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Identifying phase-varying periodic behaviour in conservative nonlinear systems.

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Summary
This summary is machine-generated.

This study introduces general asynchronous nonlinear normal modes (NNMs) and phase-varying backbone curves, expanding the understanding of nonlinear mechanical systems beyond synchronous and out-of-unison motions.

Keywords:
backbone curvesnonlinear normal modesphase–amplitude couplingreduced-order modellingstructural dynamics

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Area of Science:

  • Mechanical Engineering
  • Nonlinear Dynamics
  • Vibrational Analysis

Background:

  • Nonlinear normal modes (NNMs) are essential for nonlinear mechanical systems analysis.
  • Commonly observed NNMs include synchronous (in-phase, anti-phase) and asynchronous (90° phase difference) types.
  • Existing methods lack the framework to analyze NNMs with arbitrary phase differences.

Purpose of the Study:

  • To introduce and define general asynchronous nonlinear normal modes (NNMs).
  • To investigate the evolution of out-of-unison NNMs into general asynchronous NNMs.
  • To establish the concept of phase-varying backbone curves for nonlinear systems.

Main Methods:

  • Analysis of a single-mass, 2 degrees-of-freedom (d.f.) model.
  • Analytical investigation of NNM evolution and phase relationships.
  • Modeling of a cable with an off-center support to demonstrate practical application.

Main Results:

  • Demonstrated that out-of-unison NNMs evolve into general asynchronous NNMs when system orthogonality breaks.
  • Revealed amplitude-dependent phase relationships in evolving NNM branches.
  • Identified and termed these branches as phase-varying backbone curves.

Conclusions:

  • General asynchronous NNMs and phase-varying backbone curves exist in nonlinear systems, particularly when geometric orthogonality is compromised.
  • These concepts provide a more comprehensive understanding of nonlinear system dynamics.
  • The findings are validated in a practical engineering structure (a cable model).