Chaotic Motions in Resonant Separatrix Zones of Periodically Forced, Axially Travelling, Thin Plates

Abstract

The analytical conditions for chaotic motions of axially travelling, thin plates are obtained from the incremental energy approach. A numerical prediction of chaotic motions from the scenario of the conservative energy varying with excitation amplitude is also presented through the symplectic Runge-Kutta method. The chaotic motions in the primary resonant and homoclinic separatrix zones of axially travelling plates are exhibited through Poincaré mapping sections. From this study, chaotic motion might occur in the small-amplitude oscillations of the axially travelling, thin plates once the geometrical nonlinearity is considered. The chaotic motions of post-buckled plates are much more easily observed than pre-buckled plates. Because the buckling of travelling plates is caused by high translation speeds, chaotic motions of thin plates travelling with high transport speeds can be easily observed.