Journal
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
Volume 49, Issue -, Pages 40-49Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijnonlinmec.2012.08.003
Keywords
Axially moving beams; Time-dependent axial speed; Non-linear dynamics; Bifurcation diagrams
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This paper investigates the non-linear dynamics of an axially moving beam with time-dependent axial speed, including numerical results for the non-linear resonant response of the system in the sub-critical speed regime and global dynamical behavior. Using Galerkin's technique, the non-linear partial differential equation of motion is discretized and reduced to a set of ordinary differential equations (ODEs) by choosing the basis functions to be eigenfunctions of a stationary beam. The set of ODEs is solved by the pseudo-arclength continuation technique, for the system in the sub-critical axial speed regime, and by direct time integration to investigate the global dynamics. Results are shown through frequency-response curves as well as bifurcation diagrams of the Poincare maps. Points of interest in the parameter space in the form of time traces, phase-plane portraits, Poincare maps, and fast Fourier transforms (FFTs) are also highlighted. Numerical results indicate that the system displays a wide variety of rich and interesting dynamical behavior. (C) 2012 Elsevier Ltd. All rights reserved.
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