Nonlinear dynamics of axially moving plates

The nonlinear dynamics for forced motions of an axially moving plate is numerically investigated using Von Kármán plate theory and retaining in-plane displacements and inertia. The equations of motion are obtained via an energy method based on Lagrange equations. This yields a set of second-order nonlinear ordinary differential equations with coupled terms. The equations are transformed into a set of first-order nonlinear ordinary differential equations and are solved via the pseudo-arclength continuation technique. The near-resonance nonlinear dynamics is examined via plotting the frequency–response curves of the system. Results are shown through frequency–response curves, time histories, and phase-plane diagrams. The effect of system parameters, such as the axial speed and the pretension, on the resonant responses is also highlighted.