Summary
In this paper, the nonstationary response of nonlinear single-degree-of-freedom systems subject to stochastic excitations is examined. A version of the Path Integral (PI) approach is developed for determining the evolution of the response probability density function (PDF). Specifically, the PI approach is here employed in conjunction with the Laplace’s method of integration. In this manner, an approximate analytical solution of the integral involved in the Chapman-Kolmogorov equation is obtained, thus circumventing the repetitive integrations generally required in the conventional numerical implementation of the procedure. The reliability of the procedure is assessed considering the case of a Duffing nonlinear oscillator, and appropriate comparisons with Monte Carlo simulation data are presented demonstrating the accuracy of the proposed approach.
