Non-linear modal analysis for beams subjected to axial loads: Analytical and Finite Element solutions

Carlos E. N. Mazzilli, Cesar T. Sanches, Odulpho G. P. Baracho Neto, Marian Wiercigroch, Marko Keber

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


A rigorous derivation of non-linear equations governing the dynamics of an axially loaded beam is given with a clear focus to develop robust low-dimensional models. Two important loading scenarios were considered, where a structure is subjected to a uniformly distributed axial and a thrust force. These loads are to mimic the main forces acting on an offshore riser, for which an analytical methodology has been developed and applied. In particular, non-linear normal modes (NNMs) and non-linear multi-modes (NMMs) have been constructed by using the method of multiple scales. This is to effectively analyse the transversal vibration responses by monitoring the modal responses and mode interactions. The developed analytical models have been crosschecked against the results from FEM simulation. The FEM model having 26 elements and 77 degrees-of-freedom gave similar results as the low-dimensional (one degree-of-freedom) non-linear oscillator, which was developed by constructing a so-called invariant manifold. The comparisons of the dynamical responses were made in terms of time histories, phase portraits and mode shapes.

Original languageEnglish
Pages (from-to)551-561
Number of pages11
JournalInternational Journal of Non-Linear Mechanics
Issue number6
Early online date17 Apr 2008
Publication statusPublished - Jul 2008


  • non-linear normal modes
  • non-linear multi-modes
  • axially loaded beams
  • vertical risers


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