Bifurcations and Chaos of an Axially Moving Plate Under External and Parametric Excitations

The chaos and bifurcations in transverse motion of an axially moving thin plate under external and parametric excitations are studied herein. The geometric nonlinearity is introduced by using the von Karman large deflection theory. The coupled partial differential equations of transverse deflection and stress are truncated into a set of ordinary differential equations. By using the Poincaré map and the largest Lyapunov exponent, the dynamical behaviors including chaos are identified based on numerical solutions of the ordinary differential equations. The bifurcation diagrams are presented for different parameters, such as axially moving velocity, damping, external and parametric excitation amplitudes. The chaos is detected in both cases of external and parametric excitations. The interesting relevance between onset of chaos with the corresponding linear instability range are indicated in the external and parametric responses.