Nonstationary Stochastic Response Determination of Nonlinear Systems: A Wiener Path Integral Formalism

A novel approximate analytical technique is developed for determining the nonstationary response probability density function (PDF) of randomly excited nonlinear multidegree-of-freedom (MDOF) systems. Specifically, the concept of the Wiener path integral (WPI) is used in conjunction with a variational formulation to derive an approximate closed-form solution for the system response PDF. Notably, determining the nonstationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by existing alternative numerical path integral solution schemes, which rely on a discrete version of the Chapman-Kolmogorov (C-K) equation. In this manner, the analytical WPI-based technique developed by the authors is extended and generalized herein to account for hysteretic nonlinearities and MDOF systems. This enhancement of the technique affords circumventing approximations associated with the stochastic averaging treatment of the previously developed technique. Hopefully the technique can be used as a convenient tool for assessing the accuracy of alternative, more computationally intensive stochastic dynamics solution methods. The accuracy of the technique is demonstrated by pertinent Monte Carlo simulations. (C) 2014 American Society of Civil Engineers.