Stochastic averaging of MDOF quasi integrable Hamiltonian systems under wide-band random excitation

A stochastic averaging method for predicting the response of multi-degree-of-freedom (MDOF) quasi-integrable Hamiltonian systems to external and/or parametric wide-band random excitations is proposed. The motion equations governing a MDOF quasi-integrable Hamiltonian system is reduced to a set of averaged Itô stochastic differential equations via stochastic averaging and the associated averaged Fokker–Planck–Kolmogorov (FPK) equation is derived. The joint probability density of amplitudes and/or energies is obtained from solving the FPK equation. One example is given to illustrate the proposed method in detail and the effectiveness of the proposed method is verified via comparing the analytical results with those from Monte Carlo simulation.