Journal
CHAOS SOLITONS & FRACTALS
Volume 93, Issue -, Pages 39-47Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2016.10.001
Keywords
Fractional-order derivative; Rayleigh beams; Pasternak foundation; Moving loads; Horseshoes chaos; Beam stability
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Funding
- Alexander von Humboldt Foundation
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The standard averaging method is used to provide an analytical explanation on the effects of spacing loads, load velocity, order of the fractional viscoelastic property of shear layer material on the amplitude of the beam. The geometric nonlinearity is taken into account in the model. The analysis shows that, when the moving loads are uniformly distributed upon all the length of the structure, it vibrates the least possible. Moreover, as the order of the derivative increases, the resonant amplitude of the beam vibration decreases. In other hand, by means of Melnikov technique, a necessary condition for onset of horseshoes chaos resulting from heteroclinic bifurcation is derived analytically. We point out the critical weight of moving loads and order of the fractional derivative above which the system becomes unstable. (C) 2016 Elsevier Ltd. All rights reserved.
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