Thermo-mechanical dynamics of three-dimensional axially moving beams

Mergen H. Ghayesh*, Hamed Farokhi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


The thermo-mechanical nonlinear dynamics of a three-dimensional axially moving beam is examined numerically in this paper. Hamilton’s principle is employed to derive the nonlinear partial differential equations governing the motion of the system in the longitudinal, transverse, and lateral directions. The discretized equations of motion, which are in the form of second-order nonlinear ordinary differential equations, are obtained by applying the Galerkin technique to the nonlinear partial differential equations of motion. A change of variables is introduced to this set of equations, yielding a set of first-order nonlinear ordinary differential equations. The pseudo-arclength continuation technique is employed to solve this set of equations numerically so as to construct the frequency–response curves; this method allows continuation of both stable and unstable solution branches. The effect of modal interactions on the resonant dynamic behaviour of a fully symmetrical system (about the centreline) is also examined.

Original languageEnglish
Pages (from-to)1643-1660
Number of pages18
JournalNonlinear Dynamics
Issue number3
Early online date25 Feb 2015
Publication statusPublished - 1 May 2015


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