A memory-free method for fractional-order Duffing systems subjected to combined periodic and colored excitation

A statistical linearization-based memory-free method is proposed for determining the non-stationary response of single-degree-of-freedom Duffing systems endowed with fractional elements and subjected to excitation combined with periodic and colored noise. Specifically，by decomposing the system response as a combination of a periodic and of a zero-mean stochastic component，the original nonlinear motion equation can be equivalently transformed into two coupled fractional-order differential sub-equations，governing the deterministic and the stochastic component，respectively. Relying on a memory-free method，these fractional-order stochastic/deterministic differential equations are transformed into a set of ordinary differential equations without fractional derivatives. The Lyapunov differential equation governing the second moment of the stochastic response component is obtained by resorting to the statistical linearization method for the derived stochastic ordinary differential equations. The Lyapunov differential equation and the deterministic ordinary differential equations are solved simultaneously using standard numerical algorithms. Pertinent Monte Carlo simulations demonstrate the applicability and accuracy of the proposed method. © 2023 Nanjing University of Aeronautics an Astronautics. All rights reserved.