Transient stochastic response of quasi non-integerable Hamiltonian system

• The approximate transient response of non-integrable Hamiltonian system is investigated.
• The approximate transient solution is expressed as a series of new basis functions.
• The computation time can by saved with appropriate parameter value in basis functions.

The approximate transient response of multi-degree-of-freedom (MDOF) quasi non-integrable Hamiltonian system under Gaussian white noise excitation is investigated. First, the averaged Itô equation for Hamiltonian and the associated Fokker–Planck–Kolmogorov (FPK) equation governing the transient probability density of Hamiltonian of the system are derived by applying the stochastic averaging method for quasi non-integrable Hamiltonian systems. Then, the approximate solution of the transient probability density of Hamiltonian is obtained by applying the Galerkin method to solve the FPK equation. The approximate transient solution is expressed as a series in terms of properly selected basis functions with time-dependent coefficients. The transient probability densities of displacements and velocities can be derived from that of Hamiltonian. One example is given to illustrate the application of the proposed procedure. It is shown that the results for the example obtained by using the proposed procedure agree well with those from Monte Carlo simulation of the original system.