Stochastic averaging of quasi-integrable Hamiltonian systems under bounded noise excitations

A stochastic averaging method is proposed to predict approximately the response of quasi-integrable Hamiltonian systems to bounded noise excitations. Two cases of external resonance only and both internal and external resonances are considered separately. The reduced averaged Fokker–Planck–Kolmogorov equation is solved by using the combination of the finite difference method and the successive over relaxation method. An example of two coupled Duffing oscillators under bounded noise excitations is given to illustrate the application of the proposed procedure. It is shown that the analytical results agree well with those from digital simulation of original system.