Steady-state transverse response of an axially moving beam with time-dependent axial speed

This paper investigates the non-linear dynamics of an axially moving beam with time-dependent axial speed, including numerical results for the non-linear resonant response of the system in the sub-critical speed regime and global dynamical behavior. Using Galerkin's technique, the non-linear partial differential equation of motion is discretized and reduced to a set of ordinary differential equations (ODEs) by choosing the basis functions to be eigenfunctions of a stationary beam. The set of ODEs is solved by the pseudo-arclength continuation technique, for the system in the sub-critical axial speed regime, and by direct time integration to investigate the global dynamics. Results are shown through frequency-response curves as well as bifurcation diagrams of the Poincare maps. Points of interest in the parameter space in the form of time traces, phase-plane portraits, Poincare maps, and fast Fourier transforms (FFTs) are also highlighted. Numerical results indicate that the system displays a wide variety of rich and interesting dynamical behavior. (C) 2012 Elsevier Ltd. All rights reserved.