Journal
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
Volume 58, Issue -, Pages 11-21Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijnonlinmec.2013.08.012
Keywords
Pipe conveying fluid; Supercritical; Non-linearity; Internal resonance; Gyroscopic system; Method of multiple scales
Categories
Funding
- National Outstanding Young Scientists Foundation of China [10725209]
- State Key Program of National Natural Science of China [11232009]
- National Natural Science Foundation of China [11302122]
- Shanghai Rising-Star Program [11QA1402300]
- Shanghai Leading Academic Discipline Project [S30106]
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Non-linear vibration of viscoelastic pipes conveying fluid around curved equilibrium due to the supercritical flow is investigated with the emphasis on steady-state response in external and internal resonances. The governing equation, a non-linear integro-partial-differential equation, is truncated into a perturbed gyroscopic system via the Galerkin method. The method of multiple scales is applied to establish the solvability condition in the first primary resonance and the 2:1 internal resonance. The approximate analytical expressions are derived for the frequency amplitude curves of the steady-state responses. The stabilities of the steady-state responses are determined. The generation and the vanishing of a double-jumping phenomenon on the frequency amplitude curves are examined. The analytical results are supported by the numerical integration results. (C) 2013 Elsevier Ltd. All rights reserved.
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