Skip to main content
Journal cover image

Control-based continuation for investigating nonlinear experiments

Publication ,  Journal Article
Barton, DAW; Mann, BP; Burrow, SG
Published in: JVC/Journal of Vibration and Control
April 1, 2012

In this paper we present a systematic experimental study of two one-degree-of-freedom nonlinear devices using the newly introduced control-based continuation method of Sieber and Krauskopf. By considering hardening, softening and bistable spring characteristics, we demonstrate the versatility and power of the control-based continuation method for investigating nonlinear experiments. We show that, using this method, it is possible to track the stable orbits of the devices through a saddle-node bifurcation (fold) where they lose stability and continue them up to the resonance peak where they undergo a second saddle-node bifurcation. For the bistable case, a bifurcation diagram is produced that is strongly reminiscent of the bifurcation diagram produced using the classical harmonic balance solution. A detailed introduction to general continuation methods is included to enable implementation by other experimentalists. © 2011 The Author(s).

Duke Scholars

Published In

JVC/Journal of Vibration and Control

DOI

EISSN

1741-2986

ISSN

1077-5463

Publication Date

April 1, 2012

Volume

18

Issue

4

Start / End Page

509 / 520

Related Subject Headings

  • Acoustics
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 0913 Mechanical Engineering
  • 0906 Electrical and Electronic Engineering
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Barton, D. A. W., Mann, B. P., & Burrow, S. G. (2012). Control-based continuation for investigating nonlinear experiments. JVC/Journal of Vibration and Control, 18(4), 509–520. https://doi.org/10.1177/1077546310384004
Barton, D. A. W., B. P. Mann, and S. G. Burrow. “Control-based continuation for investigating nonlinear experiments.” JVC/Journal of Vibration and Control 18, no. 4 (April 1, 2012): 509–20. https://doi.org/10.1177/1077546310384004.
Barton DAW, Mann BP, Burrow SG. Control-based continuation for investigating nonlinear experiments. JVC/Journal of Vibration and Control. 2012 Apr 1;18(4):509–20.
Barton, D. A. W., et al. “Control-based continuation for investigating nonlinear experiments.” JVC/Journal of Vibration and Control, vol. 18, no. 4, Apr. 2012, pp. 509–20. Scopus, doi:10.1177/1077546310384004.
Barton DAW, Mann BP, Burrow SG. Control-based continuation for investigating nonlinear experiments. JVC/Journal of Vibration and Control. 2012 Apr 1;18(4):509–520.
Journal cover image

Published In

JVC/Journal of Vibration and Control

DOI

EISSN

1741-2986

ISSN

1077-5463

Publication Date

April 1, 2012

Volume

18

Issue

4

Start / End Page

509 / 520

Related Subject Headings

  • Acoustics
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 0913 Mechanical Engineering
  • 0906 Electrical and Electronic Engineering