A new fractional equivalent linearization method for nonlinear stochastic dynamic analysis

Abstract

In this paper, a novel fractional equivalent linearization (NFEL) approach is developed by introducing fractional derivative term into the conventional equivalent linear equation. By appropriately formulating the fractional linearization coefficients with aid of the frequency response function of fractional equivalent linear system, an efficient iteration scheme is developed for determining these coefficients. Thus, the solution of fractional equivalent linear equation can be used to approximate the response of randomly excited nonlinear system. The contribution of the new added fractional derivative term to the classical damping force and the elastic restoring force is then quantitatively illustrated by virtue of the frequency response function of fractional system. The effectiveness of the NFEL is finally demonstrated by a nonlinear and a Duffing oscillator that is subjected to Gaussian white noise. The results are compared with the conventional equivalent linearization and exact solution.