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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 Lab. (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.
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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
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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.
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@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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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/1.5099459
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Cited by: 3 works
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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
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    Demonstration of Multiple Internal Resonances in a Microelectromechanical Self-Sustained Oscillator
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