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