An Explanation for Why Natural Frequencies Shifting in Structures with Membrane Stresses, Using Backbone Curve Models

Xiang Liu, David J Wagg, Simon Neild

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

2 Citations (Scopus)
212 Downloads (Pure)


In this paper, the phenomenon of natural frequencies shifting due to the nonlinear stiffness effects from membrane stress is studied using a nonlinear reduced order model based on backbone curves. The structure chosen for study in this paper is a rectangular plate with a pinned constraint along all edges. To analytically explore the frequency varying phenomenon, a four nonlinear-mode based reduced-order model that contains both single-mode and coupled-mode nonlinear terms is derived. The process of deriving the reduced order model is based on a normal form transformation, combined with a Galerkin type decomposition of the governing partial differential equation of the plate. This allows a low number of ordinary differential equations to be obtained, which in turn can be used to derive backbone curves that relate directly to the nonlinear normal modes (NNMs). The frequency shifting is then investigated relative to the backbone curves. Modal interactions, caused by nonlinear terms are shown to cause the frequency shifts. In the final part of the paper, an attempt is made to quantify the frequency shifting due to different nonlinear effects.
Original languageEnglish
Title of host publicationNonlinear Dynamics, Volume 1
Subtitle of host publicationProceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics 2017
EditorsGaetan Kerschen
PublisherSpringer International Publishing AG
Number of pages11
ISBN (Electronic)9783319544045
ISBN (Print)9783319544038
Publication statusPublished - 4 May 2017

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
ISSN (Print)2191-5644


  • Nonlinear reduced order model
  • Backbone curves
  • Nonlinear modal interaction
  • Second-order normal form method
  • Thin plate

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