NONLINEAR DYNAMICAL BEHAVIORS OF AXIALLY MOVING LARGE DEFLECTION PLATES

The stability and bifurcations of axially moving plates with large transverse deflections are investigated. The governing equations of an axially moving plate are derived through the D’Alembert’s principle based on von Kàrmàn’s nonlinear plate theory. The Galerkin metod is employed to discretize the governing partial differential equations into a set of ordinary differential equations. By a numerical method, the bifurcation diagrams are presented with respect to some parameters such as transport speed, amplitude of exciting, the ratio of the length to the width of plates and the longitudinal tension. The dynamical behaviors are identified based on the Poincaré map and the Largest Lyapunov Exponent. Periodic, quasi-periodic and even chaotic motions are located in the bifurcation diagram for the transverse vibration of the axially moving plate.