Journal
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
Volume 49, Issue 1, Pages 227-243Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijsolstr.2011.10.007
Keywords
Axially moving beams; Nonlinear dynamics; Bifurcation diagrams; Stability
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The sub- and super-critical dynamics of an axially moving beam subjected to a transverse harmonic excitation force is examined for the cases where the system is tuned to a three-to-one internal resonance as well as for the case where it is not. The governing equation of motion of this gyroscopic system is discretized by employing Galerkin's technique which yields a set of coupled nonlinear differential equations. For the system in the sub-critical speed regime, the periodic solutions are studied using the pseudo-arclength continuation method, while the global dynamics is investigated numerically. In the latter case, bifurcation diagrams of Poincare maps are obtained via direct time integration. Moreover, for a selected set of system parameters, the dynamics of the system is presented in the form of time histories, phase-plane portraits, and Poincare maps. Finally, the effects of different system parameters on the amplitude-frequency responses as well as bifurcation diagrams are presented. (C) 2011 Elsevier Ltd. All rights reserved.
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