Nonlinear modeling of squeeze-film phenomena

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.

[1]  T. Veijola,et al.  Compact Squeezed-Film Damping Model for Perforated Surface , 2001 .

[2]  M. Younis,et al.  A new approach to the modeling and simulation of flexible microstructures under the effect of squeeze-film damping , 2004 .

[3]  M. Farid Golnaraghi,et al.  Development and Analysis of a Simplified Nonlinear Model of a Hydraulic Engine Mount , 2001 .

[4]  Ali H. Nayfeh,et al.  Modeling Squeeze-Film Damping of Electrostatically Actuated Microplates Undergoing Large Deflections , 2005 .

[5]  Rashid Bashir,et al.  Novel fabrication method for surface micromachined thin single-crystal silicon cantilever beams , 2003 .

[6]  M. Younis,et al.  A Study of the Nonlinear Response of a Resonant Microbeam to an Electric Actuation , 2003 .

[7]  Yuancheng Sun,et al.  Modified Reynolds' equation and analytical analysis of squeeze-film air damping of perforated structures , 2003 .

[8]  鈴木 増雄.  A. H. Nayfeh and D. T. Mook: Nonlinear Oscillations, John Wiley, New York and Chichester, 1979, xiv+704ページ, 23.5×16.5cm, 10,150円. , 1980 .

[9]  Ali H. Nayfeh,et al.  Finite-Amplitude Motions of Beam Resonators and Their Stability , 2004 .

[10]  Ali H. Nayfeh,et al.  A reduced-order model for electrically actuated microbeam-based MEMS , 2003 .

[11]  Ali H. Nayfeh,et al.  Dynamic Analysis of MEMS Resonators Under Primary-Resonance Excitation , 2005 .

[12]  A. Nayfeh,et al.  Modeling and design of variable-geometry electrostatic microactuators , 2005 .

[13]  RewieÅ ski,et al.  A trajectory piecewise-linear approach to model order reduction of nonlinear dynamical systems , 2003 .

[14]  M. Gretillat,et al.  Effect of air damping on the dynamics of nonuniform deformations of microstructures , 1997, Proceedings of International Solid State Sensors and Actuators Conference (Transducers '97).

[15]  Ebrahim Esmailzadeh,et al.  Existence of Periodic Solution for Beams With Harmonically Variable Length , 1997 .

[16]  W. E. Langlois.  Isothermal squeeze films , 1961 .

[17]  M. K. Andrews,et al.  Damping and gas viscosity measurements using a microstructure , 1995 .

[18]  Joseph Y.-J. Young,et al.  Squeeze-film damping for MEMS structures , 1998 .

[19]  Tamal Mukherjee,et al.  Hierarchical Design and Test of Integrated Microsystems , 1999, IEEE Des. Test Comput..

[20]  Ali H. Nayfeh,et al.  Modeling and simulations of thermoelastic damping in microplates , 2004 .

[21]  M. Madou.  Fundamentals of microfabrication : the science of miniaturization , 2002 .

[22]  Michael Kraft,et al.  Modelling squeeze film effects in a MEMS accelerometer with a levitated proof mass , 2005 .

[23]  M. K. Andrews,et al.  A comparison of squeeze-film theory with measurements on a microstructure , 1993 .

[24]  Pramod Malatkar,et al.  Nonlinear Vibrations of Cantilever Beams and Plates , 2003 .

[25]  Weng Kong Chan,et al.  A slip model with molecular dynamics , 2002 .

[26]  A. Burgdorfer.  The Influence of the Molecular Mean Free Path on the Performance of Hydrodynamic Gas Lubricated Bearings , 1959 .

[27]  S. D. Senturia,et al.  Generating efficient dynamical models for microelectromechanical systems from a few finite-element simulation runs , 1999 .

[28]  J. J. Blech.  On Isothermal Squeeze Films , 1983 .

[29]  Yong P. Chen,et al.  A Quadratic Method for Nonlinear Model Order Reduction , 2000 .

[30]  Ali H. Nayfeh,et al.  Modeling and simulation methodology for impact microactuators , 2004 .

[31]  J. B. Starr.  Squeeze-film damping in solid-state accelerometers , 1990, IEEE 4th Technical Digest on Solid-State Sensor and Actuator Workshop.

[32]  Qing Jiang,et al.  Characterization of the squeeze film damping effect on the quality factor of a microbeam resonator , 2004 .

[33]  S. Senturia,et al.  Pull-in time dynamics as a measure of absolute pressure , 1997, Proceedings IEEE The Tenth Annual International Workshop on Micro Electro Mechanical Systems. An Investigation of Micro Structures, Sensors, Actuators, Machines and Robots.

[34]  Timo Veijola,et al.  The influence of gas-surface interaction on gas-film damping in a silicon accelerometer , 1998 .

[36]  Ali H. Nayfeh,et al.  Characterization of the mechanical behavior of an electrically actuated microbeam , 2002 .

[37]  Palghat S. Ramesh,et al.  DYNAMIC ANALYSIS OF MICRO‐ELECTRO‐MECHANICAL SYSTEMS , 1996 .

[38]  J.E. Schutt-Aine,et al.  Reduced-order modeling of weakly nonlinear MEMS devices with Taylor-series expansion and Arnoldi approach , 2004, Journal of Microelectromechanical Systems.

[39]  G. Nakhaie Jazar,et al.  Optimization of Classical Hydraulic Engine Mounts Based on RMS Method , 2005 .

[40]  S. Mukherjee,et al.  Squeeze film damping effect on the dynamic response of a MEMS torsion mirror , 1998 .

[41]  Cengiz S. Ozkan,et al.  Analysis, control and augmentation of microcantilever deflections in bio-sensing systems , 2003 .

[42]  A White,et al.  A Review of Some Current Research in Microelectromechanical Systems (MEMS) with Defence Applications , 2002 .

[43]  Robert B. Darling,et al.  Compact analytical modeling of squeeze film damping with arbitrary venting conditions using a Green's function approach , 1998 .

[44]  Ali H. Nayfeh,et al.  A reduced-order model for electrically actuated clamped circular plates , 2005 .

[45]  G. Nakhaie Jazar,et al.  Nonlinear Modeling, Experimental Verification, and Theoretical Analysis of a Hydraulic Engine Mount , 2002 .

[46]  H. H. Richardson,et al.  A Study of Fluid Squeeze-Film Damping , 1966 .

[47]  M. Esashi,et al.  Energy dissipation in submicrometer thick single-crystal silicon cantilevers , 2002 .

[48]  S. Lyshevski.  Nano- and Micro-Electromechanical Systems: Fundamentals of Nano- and Microengineering, Second Edition , 2005 .

[49]  S.K. De,et al.  Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS , 2004, Journal of Microelectromechanical Systems.