NONLINEAR ROCKING MOTIONS .2. OVERTURNING UNDER RANDOM EXCITATIONS

Rocking responses of rigid objects under combined deterministic and st ochastic excitations of arbitrary relative intensities are examined fr om a fully probabilistic perspective. The associated Fokker-Planck equ ation is derived and numerically solved by a path-integral solution pr ocedure to obtain the joint probability density functions (JPDFs). The evolutions and the steady states of the JPDFs are employed to elucida te the global behaviour of the rocking responses. As found in the comp anion paper, numerical results confirm that the presence of stochastic excitation bridges the domains of attraction of coexisting responses, and that overturning attractors are of the greatest relative stabilit y. Thus, all rocking response trajectories that visit near the heteroc linic orbit will eventually lead to overturning under the influence of stochastic excitation. A rapid leakage of the probability (mass) out of the ''safe'' (bounded, chaotic) domain to the overturning regime im plies weak stability of the chaotic attractor. Using mean first-passag e time as a performance index, sensitivity of rocking responses to sys tem parameters and (non)stationarity of the stochastic excitation is a lso investigated.