In order to compensate for the loss of performance when scaling resonant sensors down to NEMS, a complete analytical model, including all main sources of nonlinearities, is presented as a predictive tool for the dynamic behavior of clamped-clamped nanoresonators electrostatically actuated. The nonlinear dynamics of such NEMS under superharmonic resonance of an order half their fundamental natural frequencies is investigated. It is shown that the critical amplitude has the same dependence on the quality factor Q and the thickness h as the case of the primary resonance. Finally, a way to retard the pull-in by decreasing the AC voltage is proposed in order to enhance the performance of NEMS resonators.
Issue Section:
Research Papers
References
1.
Feng
, X. L.
, 2007, “Phase Noise and Frequency Stability of Very-High Frequency Silicon Nanowire Nanomechanical Resonators
,” Proceedings of 14th International Conference on Solid-State Sensors, Actuators and Microsystems, pp. 327
–330
.2.
Robins
, W. P.
, 1984, Phase Noise in Signal Sources
, Institution of Engineering and Technology
, London
.3.
Roessig
, T. A.
, Howe
, R. T.
, and Pisano
, A. P.
, 1997, “Nonlinear Mixing in Surface-Micromachined Tuning Fork Oscillators
,” Proceedings of the 1997 IEEE International Frequency Control Symposium, pp. 778
–782
.4.
Kaajakari
, V.
, Koskinen
, J. K.
, and Mattila
, T.
, 2005. “Phase Noise in Capacitively Coupled Micromechanical Oscillators
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control
, 52
(12
), pp. 2322
–2331
. 5.
Kacem
, N.
, Hentz
, S.
, Fontaine
, H.
, Nguyen
, V.
, Robert
, P.
, Legrand
, B.
, and Buchaillot
, L.
, 2008, “From MEMS to NEMS: Modelling and Characterization of the Nonlinear Dynamics of Resonators: A Way to Enhance the Dynamic Range
,” Proceedings of the International Conference of Nanotechnology, Boston, MA.6.
Postma
, H. W. C.
, Kozinsky
, I.
, Husain
, A.
, and Roukes
, M. L.
, 2005, “Dynamic Range of Nanotube- and Nanowire-Based Electromechanical Systems
,” Appl. Phys. Lett.
, 86
(22
), 223105
. 7.
Kacem
, N.
, Hentz
, S.
, Pinto
, D.
, Reig
, B.
, and Nguyen
, V.
, 2009. “Nonlinear Dynamics of Nanomechanical Beam Resonators: Improving the Performance of NEMS-Based Sensors
,” Nanotechnology
, 20
(27
), 275501
. 8.
Kacem
, N.
, Arcamone
, J.
, Perez-Murano
, F.
, and Hentz
, S.
, 2010, “Dynamic Range Enhancement of Nonlinear Nanomechanical Resonant Cantilevers for Highly Sensitive NEMS Gas/Mass Sensor Applications
,” J. Micromech. Microeng.
, 20
(4
), 045023
. 9.
Kacem
, N
, and Hentz
, S.
, 2009, “Bifurcation Topology Tuning of a Mixed Behavior in Nonlinear Micromechanical Resonators
,” Appl. Phys. Lett.
, 95
(18
), 183104
. 10.
Kacem
, N.
, Baguet
, S.
, Hentz
, S.
, and Dufour
, R.
, 2010, “Nonlinear Phenomena in Nanomechanical Resonators: Mechanical Behaviors and Physical Limitations
,” Mécanique Industries
, 11
(6
), pp. 521
–529
.11.
Jin
, Z.
, and Wang
, Y.
, 1998, “Electrostatic Resonator With Second Superharmonic Resonance
,” Sens. Actuators, A
, 64
(3
), pp. 273
–279
. 12.
Turner
, K. L.
, Miller
, S. A.
, Hartwell
, P. G.
, MacDonald
, N. C.
, Strogatz
, H. S.
, and Adams
, S. G.
, 1998, “Five Parametric Resonances in a Microelectromechanical System
,” Nature
, 396
, pp. 149
–152
. 13.
Rugar
, D.
, and Grütter
, P.
, 1991, “Mechanical Parametric Amplification and Thermomechanical Noise Squeezing
,” Phys. Rev. Lett.
, 67
(6
), pp. 699
–702
. 14.
Carr
, D. W.
, Evoy
, S.
, Sekaric
, L.
, Craighead
, H. G.
, and Parpia
, J. M.
, 2000, “Parametric Amplification in a Torsional Microresonator
,” Appl. Phys. Lett.
, 77
(10
), pp. 1545
–1547
. 15.
Carr
, D. W.
, Evoy
, S.
, Sekaric
, L.
, Craighead
, H. G.
, and Parpia
, J. M.
, 1999, “Measurement of Mechanical Resonance and Losses in Nanometer Scale Silicon Wires
,” Appl. Phys. Lett.
, 75
(7
), pp. 920
–922
. 16.
Younis
, M.
, and Nayfeh
, A. H.
, 2003, “A Study of the Nonlinear Response of a Resonant Microbeam to an Electric Actuation
,” Nonlinear Dyn.
, 31
(1
), pp. 91
–117
. 17.
Abdel-Rahman
, E. M.
, and Nayfeh
, A. H.
, 2003, “Secondary Resonances of Electrically Actuated Resonant Microsensors
,” J. Micromech. Microeng.
, 13
(3
), pp. 491
–501
. 18.
