NONLINEAR ROCKING MOTIONS .1. CHAOS UNDER NOISY PERIODIC EXCITATIONS

The effects of low-intensity random perturbations on the stability of chaotic response of rocking objects under otherwise periodic excitatio ns are examined analytically and via simulations. A stochastic Melniko v process is developed to identify a lower bound for the domain of pos sible chaos. An average phase-flux rate is computed to demonstrate noi se effects on transitions from chaos to overturning. A mean Poincare m apping technique is employed to reconstruct embedded chaotic attractor s under random noise on Poincare sections. Extensive simulations are e mployed to examine chaotic behaviors from an ensemble perspective. Ana lysis predicts that the presence of random perturbations enlarges the possible chaotic domain and bridges the domains of attraction of coexi sting attractors. Numerical results indicate that overturning attracto rs are of the greatest strength among coexisting ones; and, because of the weak stability of chaotic attractors, the presence of random nois e will eventually lead chaotic rocking responses to overturning. Exist ence of embedded strange attractors (reconstructed using mean Poincare maps) indicates that rocking objects may experience transient chaos p rior to overturn.