Bifurcation diagram and dynamic response of a MEMS resonator with a 1:3 internal resonance
Abstract
Here, the dynamic response of a nonlinear resonator in the presence of resonant mode coupling is studied experimentally and theoretically. For the case of a clamped-clamped beam resonator in the presence of a 1:3 internal resonance, we show that at the onset of internal resonance, steady state oscillations cannot be sustained. At higher drive levels, stable oscillations can be maintained but the resonator amplitude undergoes amplitude modulated responses. In this work, we utilize these dynamic responses to build a bifurcation diagram that can be described remarkably well with a simple model consisting of a Duffing resonator coupled to a linear one.
- Authors:
-
- Argonne National Lab. (ANL), Lemont, IL (United States)
- Michigan State Univ., East Lansing, MI (United States)
- Ben-Gurion Univ. of the Negev, Beer-Sheva (Israel)
- Florida Inst. of Technology, Melbourne, FL (United States)
- Publication Date:
- Research Org.:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF)
- OSTI Identifier:
- 1570436
- Alternate Identifier(s):
- OSTI ID: 1529407
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Applied Physics Letters
- Additional Journal Information:
- Journal Volume: 114; Journal Issue: 25; Journal ID: ISSN 0003-6951
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING
Citation Formats
Czaplewski, David A., Strachan, Scott, Shoshani, Oriel, Shaw, Steven W., and López, Daniel. Bifurcation diagram and dynamic response of a MEMS resonator with a 1:3 internal resonance. United States: N. p., 2019.
Web. doi:10.1063/1.5099459.
Czaplewski, David A., Strachan, Scott, Shoshani, Oriel, Shaw, Steven W., & López, Daniel. Bifurcation diagram and dynamic response of a MEMS resonator with a 1:3 internal resonance. United States. https://doi.org/10.1063/1.5099459
Czaplewski, David A., Strachan, Scott, Shoshani, Oriel, Shaw, Steven W., and López, Daniel. Tue .
"Bifurcation diagram and dynamic response of a MEMS resonator with a 1:3 internal resonance". United States. https://doi.org/10.1063/1.5099459. https://www.osti.gov/servlets/purl/1570436.
@article{osti_1570436,
title = {Bifurcation diagram and dynamic response of a MEMS resonator with a 1:3 internal resonance},
author = {Czaplewski, David A. and Strachan, Scott and Shoshani, Oriel and Shaw, Steven W. and López, Daniel},
abstractNote = {Here, the dynamic response of a nonlinear resonator in the presence of resonant mode coupling is studied experimentally and theoretically. For the case of a clamped-clamped beam resonator in the presence of a 1:3 internal resonance, we show that at the onset of internal resonance, steady state oscillations cannot be sustained. At higher drive levels, stable oscillations can be maintained but the resonator amplitude undergoes amplitude modulated responses. In this work, we utilize these dynamic responses to build a bifurcation diagram that can be described remarkably well with a simple model consisting of a Duffing resonator coupled to a linear one.},
doi = {10.1063/1.5099459},
journal = {Applied Physics Letters},
number = 25,
volume = 114,
place = {United States},
year = {2019},
month = {6}
}
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Works referenced in this record:
An atomic-resolution nanomechanical mass sensor
journal, July 2008
- Jensen, K.; Kim, Kwanpyo; Zettl, A.
- Nature Nanotechnology, Vol. 3, Issue 9
Single spin detection by magnetic resonance force microscopy
journal, July 2004
- Rugar, D.; Budakian, R.; Mamin, H. J.
- Nature, Vol. 430, Issue 6997
Surpassing Fundamental Limits of Oscillators Using Nonlinear Resonators
journal, April 2013
- Villanueva, L. G.; Kenig, E.; Karabalin, R. B.
- Physical Review Letters, Vol. 110, Issue 17
Toward Attogram Mass Measurements in Solution with Suspended Nanochannel Resonators
journal, July 2010
- Lee, Jungchul; Shen, Wenjiang; Payer, Kris
- Nano Letters, Vol. 10, Issue 7
Frequency stabilization in nonlinear micromechanical oscillators
journal, January 2012
- Antonio, Dario; Zanette, Damián H.; López, Daniel
- Nature Communications, Vol. 3, Issue 1
Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks
journal, September 2016
- Mangussi, Franco; Zanette, Damián H.
- PLOS ONE, Vol. 11, Issue 9
A nanomechanical mass sensor with yoctogram resolution
journal, April 2012
- Chaste, J.; Eichler, A.; Moser, J.
- Nature Nanotechnology, Vol. 7, Issue 5
Limit cycles and bifurcations in a nonlinear MEMS resonator with a 1:3 internal resonance
journal, March 2019
- Houri, S.; Hatanaka, D.; Asano, M.
