Journal
JOURNAL OF SOUND AND VIBRATION
Volume 329, Issue 13, Pages 2603-2615Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jsv.2010.01.010
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A general vibrational model of a continuous system with arbitrary linear and cubic operators is considered. Approximate analytical solutions are found using the method of multiple scales. The primary resonances of the external excitation and three-to-one internal resonances between two arbitrary natural frequencies are treated. The amplitude and phase modulation equations are derived. The steady-state solutions and their stability are discussed. The solution algorithm is applied to two specific problems: (1) axially moving Euler-Bernoulli beam, and (2) axially moving viscoelastic beam. (C) 2010 Elsevier Ltd. All rights reserved.
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