Stochastic averaging of quasi-partially integrable Hamiltonian systems under combined Gaussian and Poisson white noise excitations

• A stochastic averaging method for quasi-Hamiltonian systems has been developed.
• The Hamiltonian system is partially integrable and non-resonant.
• The excitations are combined Gaussian and Poisson white noises.
• The finite difference method is used to solve the averaged GFPK equation.
• An example is worked out to show the effectiveness of the proposed method.

A stochastic averaging method for predicting the response of quasi-partially integrable and non-resonant Hamiltonian systems to combined Gaussian and Poisson white noise excitations is proposed. For the case with r(1