Bifurcation diagram and dynamic response of a MEMS resonator with a 1:3 internal resonance

Czaplewski, David A.; Strachan, Scott; Shoshani, Oriel; Shaw, Steven W.; López, Daniel

doi:10.1063/1.5099459

Title: Bifurcation diagram and dynamic response of a MEMS resonator with a 1:3 internal resonance

Journal Article · 24 June 2019 · Applied Physics Letters

DOI: https://doi.org/10.1063/1.5099459 · OSTI ID:1570436

^[1]; Strachan, Scott ^[2];

^[3]; Shaw, Steven W. ^[4];

^[1]

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)

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC); National Science Foundation (NSF)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1570436

Alternate ID(s):: OSTI ID: 1529407

Journal Information:: Applied Physics Letters, Journal Name: Applied Physics Letters Journal Issue: 25 Vol. 114; ISSN 0003-6951

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (29)

A review of MEMS oscillators for frequency reference and timing applications van Beek, J. T. M.; Puers, R. Journal of Micromechanics and Microengineering, Vol. 22, Issue 1 https://doi.org/10.1088/0960-1317/22/1/013001	journal	December 2011
A hybrid on-chip opto-nanomechanical transducer for ultra-sensitive force measurements Gavartin, Emanuel; Verlot, Pierre; Kippenberg, Tobias J. arXiv https://doi.org/10.48550/arxiv.1112.0797	text	January 2011
Coherent Sensing of a Mechanical Resonator with a Single-Spin Qubit Kolkowitz, S.; Bleszynski Jayich, A. C.; Unterreithmeier, Q. P. Science, Vol. 335, Issue 6076 https://doi.org/10.1126/science.1216821	journal	February 2012
Sensitivity enhancement of a resonant mass sensor based on internal resonance Zhang, Tianyi; Wei, Xueyong; Jiang, Zhuangde Applied Physics Letters, Vol. 113, Issue 22 https://doi.org/10.1063/1.5057439	journal	November 2018
Measurement of the Casimir Force between Dissimilar Metals Decca, R. S.; López, D.; Fischbach, E. Physical Review Letters, Vol. 91, Issue 5 https://doi.org/10.1103/PhysRevLett.91.050402	journal	July 2003
Energy-dependent path of dissipation in nanomechanical resonators Güttinger, Johannes; Noury, Adrien; Weber, Peter Nature Nanotechnology, Vol. 12, Issue 7 https://doi.org/10.1038/nnano.2017.86	journal	May 2017
Direct observation of coherent energy transfer in nonlinear micromechanical oscillators Chen, Changyao; Zanette, Damián H.; Czaplewski, David A. Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms15523	journal	May 2017
Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode Verhagen, E.; Deléglise, S.; Weis, S. Nature, Vol. 482, Issue 7383 https://doi.org/10.1038/nature10787	journal	February 2012
Nanomechanical mass sensing and stiffness spectrometry based on two-dimensional vibrations of resonant nanowires Gil-Santos, Eduardo; Ramos, Daniel; Martínez, Javier Nature Nanotechnology, Vol. 5, Issue 9 https://doi.org/10.1038/nnano.2010.151	journal	August 2010
Measurement of the Casimir force between dissimilar metals Decca, R. S.; López, D.; Fischbach, E. arXiv https://doi.org/10.48550/arxiv.quant-ph/0306136	text	January 2003
A hybrid on-chip optomechanical transducer for ultrasensitive force measurements Gavartin, E.; Verlot, P.; Kippenberg, T. J. Nature Nanotechnology, Vol. 7, Issue 8, p. 509-514 https://doi.org/10.1038/nnano.2012.97	journal	June 2012
Bifurcations in Dynamical Systems With Internal Resonance Sethna, P. R.; Bajaj, A. K. Journal of Applied Mechanics, Vol. 45, Issue 4 https://doi.org/10.1115/1.3424438	journal	December 1978
Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode Verhagen, E.; Deléglise, S.; Weis, S. arXiv https://doi.org/10.48550/arxiv.1107.3761	text	January 2011
MEMS-based force sensor: Design and applications López, Daniel; Decca, Ricardo S.; Fischbach, Ephraim Bell Labs Technical Journal, Vol. 10, Issue 3 https://doi.org/10.1002/bltj.20104	journal	September 2005
Surpassing Fundamental Limits of Oscillators Using Nonlinear Resonators Villanueva, L. G.; Kenig, E.; Karabalin, R. B. Physical Review Letters, Vol. 110, Issue 17 https://doi.org/10.1103/PhysRevLett.110.177208	journal	April 2013
