Comparison of different methodologies for the computation of damped nonlinear normal modes and resonance prediction of systems with non-conservative nonlinearities

Yekai Sun*, Jie Yuan, Alessandra Vizzaccaro, Loïc Salles

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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The nonlinear modes of a non-conservative nonlinear system are sometimes referred to as damped nonlinear normal modes (dNNMs). Because of the non-conservative characteristics, the dNNMs are no longer periodic. To compute non-periodic dNNMs using classic methods for periodic problems, two concepts have been developed in the last two decades: complex nonlinear mode (CNM) and extended periodic motion concept (EPMC). A critical assessment of these two concepts applied to different types of non-conservative nonlinearities and industrial full-scale structures has not been thoroughly investigated yet. Furthermore, there exist two emerging techniques which aim at predicting the resonant solutions of a nonlinear forced response using the dNNMs: extended energy balance method (E-EBM) and nonlinear modal synthesis (NMS). A detailed assessment between these two techniques has been rarely attempted in the literature. Therefore, in this work, a comprehensive comparison between CNM and EPMC is provided through two illustrative systems and one engineering application. The EPMC with an alternative damping assumption is also derived and compared with the original EPMC and CNM. The advantages and limitations of the CNM and EPMC are critically discussed. In addition, the resonant solutions are predicted based on the dNNMs using both E-EBM and NMS. The accuracies of the predicted resonances are also discussed in detail.

Original languageEnglish
Pages (from-to)3077-3107
Number of pages31
JournalNonlinear Dynamics
Issue number4
Publication statusPublished - Jun 2021

Bibliographical note

Funding Information:
We thank Dr. Xing Wang (Sun Yat-sen University, China) for useful discussions. We are thankful to the two reviewers in the revision process for providing very constructive comments.

Funding Information:
Dr. Yekai Sun is grateful to China Scholarship Council (File No. 201708060239) for providing the financial support for this project. Dr. Jie Yuan acknowledges financial support from EPSRC (SYSDYMATS Project WP3). Dr. Loïc Salles thanks Rolls-Royce plc and the EPSRC for the support under the Prosperity Partnership Grant “Cornerstone: Mechanical Engineering Science to Enable Aero Propulsion Futures”, Grant Ref: EP/R004951/1.

Publisher Copyright:
© 2021, The Author(s).


  • Damped nonlinear normal modes
  • Nonlinear damping
  • Nonlinear modal analysis
  • Nonlinear vibration


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