A Wiener Path Integral Technique for Non-Stationary Response Determination of Nonlinear Oscillators with Fractional Derivative Elements

Abstract

In this paper a novel approximate analytical technique for determining the nonstationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators with fractional derivative elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response nonstationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes. In this manner, the analytical Wiener path integral based technique developed by some of the authors is extended and generalized herein to account for systems with fractional derivative terms. Results are compared with pertinent Monte Carlo simulations demonstrating the reliability of the technique.