Response Analysis using Moment Equations of a System including Fractional Derivatives subjected to Non-White Random Excitation

Abstract

In recent years, research on random response analysis of a system including viscoelastic elements modeled by fractional derivative has begun to attract attention. The moment equation method is a typical method in the field of random response analysis of a system including integer-order derivative. In this study, the method to derive the moment equation corresponding to a linear system including fractional-order derivative of order 1/2 and to evaluate the statistics of the response is proposed. In addition, it is also shown that the value of the cross-correlation term between the input and the response in the moment equation can be evaluated by the fractional-order differentiation of the cross-correlation function between the input and the response. It is demonstrated that this method is effective for various non-white random excitation through analysis examples.