- Applied Physics Letters, Vol. 114, Issue 10
Direct observation of coherent energy transfer in nonlinear micromechanical oscillators
journal, May 2017
- Chen, Changyao; Zanette, Damián H.; Czaplewski, David A.
- Nature Communications, Vol. 8, Issue 1
Bifurcations in Dynamical Systems With Internal Resonance
journal, December 1978
- Sethna, P. R.; Bajaj, A. K.
- Journal of Applied Mechanics, Vol. 45, Issue 4
Measurement of the Casimir Force between Dissimilar Metals
journal, July 2003
- Decca, R. S.; López, D.; Fischbach, E.
- Physical Review Letters, Vol. 91, Issue 5
Single Molecule Detection of Nanomechanical Motion
journal, March 2013
- Puller, Vadim; Lounis, Brahim; Pistolesi, Fabio
- Physical Review Letters, Vol. 110, Issue 12
Sensitivity enhancement of a resonant mass sensor based on internal resonance
journal, November 2018
- Zhang, Tianyi; Wei, Xueyong; Jiang, Zhuangde
- Applied Physics Letters, Vol. 113, Issue 22
Inertial imaging with nanomechanical systems
journal, March 2015
- Hanay, M. Selim; Kelber, Scott I.; O'Connell, Cathal D.
- Nature Nanotechnology, Vol. 10, Issue 4
Ultrasensitive force detection with a nanotube mechanical resonator
journal, June 2013
- Moser, J.; Güttinger, J.; Eichler, A.
- Nature Nanotechnology, Vol. 8, Issue 7
Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope
journal, March 2015
- Nitzan, Sarah H.; Zega, Valentina; Li, Mo
- Scientific Reports, Vol. 5, Issue 1
MEMS-based force sensor: Design and applications
journal, September 2005
- López, Daniel; Decca, Ricardo S.; Fischbach, Ephraim
- Bell Labs Technical Journal, Vol. 10, Issue 3
Coherent Sensing of a Mechanical Resonator with a Single-Spin Qubit
journal, February 2012
- Kolkowitz, S.; Bleszynski Jayich, A. C.; Unterreithmeier, Q. P.
- Science, Vol. 335, Issue 6076
A review of MEMS oscillators for frequency reference and timing applications
journal, December 2011
- van Beek, J. T. M.; Puers, R.
- Journal of Micromechanics and Microengineering, Vol. 22, Issue 1
Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode
journal, February 2012
- Verhagen, E.; Deléglise, S.; Weis, S.
- Nature, Vol. 482, Issue 7383
Nanomechanical mass sensing and stiffness spectrometry based on two-dimensional vibrations of resonant nanowires
journal, August 2010
- Gil-Santos, Eduardo; Ramos, Daniel; Martínez, Javier
- Nature Nanotechnology, Vol. 5, Issue 9
A hybrid on-chip optomechanical transducer for ultrasensitive force measurements
journal, June 2012
- Gavartin, E.; Verlot, P.; Kippenberg, T. J.
- Nature Nanotechnology, Vol. 7, Issue 8, p. 509-514
Bifurcation Generated Mechanical Frequency Comb
journal, December 2018
- Czaplewski, David A.; Chen, Changyao; Lopez, Daniel
- Physical Review Letters, Vol. 121, Issue 24
Entangling Mechanical Motion with Microwave Fields
journal, October 2013
- Palomaki, T. A.; Teufel, J. D.; Simmonds, R. W.
- Science, Vol. 342, Issue 6159
Energy-dependent path of dissipation in nanomechanical resonators
journal, May 2017
- Güttinger, Johannes; Noury, Adrien; Weber, Peter
- Nature Nanotechnology, Vol. 12, Issue 7
Quantum-Coherent Coupling of a Mechanical Oscillator to an Optical Cavity Mode
conference, January 2012
- Verhagen, Ewold; Deléglise, Samuel; Weis, Stefan
- CLEO: Applications and Technology, Conference on Lasers and Electro-Optics 2012
Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode
text, January 2011
- Verhagen, E.; Deléglise, S.; Weis, S.
- arXiv
A hybrid on-chip opto-nanomechanical transducer for ultra-sensitive force measurements
text, January 2011
- Gavartin, Emanuel; Verlot, Pierre; Kippenberg, Tobias J.
- arXiv
Measurement of the Casimir force between dissimilar metals
text, January 2003
- Decca, R. S.; López, D.; Fischbach, E.
- arXiv
Works referencing / citing this record:
Demonstration of Multiple Internal Resonances in a Microelectromechanical Self-Sustained Oscillator
journal, January 2020
- Houri, S.; Hatanaka, D.; Asano, M.
- Physical Review Applied, Vol. 13, Issue 1
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