Hopf bifurcation in a disk-shaped NEMS

Maxim Zalalutdinov; Jeevak Parpia; Keith Aubin; Harold G. Craighead; Tuncay Alan; Alan Zehnder; Richard Rand

Hopf bifurcation in a disk-shaped NEMS

Maxim Zalalutdinov, Jeevak Parpia, Keith Aubin, Harold G. Craighead, Tuncay Alan, Alan Zehnder, Richard Rand

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Self-sustained mechanical vibrations of a disc-type micro-fabricated resonator were experimentally observed when a continuous wave (CW) laser beam was focused on the periphery of the disc (for a 40 μm diameter resonator, natural frequency 0.89MHz, the laser power above a 250 W threshold was required). A theoretical model for self-oscillatory behavior has been developed based on FEM analysis of a stress pattern created within the resonator by the focused laser beam. This model accounts for the fact that the amount of absorbed laser light is modulated due to the motion of the resonator through the optical interferometric pattern. Analytical study reveals the presence of a Hopf-type bifurcation with a critical laser power close to the experimentally observed value. Harmonic balance analysis indicates the existence of a stable limit cycle in the phase plane determining the amplitude of self-oscillations.

Original language	English
Title of host publication	Proceedings of the ASME Design Engineering Technical Conference
Pages	1759-1769
Number of pages	11
Volume	5 B
State	Published - Dec 1 2003
Event	2003 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference - Chicago, IL, United States Duration: Sep 2 2003 → Sep 6 2003

Other

Other	2003 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Country	United States
City	Chicago, IL
Period	9/2/03 → 9/6/03

ASJC Scopus subject areas

Engineering(all)

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title = "Hopf bifurcation in a disk-shaped NEMS",

abstract = "Self-sustained mechanical vibrations of a disc-type micro-fabricated resonator were experimentally observed when a continuous wave (CW) laser beam was focused on the periphery of the disc (for a 40 μm diameter resonator, natural frequency 0.89MHz, the laser power above a 250 W threshold was required). A theoretical model for self-oscillatory behavior has been developed based on FEM analysis of a stress pattern created within the resonator by the focused laser beam. This model accounts for the fact that the amount of absorbed laser light is modulated due to the motion of the resonator through the optical interferometric pattern. Analytical study reveals the presence of a Hopf-type bifurcation with a critical laser power close to the experimentally observed value. Harmonic balance analysis indicates the existence of a stable limit cycle in the phase plane determining the amplitude of self-oscillations.",

author = "Maxim Zalalutdinov and Jeevak Parpia and Keith Aubin and Craighead, {Harold G.} and Tuncay Alan and Alan Zehnder and Richard Rand",

year = "2003",

month = dec,

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language = "English",

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T1 - Hopf bifurcation in a disk-shaped NEMS

AU - Zalalutdinov, Maxim

AU - Parpia, Jeevak

AU - Aubin, Keith

AU - Craighead, Harold G.

AU - Alan, Tuncay

AU - Zehnder, Alan

AU - Rand, Richard

PY - 2003/12/1

Y1 - 2003/12/1

N2 - Self-sustained mechanical vibrations of a disc-type micro-fabricated resonator were experimentally observed when a continuous wave (CW) laser beam was focused on the periphery of the disc (for a 40 μm diameter resonator, natural frequency 0.89MHz, the laser power above a 250 W threshold was required). A theoretical model for self-oscillatory behavior has been developed based on FEM analysis of a stress pattern created within the resonator by the focused laser beam. This model accounts for the fact that the amount of absorbed laser light is modulated due to the motion of the resonator through the optical interferometric pattern. Analytical study reveals the presence of a Hopf-type bifurcation with a critical laser power close to the experimentally observed value. Harmonic balance analysis indicates the existence of a stable limit cycle in the phase plane determining the amplitude of self-oscillations.

AB - Self-sustained mechanical vibrations of a disc-type micro-fabricated resonator were experimentally observed when a continuous wave (CW) laser beam was focused on the periphery of the disc (for a 40 μm diameter resonator, natural frequency 0.89MHz, the laser power above a 250 W threshold was required). A theoretical model for self-oscillatory behavior has been developed based on FEM analysis of a stress pattern created within the resonator by the focused laser beam. This model accounts for the fact that the amount of absorbed laser light is modulated due to the motion of the resonator through the optical interferometric pattern. Analytical study reveals the presence of a Hopf-type bifurcation with a critical laser power close to the experimentally observed value. Harmonic balance analysis indicates the existence of a stable limit cycle in the phase plane determining the amplitude of self-oscillations.

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AN - SCOPUS:1842686730

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Y2 - 2 September 2003 through 6 September 2003

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