A nanomechanical mass sensor with yoctogram resolution Chaste, J.; Eichler, A.; Moser, J. Nature Nanotechnology, Vol. 7, Issue 5 https://doi.org/10.1038/nnano.2012.42	journal	April 2012
Ultrasensitive force detection with a nanotube mechanical resonator Moser, J.; Güttinger, J.; Eichler, A. Nature Nanotechnology, Vol. 8, Issue 7 https://doi.org/10.1038/nnano.2013.97	journal	June 2013
Frequency stabilization in nonlinear micromechanical oscillators Antonio, Dario; Zanette, Damián H.; López, Daniel Nature Communications, Vol. 3, Issue 1 https://doi.org/10.1038/ncomms1813	journal	January 2012
Single Molecule Detection of Nanomechanical Motion Puller, Vadim; Lounis, Brahim; Pistolesi, Fabio Physical Review Letters, Vol. 110, Issue 12 https://doi.org/10.1103/PhysRevLett.110.125501	journal	March 2013
An atomic-resolution nanomechanical mass sensor Jensen, K.; Kim, Kwanpyo; Zettl, A. Nature Nanotechnology, Vol. 3, Issue 9 https://doi.org/10.1038/nnano.2008.200	journal	July 2008
Single spin detection by magnetic resonance force microscopy Rugar, D.; Budakian, R.; Mamin, H. J. Nature, Vol. 430, Issue 6997 https://doi.org/10.1038/nature02658	journal	July 2004
Bifurcation Generated Mechanical Frequency Comb Czaplewski, David A.; Chen, Changyao; Lopez, Daniel Physical Review Letters, Vol. 121, Issue 24 https://doi.org/10.1103/PhysRevLett.121.244302	journal	December 2018
Quantum-Coherent Coupling of a Mechanical Oscillator to an Optical Cavity Mode Verhagen, Ewold; Deléglise, Samuel; Weis, Stefan CLEO: Applications and Technology, Conference on Lasers and Electro-Optics 2012 https://doi.org/10.1364/cleo_at.2012.jm1k.1	conference	January 2012
Inertial imaging with nanomechanical systems Hanay, M. Selim; Kelber, Scott I.; O'Connell, Cathal D. Nature Nanotechnology, Vol. 10, Issue 4 https://doi.org/10.1038/nnano.2015.32	journal	March 2015
Entangling Mechanical Motion with Microwave Fields Palomaki, T. A.; Teufel, J. D.; Simmonds, R. W. Science, Vol. 342, Issue 6159 https://doi.org/10.1126/science.1244563	journal	October 2013
Toward Attogram Mass Measurements in Solution with Suspended Nanochannel Resonators Lee, Jungchul; Shen, Wenjiang; Payer, Kris Nano Letters, Vol. 10, Issue 7 https://doi.org/10.1021/nl101107u	journal	July 2010
Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope Nitzan, Sarah H.; Zega, Valentina; Li, Mo Scientific Reports, Vol. 5, Issue 1 https://doi.org/10.1038/srep09036	journal	March 2015
Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks Mangussi, Franco; Zanette, Damián H. PLOS ONE, Vol. 11, Issue 9 https://doi.org/10.1371/journal.pone.0162365	journal	September 2016
Limit cycles and bifurcations in a nonlinear MEMS resonator with a 1:3 internal resonance Houri, S.; Hatanaka, D.; Asano, M. Applied Physics Letters, Vol. 114, Issue 10 https://doi.org/10.1063/1.5085219	journal	March 2019

Cited By (1)

Demonstration of Multiple Internal Resonances in a Microelectromechanical Self-Sustained Oscillator Houri, S.; Hatanaka, D.; Asano, M. Physical Review Applied, Vol. 13, Issue 1 https://doi.org/10.1103/physrevapplied.13.014049	journal	January 2020

Similar Records

Resonant mode interactions and the bifurcation of combustion-driven acoustic oscillations in resonance tubes

Technical Report · 1993 · OSTI ID:6732708

Margolis, S B

Resonant mode interactions and the bifurcation of combustion-driven acoustic oscillations in resonance tubes

Journal Article · 1994 · SIAM Journal of Applied Mathematics (Society for Industrial and Applied Mathematics); (United States) · OSTI ID:6796830

Margolis, S B

Resonant mode interactions and the bifurcation of combustion-driven acoustic oscillations in resonance tubes

Technical Report · 1993 · OSTI ID:10136162

Margolis, S B

Related Subjects

42 ENGINEERING

Title: Bifurcation diagram and dynamic response of a MEMS resonator with a 1:3 internal resonance

Citation Formats

References (29)

Cited By (1)

Similar Records

Related Subjects