0
Research Papers

Reduced Order Model Analysis of Frequency Response of Alternating Current Near Half Natural Frequency Electrostatically Actuated MEMS Cantilevers

[+] Author and Article Information
Dumitru I. Caruntu

e-mail: caruntud@utpa.edu; caruntud2@asme.org;
dcaruntu@yahoo.com

Israel Martinez

Mechanical Engineering Department,
University of Texas-Pan American,
Edinburg, TX 78541

Martin W. Knecht

Engineering Department,
South Texas College,
McAllen, TX 78501

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received June 1, 2012; final manuscript received November 29, 2012; published online January 25, 2013. Assoc. Editor: Henryk Flashner.

J. Comput. Nonlinear Dynam 8(3), 031011 (Jan 25, 2012) (6 pages) Paper No: CND-12-1085; doi: 10.1115/1.4023164 History: Received June 01, 2012; Revised November 29, 2012

This paper uses the reduced order model (ROM) method to investigate the nonlinear-parametric dynamics of electrostatically actuated microelectromechanical systems (MEMS) cantilever resonators under soft alternating current (AC) voltage of frequency near half natural frequency. This voltage is between the resonator and a ground plate and provides the actuation for the resonator. Fringe effect and damping forces are included. The resonator is modeled as a Euler-Bernoulli cantilever. ROM convergence shows that the five terms model accurately predicts the steady states of the resonator for both small and large amplitudes and the pull-in phenomenon either when frequency is swept up or down. It is found that the MEMS resonator loses stability and undergoes a pull-in phenomenon (1) for amplitudes about 0.5 of the gap and a frequency less than half natural frequency, as the frequency is swept up, and (2) for amplitudes of about 0.87 of the gap and a frequency about half natural frequency, as the frequency is swept down. It also found that there are initial amplitudes and frequencies lower than half natural frequency for which pull-in can occur if the initial amplitude is large enough. Increasing the damping narrows the escape band until no pull-in phenomenon can occur, only large amplitudes of about 0.85 of the gap being reached. If the damping continues to increase the peak amplitude decreases and the resonator experiences a linear dynamics like behavior. Increasing the voltage enlarges the escape band by shifting the sweep up bifurcation frequency to lower values; the amplitudes of losing stability are not affected. Fringe effect affects significantly the behavior of the MEMS resonator. As the cantilever becomes narrower the fringe effect increases. This slightly enlarges the escape band and increases the sweep up bifurcation amplitude. The method of multiple scales (MMS) fails to accurately predict the behavior of the MEMS resonator for any amplitude greater than 0.45 of the gap. Yet, for amplitudes less than 0.45 of the gap MMS predictions match perfectly ROM predictions.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Badri, A. E., Sinha, J. K., and Albarbar, A., 2010, “A Typical Filter Design to Improve the Measured Signals From MEMS Accelerometer,” Measurement, 43, pp. 1425–1430. [CrossRef]
Ozkeskin, F. M., and Gianchandani, Y. B., 2012, “Micromachined Pt-Rh and Stainless Steel Relays for High Power DC Applications,” Sens. Actuators, A, 176, pp. 130–137. [CrossRef]
Dumas, N., Trigona, C., Pons, P., Latorre, L., and Nouet, P., 2011, “Design of Smart Drivers For Electrostatic MEMS Switches,” Sens. Actuators, A, 167, pp. 422–432. [CrossRef]
Kamali, R., and Binesh, A. R., 2009, “Investigation of Gas Flow in Micro-Filters and Modification of Scaling Law,” Int. Commun. Heat Mass Transf., 36, pp. 763–767. [CrossRef]
Tang, M., Cagliani, A., and Davis, Z. J., 2011, “Pulse Mode Readout of MEMS Bulk Disk Resonator Based Mass Sensor,” Sens. Actuators A, 168, pp. 39–45. [CrossRef]
Park, K. K., Lee, H., Kupnik, M., Oralkan, O., Ramseyer, J., Lang, H. P., Hegner, M., Gerber, C., and Khuri-Yakub, B. T., 2011, “Capacitive Micromachined Ultrasonic Transducer (CMUT) as a Chemical Sensor for DMMP Detection,” Sens. Actuators B, 160, pp. 1120–1127. [CrossRef]
Huang, X., Li, S., Schultz, J. S., Wang, Q., and Lin, Q., 2009, “A MEMS Affinity Glucose Sensor Using Biocompatible Glucose Responsive Polymer,” Sens. Actuators B, 140, pp. 603–609. [CrossRef]
Caruntu, D. I., and Knecht, M., 2010, DETC2010-28612, “On MEMS/NEMS Biosensor Sensitivity Near Half Natural Frequency,” ASME 2010 Proceedings of International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, DETC2010, Mechanical Vibration and Noise (VIB), August 15-18, The American Society of Mechanical Engineers, Montreal, Quebec, Canada.
Caruntu, D. I., and Knecht, M., 2010, NEMB2010-13238, “Nonlinear parametric resonance for NEMS and MEMS biosensor applications,” Proceedings of the ASME 2010 First Global Congress on NanoEngineering for Medicine and Biology NEMB 2010, February 7-10, The American Society of Mechanical Engineers, Houston, TX.
