Global dynamics of an axially moving buckled beam

Mergen H. Ghayesh*, Marco Amabili, Hamed Farokhi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

A parametric study for post-buckling analysis of an axially moving beam is conducted considering four different axial speeds in the supercritical regime. At critical speed, the trivial equilibrium configuration of this conservative system becomes unstable and the system diverges to a new non-trivial equilibrium configuration via a pitchfork bifurcation. Post-buckling analysis is conducted considering the system undergoing a transverse harmonic excitation. In order to obtain the equations of motion about the buckled state, first the equation of motion about the trivial equilibrium position is obtained and then transformed to the new coordinate, i.e. post-buckling configuration. The equations are then discretized using the Galerkin scheme, resulting in a set of nonlinear ordinary differential equations. Using direct time integration, the global dynamics of the system is obtained and shown by means of bifurcation diagrams of Poincaré maps. Other plots such as time traces, phase-plane diagrams, and Poincaré sections are also presented to analyze the dynamics more precisely.

Original languageEnglish
Pages (from-to)195-208
Number of pages14
JournalJVC/Journal of Vibration and Control
Volume21
Issue number1
Early online date2 Jul 2013
DOIs
Publication statusPublished - 1 Jan 2015

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