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 pseudoarclength continuation method and direct time integration. The frequency-response curves of the system and the bifurcation diagrams of Poincaré maps are analyzed.
Nonlinear vibrations and stability of an axially moving beam with an intermediate spring support: two-dimensional analysis / Mergen H. Ghayesh; Marco Amabili; Michael P. Païdoussis. - In: NONLINEAR DYNAMICS. - ISSN 0924-090X. - 70(2012), pp. 335-354. [10.1007/s11071-012-0458-3]