Journal
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
Volume 36, Issue 1, Pages 107-115Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/S0020-7462(99)00090-6
Keywords
non-linear vibrations; axially moving material; perturbation methods
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Non-linear vibrations of an axially moving beam are investigated. The non-linearity is introduced by including stretching effect of the beam. The beam is moving with a time-dependent velocity, namely a harmonically varying velocity about a constant mean velocity. Approximate solutions are sought using the method of multiple scales. Depending on the variation of velocity, three distinct cases arise: (i) frequency away from zero or two times the natural frequency, (ii) frequency close to zero, (iii) frequency close to two times the natural frequency. Amplitude-dependent non-linear frequencies are derived. For frequencies close to two times the natural frequency, stability and bifurcations of steady-state solutions are analyzed. For frequencies close to zero, it is shown that the amplitudes are bounded in time. (C) 2000 Elsevier Science Ltd. All rights reserved.
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