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.