Comparing Analytical Approximation Methods with Numerical Results for Nonlinear Systems

A J Elliott, Andrea Cammarano, Simon Neild

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

3 Citations (Scopus)
307 Downloads (Pure)


Modelling the dynamics of nonlinear systems poses a much more challenging problem than for their linear counterparts; as such, analytical solutions are rarely achievable and numerical or analytical approximations are often necessary to understand the system’s behaviour. While numerical techniques are undoubtedly accurate, it is possible to gain a greater understanding of the processes underpinning the workings of the dynamics. Therefore, it is valuable to investigate the accuracy and practicality of the aforementioned analytical approximation techniques and compare the results with numerical which are known to be accurate. In this paper, the unforced, undamped dynamics (known as backbone curves) of a non-symmetric two-mass oscillator will be calculated using the second-order normals forms (SONF), harmonic balance, and multiple scales techniques. The results of these will then be compared to responses found using numerical continuation. Furthermore, the forced responses will be approximated using the SONF and harmonic balance techniques. In addition, recent work has reported the possibility of using such analytical expressions for parameter estimation from experimental data.
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 pages13
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


  • Backbone curves
  • Second-order normal forms
  • Harmonic balance
  • Multiple scales
  • Modal analysis


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