Lu, M., Lee, D., Xue, W., and Cui, T., 2009, “Flexible and Disposable Immunosensors Based on Layer-By-Layer Self-Assembled Carbon Nanotubes and Biomolecules,” Sens. Actuators, A, 150, pp. 280–285. [CrossRef]
Adrega, T., Prazeres, D. M. F., Chu, V., and Conde, J. P., 2006, “Thin-Film Silicon MEMS DNA Sensors,” J. Non-Cryst. Solids, 352, pp. 1999–2003. [CrossRef]
Stulemeijer, J., Bielen, J. A., Steeneken, P. G., and Bouwe van der Berg, J., 2009, “Numerical Path Following as an Analysis Method for Electrostatic MEMS,” J.Microelectromech. Syst., 18(2), pp. 488–499. [CrossRef]
Nayfeh, A. H., Younis, M. I., and Abdel-Rahman, E. M., 2007, “Dynamic Pull-In Phenomenon in MEMS Resonators,” Nonlinear Dyn., 48, pp. 153–163. [CrossRef]
Abdel-Rahman, E. M., Nayfeh, A. H., and Younis, M. I., 2003, “Dynamics of an Electrically Actuated Resonant Microsensor,” Proceedings of the International Conference on MEMS, NANO and Smart Systems (ICMENS'03), IEEE.
Zand, M. M., Ahmadian, M. T., and Rashidian, B., 2009, “Semi-Analytic Solutions to Nonlinear Vibrations of Microbeams Under Suddenly Applied Voltages,” J. Sound Vib., 325, pp. 382–396. [CrossRef]
Ramezani, A., Alasty, A., and Akbari, J., 2007, “Closed-Form Solutions of the Pull-In Instability in Nano-Cantilevers Under Electrostatic and Intermolecular Surface Forces,” Int. J. Solids Struct., 44, pp. 4925–4941. [CrossRef]
Zamanian, M., and Khadem, S. E., 2010, “Analysis of Thermoelastic Damping in Microresonators by Considering the Stretching Effect,” Int. J. Mech. Sci., 52, pp. 1366–1375. [CrossRef]
Younis, M. I., Abdel-Rahman, E. M., and Nayfeh, A. H., 2003, “A Reduced-Order Model for Electrically Actuated Microbeam-Based MEMS,” J. Microelectromech. Syst., 12(5), pp. 672–680. [CrossRef]
Moghimi Zand, M., Ahmadian, M. T., and Rashidian, B., 2009, “Semi-analytic Solutions to Nonlinear Vibrations of Microbeams under Suddenly Applied Voltages,” J. Sound Vib., 325, pp. 382–396. [CrossRef]
Rhoads, J. F., Shaw, S. W., Turner, K. L., Moehlis, J., DeMartini, B. E., and Zhang, W., 2006, “Generalized Parametric Resonance in Electrostatically Actuated Microelectromechanical Oscillators,” J. Sound Vib., 296, pp. 797–829. [CrossRef]
Caruntu, D. I., and Knecht, M., 2011, “On Nonlinear Response Near Half Natural Frequency of Electrostatically Actuated Microresonators,” Int. J. Struct. Stab. Dyn., 11(4), pp. 641–672. [CrossRef]
Caruntu, D. I., 2007, “Classical Jacobi Polynomials, Closed-Form Solutions For Transverse Vibrations,” J. Sound Vib., 306(3–5), pp. 467–494. [CrossRef]
Caruntu, D. I., 2009, “Dynamic Modal Characteristics of Transverse Vibrations of Cantilevers of Parabolic Thickness,” Mech. Res. Commun.33(3), pp. 391–404. [CrossRef]
Caruntu, D. I., and Solis Silva, J. C., 2011, IMECE2011-64854, “Reduced Order Model of MEMS Sensors Near Natural Frequency”, ASME Proceedings of International Mechanical Engineering Congress and Exposition 2011, November 11–17, Denver, CO, © The American Society of Mechanical Engineers.
Doedel, E. J., and Oldeman, B. E., 2009, “AUTO-07P: Continuation and Bifurcation Software For Ordinary Differential Equations,” Concordia University, Montréal, Canada.
Caruntu, D. I., and Knecht, M., 2009, IMECE2009-10663, “Parametric Response of Capacitive Sensors Near Half of Natural Frequency,” ASME Proceedings of International Mechanical Engineering Congress and Exposition 2009, November 13-19, The American Society of Mechanical Engineers, Lake Buena Vista, FL.
Batra, R. C., Porfiri, M., and Spinello, D., 2006, “Electromechanical Model of Electrically Actuated Narrow Beams,” J. Microelectromech. Syst., 15, pp. 1175–1189. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Uniform MEMS resonator

Grahic Jump Location
Fig. 2

Amplitude frequency response for AC near half natural frequency using the MMS [21] and a five term ROM (annotated) for dimensionless parameter values b* = 0.01, δ = 0.1, and f = 0.26

Grahic Jump Location
Fig. 3

Amplitude frequency response for AC near half natural frequency using a two, three, four, and five term ROM for dimensionless parameter values b* = 0.01, δ = 0.1, and f = 0.26

Grahic Jump Location
Fig. 4

Amplitude-frequency response showing the influence of the dimensionless damping parameter b* for dimensionless parameter values δ = 0.1 and f = 0.26 using the MMS [21] and a five term ROM

Grahic Jump Location
Fig. 5

Amplitude-frequency response showing the influence of the voltage parameter δ for dimensionless parameter values b* = 0.01 and f = 0.26 using the MMS [21] and a five term ROM

Grahic Jump Location
Fig. 6

Amplitude-frequency response showing the influence of the fringe correction f for dimensionless parameter values b* = 0.01 and δ = 0.1 using the MMS [21] and a five term ROM

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In