Bifurcation Generated Mechanical Frequency Comb
Abstract
Here, we demonstrate a novel response of a nonlinear micromechanical resonator when operated in a region of strong, nonlinear mode coupling. The system is excited with a single drive signal and its response is characterized by periodic amplitude modulations that occur at timescales based on system parameters. The periodic amplitude modulations of the resonator are a consequence of nonlinear mode coupling and are responsible for the emergence of a “frequency-comb” regime in the spectral response. By considering a generic model for a 1:3 internal resonance, we demonstrate that the novel behavior results from a saddle node on an invariant circle (SNIC) bifurcation. The ability to control the operating parameters of the micromechanical structures reported here makes the simple micromechanical resonator an ideal test bed to study the dynamic response of SNIC behavior demonstrated in mechanical, optical, and biological systems.
- Authors:
-
- Argonne National Lab. (ANL), Lemont, IL (United States)
- Ben-Gurion Univ. of the Negev, Beer-sheva (Israel)
- Chalmers Univ. of Technology, Goteborg (Sweden)
- Michigan State Univ., East Lansing, MI (United States)
- Florida Institute of Technology, Melbourne, FL (United States)
- Publication Date:
- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- National Science Foundation (NSF); USDOE Office of Science (SC); Swedish Research Council (SRC)
- OSTI Identifier:
- 1488453
- Alternate Identifier(s):
- OSTI ID: 1486906
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 121; Journal Issue: 24; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 47 OTHER INSTRUMENTATION; 42 ENGINEERING
Citation Formats
Czaplewski, David A., Chen, Changyao, Lopez, Daniel, Shoshani, Oriel, Eriksson, Axel M., Strachan, Scott, and Shaw, Steven W. Bifurcation Generated Mechanical Frequency Comb. United States: N. p., 2018.
Web. doi:10.1103/PhysRevLett.121.244302.
Czaplewski, David A., Chen, Changyao, Lopez, Daniel, Shoshani, Oriel, Eriksson, Axel M., Strachan, Scott, & Shaw, Steven W. Bifurcation Generated Mechanical Frequency Comb. United States. https://doi.org/10.1103/PhysRevLett.121.244302
Czaplewski, David A., Chen, Changyao, Lopez, Daniel, Shoshani, Oriel, Eriksson, Axel M., Strachan, Scott, and Shaw, Steven W. 2018.
"Bifurcation Generated Mechanical Frequency Comb". United States. https://doi.org/10.1103/PhysRevLett.121.244302. https://www.osti.gov/servlets/purl/1488453.
@article{osti_1488453,
title = {Bifurcation Generated Mechanical Frequency Comb},
author = {Czaplewski, David A. and Chen, Changyao and Lopez, Daniel and Shoshani, Oriel and Eriksson, Axel M. and Strachan, Scott and Shaw, Steven W.},
abstractNote = {Here, we demonstrate a novel response of a nonlinear micromechanical resonator when operated in a region of strong, nonlinear mode coupling. The system is excited with a single drive signal and its response is characterized by periodic amplitude modulations that occur at timescales based on system parameters. The periodic amplitude modulations of the resonator are a consequence of nonlinear mode coupling and are responsible for the emergence of a “frequency-comb” regime in the spectral response. By considering a generic model for a 1:3 internal resonance, we demonstrate that the novel behavior results from a saddle node on an invariant circle (SNIC) bifurcation. The ability to control the operating parameters of the micromechanical structures reported here makes the simple micromechanical resonator an ideal test bed to study the dynamic response of SNIC behavior demonstrated in mechanical, optical, and biological systems.},
doi = {10.1103/PhysRevLett.121.244302},
url = {https://www.osti.gov/biblio/1488453},
journal = {Physical Review Letters},
issn = {0031-9007},
number = 24,
volume = 121,
place = {United States},
year = {Fri Dec 14 00:00:00 EST 2018},
month = {Fri Dec 14 00:00:00 EST 2018}
}
Web of Science
Works referenced in this record:
Noise-induced intermittency in a superconducting microwave resonator
journal, January 2010
- Bachar, G.; Segev, E.; Shtempluck, O.
- EPL (Europhysics Letters), Vol. 89, Issue 1
Correlated anomalous phase diffusion of coupled phononic modes in a sideband-driven resonator
journal, August 2016
- Sun, F.; Dong, X.; Zou, J.
- Nature Communications, Vol. 7, Issue 1
Phononic frequency comb via three-mode parametric resonance
journal, January 2018
- Ganesan, Adarsh; Do, Cuong; Seshia, Ashwin
- Applied Physics Letters, Vol. 112, Issue 2
A new mathematical explanation of what triggered the catastrophic torsional mode of the Tacoma Narrows Bridge
journal, January 2015
- Arioli, Gianni; Gazzola, Filippo
- Applied Mathematical Modelling, Vol. 39, Issue 2
Phase-coherent microwave-to-optical link with a self-referenced microcomb
journal, June 2016
- Del'Haye, Pascal; Coillet, Aurélien; Fortier, Tara
- Nature Photonics, Vol. 10, Issue 8
Frequency stabilization in nonlinear micromechanical oscillators
journal, January 2012
- Antonio, Dario; Zanette, Damián H.; López, Daniel
- Nature Communications, Vol. 3, Issue 1
Delay-induced patterns in a two-dimensional lattice of coupled oscillators
journal, February 2015
- Kantner, Markus; Schöll, Eckehard; Yanchuk, Serhiy
- Scientific Reports, Vol. 5, Issue 1
Hopf and period-doubling bifurcations in an electromechanical resonator
journal, August 2016
- Mahboob, I.; Dupuy, R.; Nishiguchi, K.