Younis
, M. I.
, Abdel-Rahman
, E. M.
, and Nayfeh
, A. H.
, 2004, “Global Dynamics of MEMS Resonators Under Superharmonic Excitation
,” Proceedings of the International Conference on MEMS, NANO, and Smart Systems (ICMENS), Banff, Canada, pp. 694
–699
.19.
Nayfeh
, A. H.
, and Younis
, M. I.
, 2005, “Dynamics of MEMS Resonators Under Superharmonic and Subharmonic Excitations
,” J. Micromech. Microeng.
, 15
(10
), pp. 1840
–1847
. 20.
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
. 21.
Landau
, L. D.
, and Lifshitz
, E. M.
, 1986, Theory of Elasticity
, Butterworth-Heinemann
, Oxford, UK
.22.
Nishiyama
, H.
, and Nakamura
, M.
, 1990, “Capacitance of a Strip Capacitor
,” IEEE Trans. Compon., Hybrids, Manuf. Technol.
, 13
(2
), pp. 417
–423
. 23.
Touzé
, C.
, and Thomas
, O.
, 2006, “Non-Linear Behaviour of Free-Edge Shallow Spherical Shells: Effect of the Geometry
,” Int. J. Non-Linear Mech.
, 41
(5
), pp. 678
–692
. 24.
Kacem
, N.
, Baguet
, S.
, Hentz
, S.
, and Dufour
, R.
, 2011, “Computational and Quasi-Analytical Models for Non-Linear Vibrations of Resonant MEMS and NEMS Sensors
,” Int. J. Non-Linear Mech.
, 46
(3
), pp. 532
–542
. 25.
Belhaq
, M.
, and Fahsi
, A.
, 2008, “2:1 and 1:1 Frequency-Locking in Fast Excited van der Pol-Mathieu-Duffing Oscillator
,” Nonlinear Dyn.
, 53
, pp. 139
–152
. 26.
Nayfeh
, A. H.
, 1981, Introduction to Perturbation Techniques
, Wiley
, New York
.27.
Yurke
, B.
, Greywall
, D. S.
, Pargellis
, A. N.
, and Busch
, P. A.
, 1995, “Theory of Amplifier-Noise Evasion in an Oscillator Employing a Nonlinear Resonator
,” Phys. Rev. A
, 51
(5
), pp. 4211
–4229
. 28.
Shao
, L. C.
, Palaniapan
, M.
, and Tan
, W. W.
, 2008, “The Nonlinearity Cancellation Phenomenon in Micromechanical Resonators
,” J. Micromech. Microeng.
, 18
(6
), 065014
. 29.
Younis
, M. I.
, Abdel-Rahman
, E. M.
, and Nayfeh
, A.
, 2003, “A Reduced-Order Model for Electrically Actuated Microbeam-Based MEMS
,” J. Microelectromech. Syst.
, 12
(5
), pp. 672
–680
. 30.
Krylov
, S.
, and Maimon
, R.
, 2004, “Pull-In Dynamics of an Elastic Beam Actuated by Continuously Distributed Electrostatic Force
,” J. Vibr. Acoust.
, 126
(3
), pp. 332
–342
. 31.
De
, S. K.
, and Aluru
, N. R.
, 2004, “Full-Lagrangian Schemes for Dynamic Analysis of Electrostatic MEMS
,” J. Microelectromech. Syst.
, 13
(5
), pp. 737
–758
. 32.
Elata
, D.
, and Bamberger
, H.
, 2006, “On the Dynamic Pull-In of Electrostatic Actuators With Multiple Degrees of Freedom and Multiple Voltage Sources
,” J. Microelectromech. Syst.
, 15
(1
), pp. 131
–140
. 33.
Fargas-Marques
, A.
, Casals-Terre
, J.
, and Shkel
, A. M.
, 2007, “Resonant Pull-In Condition in Parallel-Plate Electrostatic Actuators
,” J. Microelectromech. Syst.
, 16
(5
), pp. 1044
–1053
. 34.
Ashhab
, M.
, Salapaka
, M. V.
, Dahleh
, M.
, and Mezic
, I.
, 1999, “Melnikov-Based Dynamical Analysis of Microcantilevers in Scanning Probe Microscopy
,” Nonlinear Dyn.
, 20
(24
), pp. 197
–220
. 35.
Basso
, M.
, Giarre
, L.
, Dahleh
, M.
, and Mezic
, I.
, 2000, “Complex Dynamics in a Harmonically Excited Lennard-Jones Oscillator: Microcantilever-Sample Interaction in Scanning Probe Microscopes
,” J. Dyn. Syst., Meas., Control
, 122
(1
), pp. 240
–245
. 36.
Gottwald
, J. A.
, Virgin
, L. N.
, and Dowell
, E. H.
, 1995, “Routes to Escape From an Energy Well
,” J. Sound Vib.
, 187
(1
), pp. 133
–144
. 37.
Seeger
, J. I.
, and Crary
, S. B.
, 1997, “Stabilization of Electrostatically Actuated Mechanical Devices
,” Proceedings of the International Conference on Solid State Sensors and Actuators, 2
, pp. 1133
–1136
.38.
Chu
, P. B.
, and Pister
, S. J.
, 1994, “Analysis of Closed-Loop Control of Parallel-Plate Electrostatic Microgrippers
,” Proceedings of the IEEE International Conference on Robotics and Automation, 1
, pp. 820
–825
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