1996) Dynamic analysis of micro-electro-mechanical systems. Int J Numer Meth Eng 39(24):4119–4139
Starr JB (1990) Squeeze-film damping in solid-state accelerometers. Proceedings of technical digest IEEE solid-state sensors and actuators workshop, Hilton Head Island, SC, pp 44–47
Sudipto K, Aluru NR (2004) Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS. J Microelectromech Syst 13(5):737–758
Sun Y, Chan WK, Liu N (2002) A slip model with molecular dynamics. J Micromech Microeng 12:316–322
Veijola T, Mattila T (2001) Compact squeezed-film damping model for perforated surface. Proceedings of IEEE 11th international conference on solid-state sensors, actuators and microsystems, pp 1506–1509
Veijola T, Kuisma H, Lahdenper¨a J (1998) The influence of gas-surface interaction on gas-film damping in a silicon accelerometer. Sensors Actuators A 66:83–92
Vogl GW, Nayfeh AH (2005) A reduced-order model for electrically actuated clamped circular plates. J Micromech Microeng 15:684–690
White A (2002) Review of some current research in microelectromechanical systems (MEMS) with defence applications, DSTO Aeronautical and Maritime Research Laboratory, Fishermans Bend Vic, Australia, pp 10
Yang YJ (1998) Squeeze-film damping for MEMS structures. MS Thesis, Electrical Engineering, Massachusetts Institute of Technology
Yang YJ, Gretillat M-A, Senturia SD (1997) Effect of Air damping on the dynamics of nonuniform deformations of microstructures, international conference on solid-state. Sensors and Actuators. Chicago, 16–19 June 1997, pp 1094–1096
Yang JL, Ono T, Esashi M (2002) Energy dissipation in submicrometer thick single-crystal 116 cantilevers. J Microelectromech Syst 11(6):775–783
Yang Y-J, Senturia SD (1996) Numerical simulation of compressible squeezed-film damping. Proceedings of solid-state sensor and actuator workshop pp 76–79
Yang YJ, Senturia SD (1997) Effect of air damping on the dynamics of nonuniform deformations of microstructures. Proceedings of IEEE international conference on solid-state sensors and actuators, New York, NY, pp 1093–1096
Younis MI (2001) Investigation of the mechanical behavior of micro-beam-based MEMS devices. MS. thesis in Mechanical Engineering, Virginia Polytechnic Institute and State University, December 2001
Younis MI (2004) Modeling and simulation of micrielectromecanical system in multi-physics fields. Ph.D. thesis, Mechanicsl Engineering, Virginia Polytechnic Institute and State University
Younis MI, Abdel-Rahman EM, Nayfeh A (2003) A reduced-order model for electrically actuated microbeam-based MEMS. J Microelectromech Syst 12(5):672–680
Younis MI, Nayfeh AH (2003) A study of the nonlinear response of a resonant microbeam to electric actuation. J Nonlinear Dyn 31:91–117.
Younis MI, Nayfeh AH (2005a) Modeling squeeze-film damping of electrostatically actuated microplates undergoing large deflections. ASME 20th biennial conference on mechanical vibration and noise, 5th international conference on multibody systems, nonlinear dynamics and control, DETC2005-84421, Long Beach, CA, 24–28 September 2005
Younis MI, Nayfeh AH (2005b) Dynamic analysis of MEMS resonators under primary-resonance excitation. ASME 20th biennial conference on mechanical vibration and noise, DETC2005-84146, Long Beach, CA, 24–28 September 2005
Zhang C, Xu G, Jiang Q (2004) Characterization of the squeeze-film damping effect on the quality factor of a microbeam resonator. J Micromech Microeng 14:1302–1306
Zhao Z, Dankowicz H, Reddy CK, Nayfeh AH (2004) Modelling and simulation methodology for impact microactuators. J Micromech Microeng 14:775–784
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Jazar, R.N. (2012). Nonlinear Modeling of Squeeze-Film Phenomena. In: Dai, L., Jazar, R. (eds) Nonlinear Approaches in Engineering Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1469-8_2
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DOI: https://doi.org/10.1007/978-1-4614-1469-8_2
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