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

Journal Article · · Applied Physics Letters
DOI: https://doi.org/10.1063/1.5099459 · OSTI ID:1570436

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.

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 journal December 2011
A hybrid on-chip opto-nanomechanical transducer for ultra-sensitive force measurements text January 2011
Coherent Sensing of a Mechanical Resonator with a Single-Spin Qubit journal February 2012
Sensitivity enhancement of a resonant mass sensor based on internal resonance journal November 2018
Measurement of the Casimir Force between Dissimilar Metals journal July 2003
Energy-dependent path of dissipation in nanomechanical resonators journal May 2017
Direct observation of coherent energy transfer in nonlinear micromechanical oscillators journal May 2017
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
Measurement of the Casimir force between dissimilar metals text January 2003
A hybrid on-chip optomechanical transducer for ultrasensitive force measurements journal June 2012
Bifurcations in Dynamical Systems With Internal Resonance journal December 1978
Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode text January 2011
MEMS-based force sensor: Design and applications journal September 2005
Surpassing Fundamental Limits of Oscillators Using Nonlinear Resonators journal April 2013
A nanomechanical mass sensor with yoctogram resolution journal April 2012
Ultrasensitive force detection with a nanotube mechanical resonator journal June 2013
Frequency stabilization in nonlinear micromechanical oscillators journal January 2012
Single Molecule Detection of Nanomechanical Motion journal March 2013
An atomic-resolution nanomechanical mass sensor journal July 2008
Single spin detection by magnetic resonance force microscopy journal July 2004
Bifurcation Generated Mechanical Frequency Comb journal December 2018
Quantum-Coherent Coupling of a Mechanical Oscillator to an Optical Cavity Mode conference January 2012
Inertial imaging with nanomechanical systems journal March 2015
Entangling Mechanical Motion with Microwave Fields journal October 2013
Toward Attogram Mass Measurements in Solution with Suspended Nanochannel Resonators journal July 2010
Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope journal March 2015
Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks journal September 2016
Limit cycles and bifurcations in a nonlinear MEMS resonator with a 1:3 internal resonance journal March 2019

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