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 journalArticle

18 Citations (Scopus)

Abstract

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
Volume43
Issue number6
Early online date17 Apr 2008
DOIs
Publication statusPublished - Jul 2008

Keywords

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

Cite this

Non-linear modal analysis for beams subjected to axial loads : Analytical and Finite Element solutions. / Mazzilli, Carlos E. N.; Sanches, Cesar T.; Baracho Neto, Odulpho G. P.; Wiercigroch, Marian; Keber, Marko.

In: International Journal of Non-Linear Mechanics, Vol. 43, No. 6, 07.2008, p. 551-561.

Research output: Contribution to journalArticle

Mazzilli, Carlos E. N. ; Sanches, Cesar T. ; Baracho Neto, Odulpho G. P. ; Wiercigroch, Marian ; Keber, Marko. / Non-linear modal analysis for beams subjected to axial loads : Analytical and Finite Element solutions. In: International Journal of Non-Linear Mechanics. 2008 ; Vol. 43, No. 6. pp. 551-561.
@article{bf7b36742fed41679522b12fc191b9f1,
title = "Non-linear modal analysis for beams subjected to axial loads: Analytical and Finite Element solutions",
abstract = "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.",
keywords = "non-linear normal modes, non-linear multi-modes, axially loaded beams, vertical risers",
author = "Mazzilli, {Carlos E. N.} and Sanches, {Cesar T.} and {Baracho Neto}, {Odulpho G. P.} and Marian Wiercigroch and Marko Keber",
year = "2008",
month = "7",
doi = "10.1016/j.ijnonlinmec.2008.04.004",
language = "English",
volume = "43",
pages = "551--561",
journal = "International Journal of Non-Linear Mechanics",
issn = "0020-7462",
publisher = "Elsevier Limited",
number = "6",

}

TY - JOUR

T1 - Non-linear modal analysis for beams subjected to axial loads

T2 - Analytical and Finite Element solutions

AU - Mazzilli, Carlos E. N.

AU - Sanches, Cesar T.

AU - Baracho Neto, Odulpho G. P.

AU - Wiercigroch, Marian

AU - Keber, Marko

PY - 2008/7

Y1 - 2008/7

N2 - 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.

AB - 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.

KW - non-linear normal modes

KW - non-linear multi-modes

KW - axially loaded beams

KW - vertical risers

U2 - 10.1016/j.ijnonlinmec.2008.04.004

DO - 10.1016/j.ijnonlinmec.2008.04.004

M3 - Article

VL - 43

SP - 551

EP - 561

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

IS - 6

ER -