- Applied Physics Letters, Vol. 109, Issue 7
Coherent control of a classical nanomechanical two-level system
journal, July 2013
- Faust, T.; Rieger, J.; Seitner, M. J.
- Nature Physics, Vol. 9, Issue 8
Coherent phonon manipulation in coupled mechanical resonators
journal, July 2013
- Okamoto, Hajime; Gourgout, Adrien; Chang, Chia-Yuan
- Nature Physics, Vol. 9, Issue 8
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
Phononic Frequency Comb via Intrinsic Three-Wave Mixing
journal, January 2017
- Ganesan, Adarsh; Do, Cuong; Seshia, Ashwin
- Physical Review Letters, Vol. 118, Issue 3
Tunable phonon-cavity coupling in graphene membranes
journal, June 2016
- De Alba, R.; Massel, F.; Storch, I. R.
- Nature Nanotechnology, Vol. 11, Issue 9
Frequency division using a micromechanical resonance cascade
journal, December 2014
- Qalandar, K. R.; Strachan, B. S.; Gibson, B.
- Applied Physics Letters, Vol. 105, Issue 24
Modelling the dynamics of a MEMS resonator: Simulations and experiments
journal, March 2008
- Mestrom, R. M. C.; Fey, R. H. B.; van Beek, J. T. M.
- Sensors and Actuators A: Physical, Vol. 142, Issue 1
An electromechanical Ising Hamiltonian
journal, June 2016
- Mahboob, Imran; Okamoto, Hajime; Yamaguchi, Hiroshi
- Science Advances, Vol. 2, Issue 6
Phononic Frequency Combs through Nonlinear Resonances
journal, February 2014
- Cao, L. S.; Qi, D. X.; Peng, R. W.
- Physical Review Letters, Vol. 112, 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
Anomalous Decay of Nanomechanical Modes Going Through Nonlinear Resonance
journal, December 2017
- Shoshani, O.; Shaw, S. W.; Dykman, M. I.
- Scientific Reports, Vol. 7, 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
Nonlinear dynamics and chaos in two coupled nanomechanical resonators
journal, April 2009
- Karabalin, R. B.; Cross, M. C.; Roukes, M. L.
- Physical Review B, Vol. 79, Issue 16
Interconnect-free parallel logic circuits in a single mechanical resonator
journal, February 2011
- Mahboob, I.; Flurin, E.; Nishiguchi, K.
- Nature Communications, Vol. 2, Issue 1
Nonlinearity-Induced Synchronization Enhancement in Micromechanical Oscillators
journal, January 2015
- Antonio, Dario; Czaplewski, David A.; Guest, Jeffrey R.
- Physical Review Letters, Vol. 114, Issue 3, Article No. 034103
Neuronal Oscillations in Cortical Networks
journal, June 2004
- Buzsaki, G.
- Science, Vol. 304, Issue 5679
Parametric Oscillation, Frequency Mixing, and Injection Locking of Strongly Coupled Nanomechanical Resonator Modes
journal, June 2017
- Seitner, Maximilian J.; Abdi, Mehdi; Ridolfo, Alessandro
- Physical Review Letters, Vol. 118, Issue 25
Nonlinear and Nonplanar Dynamics of Suspended Nanotube and Nanowire Resonators
journal, June 2008
- Conley, William G.; Raman, Arvind; Krousgrill, Charles M.
- Nano Letters, Vol. 8, Issue 6
Optically Mediated Hybridization between Two Mechanical Modes
journal, January 2014
- Shkarin, A. B.; Flowers-Jacobs, N. E.; Hoch, S. W.
- Physical Review Letters, Vol. 112, Issue 1
Dynamical strong coupling and parametric amplification of mechanical modes of graphene drums
journal, June 2016
- Mathew, John P.; Patel, Raj N.; Borah, Abhinandan
- Nature Nanotechnology, Vol. 11, Issue 9
Energy-dependent path of dissipation in nanomechanical resonators
journal, May 2017
- Güttinger, Johannes; Noury, Adrien; Weber, Peter
- Nature Nanotechnology, Vol. 12, Issue 7
Tuneable electromechanical comb generation
journal, March 2012
- Mahboob, I.; Wilmart, Q.; Nishiguchi, K.
- Applied Physics Letters, Vol. 100, Issue 11
Low temperature nullifies the circadian clock in cyanobacteria through Hopf bifurcation
journal, May 2017
- Murayama, Yoriko; Kori, Hiroshi; Oshima, Chiaki
- Proceedings of the National Academy of Sciences, Vol. 114, Issue 22
Works referencing / citing this record:
Bifurcation diagram and dynamic response of a MEMS resonator with a 1:3 internal resonance
journal, June 2019
- Czaplewski, David A.; Strachan, Scott; Shoshani, Oriel
- Applied Physics Letters, Vol. 114, Issue 25
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