Journal
NONLINEAR DYNAMICS
Volume 70, Issue 1, Pages 335-354Publisher
SPRINGER
DOI: 10.1007/s11071-012-0458-3
Keywords
Axially moving beams; Non-linear dynamics; Two-dimensional analysis; Stability
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The nonlinear coupled longitudinal-transverse vibrations and stability of an axially moving beam, subjected to a distributed harmonic external force, which is supported by an intermediate spring, are investigated. A case of three-to-one internal resonance as well as that of non-resonance is considered. The equations of motion are obtained via Hamilton's principle and discretized into a set of coupled nonlinear ordinary differential equations using Galerkin's method. The resulting equations are solved via two different techniques: the pseudo-arclength continuation method and direct time integration. The frequency-response curves of the system and the bifurcation diagrams of Poincar, maps are analyzed.
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