Stochastic direct integration schemes for dynamic systems subjected to random excitations

In this work, a stochastic version of direct integration schemes is constructed, based on a general recursive state space formulation. The technique is applicable to evaluating the second order response statistics of systems subjected to non-stationary random excitations, and is potentially able to handle non-proportional damping. A specific group of these algorithms obtained using one of the most frequently used families of time stepping schemes is introduced. It is shown that statistics obtained for two multi-degree of freedom (MDOF) dynamic systems using the proposed method are in close agreement with those obtained from Monte Carlo simulation when a proper time step is used. Stability of the proposed scheme is systematically investigated and it is concluded that, for the response statistics to be bounded, the time step used in the algorithm has to lie within certain limits.