Backbone curves of coupled cubic oscillators in one-to-one internal resonance: bifurcation scenario, measurements and parameter identification

Arthur Givois (Corresponding author), Jin Jack Tan, Cyril Touze, Olivier Thomas

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)

Abstract

A system composed of two cubic nonlinear oscillators with close natural frequencies, and thus displaying a 1:1 internal resonance, is studied both theoretically and experimentally, with a special emphasis on the free oscillations and the backbone curves. The instability regions of uncoupled solutions are derived and the bifurcation scenario as a function of the parameters of the problem is established, showing in an exhaustive manner all possible solutions. The backbone curves are then experimentally measured on a circular plate, where the asymmetric modes are known to display companion configurations with close eigenfrequencies. A control system based on a Phase-Locked Loop (PLL) is used to measure the backbone curves and also the frequency response function in the forced and damped case, including unstable branches. The model is used for a complete identification of the unknown parameters and an excellent comparison is drawn out between theoretical prediction and measurements.
Original languageEnglish
Pages (from-to)481-503
Number of pages23
JournalMeccanica
Volume55
Issue number3
DOIs
Publication statusPublished - 1 Mar 2020

Keywords

  • 1:1 Resonance
  • Backbone curve
  • Bifurcations
  • Measurements
  • Model identification
  • Nonlinear vibrations
  • Stability
  • 1
  • 1 Resonance

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