Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: 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:
ORCiD logo [1];  [2]; ORCiD logo [3];  [4]; ORCiD logo [1]
+ Show Author Affiliations
  1. Argonne National Lab. (ANL), Lemont, IL (United States)
  2. Michigan State Univ., East Lansing, MI (United States)
  3. Ben-Gurion Univ. of the Negev, Beer-Sheva (Israel)
  4. 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.
Copy to clipboard
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
Copy to clipboard
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.
Copy to clipboard
@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 = {Tue Jun 25 00:00:00 EDT 2019},
month = {Tue Jun 25 00:00:00 EDT 2019}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/1.5099459
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 34 works
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1 FIG. 1: Dynamic response and bifurcation diagram of a MEMS resonator with 1:3 internal resonance. (a) Voltage response of the resonator for a drive voltage of 10 mV showing a saddle node (SN) bifurcation at $f_{SN}$ . (b) Voltage response of the resonator for a drive voltage of 20 mVmore » showing the onset of internal resonance at $f_{IR}$. (c) Voltage response of the resonator for a drive voltage of 400 mV. The dotted rectangle indicates the frequency range of interest which its shown in an expanded scale in (d). The shaded regions in (d) indicate the regions where the resonator dynamics deviate form the expected Duffing behavior. (e) Bifurcation diagram of the nonlinear resonator in presence of resonant mode coupling. The dashed lines correspond to the voltage response data shown in (a), (b) and (c). The light blue data correspond to bifurcations points measured by exciting the resonator through a dynamic path like the one shown by the black arrow.« less
All figures and tables (2 total)
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

An atomic-resolution nanomechanical mass sensor
journal, July 2008

Single spin detection by magnetic resonance force microscopy
journal, July 2004

Surpassing Fundamental Limits of Oscillators Using Nonlinear Resonators
journal, April 2013

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
  • DOI: 10.1021/nl101107u

Frequency stabilization in nonlinear micromechanical oscillators
journal, January 2012

  • Antonio, Dario; Zanette, Damián H.; López, Daniel
  • Nature Communications, Vol. 3, Issue 1
  • DOI: 10.1038/ncomms1813

Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks
journal, September 2016

A nanomechanical mass sensor with yoctogram resolution
journal, April 2012

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
  • DOI: 10.1063/1.5085219

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
  • DOI: 10.1038/ncomms15523

Bifurcations in Dynamical Systems With Internal Resonance
journal, December 1978

  • Sethna, P. R.; Bajaj, A. K.
  • Journal of Applied Mechanics, Vol. 45, Issue 4
  • DOI: 10.1115/1.3424438

Measurement of the Casimir Force between Dissimilar Metals
journal, July 2003

Single Molecule Detection of Nanomechanical Motion
journal, March 2013

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
  • DOI: 10.1063/1.5057439

Inertial imaging with nanomechanical systems
journal, March 2015

  • Hanay, M. Selim; Kelber, Scott I.; O'Connell, Cathal D.
  • Nature Nanotechnology, Vol. 10, Issue 4
  • DOI: 10.1038/nnano.2015.32

Ultrasensitive force detection with a nanotube mechanical resonator
journal, June 2013

  • Moser, J.; Güttinger, J.; Eichler, A.
  • Nature Nanotechnology, Vol. 8, Issue 7
  • DOI: 10.1038/nnano.2013.97

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
  • DOI: 10.1038/srep09036

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
  • DOI: 10.1002/bltj.20104

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
  • DOI: 10.1126/science.1216821

A review of MEMS oscillators for frequency reference and timing applications
journal, December 2011

Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode
journal, February 2012

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
  • DOI: 10.1038/nnano.2010.151

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
  • DOI: 10.1038/nnano.2012.97

Bifurcation Generated Mechanical Frequency Comb
journal, December 2018

Entangling Mechanical Motion with Microwave Fields
journal, October 2013

Energy-dependent path of dissipation in nanomechanical resonators
journal, May 2017

  • Güttinger, Johannes; Noury, Adrien; Weber, Peter
  • Nature Nanotechnology, Vol. 12, Issue 7
  • DOI: 10.1038/nnano.2017.86

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
  • DOI: 10.1364/cleo_at.2012.jm1k.1

Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode
text, January 2011

A hybrid on-chip opto-nanomechanical transducer for ultra-sensitive force measurements
text, January 2011

Measurement of the Casimir force between dissimilar metals
text, January 2003

    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    Demonstration of Multiple Internal Resonances in a Microelectromechanical Self-Sustained Oscillator
    journal, January 2020

      Sort by:
      [ × clear filter / sort ]

      Figures / Tables found in this record:

      FIG. 1 (p. 2)figure
      FIG. 2 (p. 3)figure
        [ × clear filter / sort ]
        Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

        Similar Records in DOE PAGES and OSTI.GOV collections: