Nonlinear vibrations and stability of an axially moving beam with an intermediate spring support: two-dimensional analysis

Abstract

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 Poincaré maps are analyzed.