Stationary response determination of MDOF fractional nonlinear systems subjected to combined colored noise and periodic excitation

Abstract

A statistical linearization method is proposed for determining the response moment of multi-degree-of-freedom (MDOF) nonlinear systems, endowed with fractional elements and subjected to a combined stochastic and periodic excitation. Specifically, decomposing the response into a sum of a periodic and zero-mean stochastic component, leads to two coupled differential sub-equations in terms of unknown periodic and stochastic responses. These two equations are treated simultaneously, using the harmonic balance and the statistical linearization methods, respectively. The preceding treatment leads to two sets of nonlinear algebraic equations, whose solutions are found through apropos standard algorithms. Numerical examples, including a Single-Degree-of-Freedom(SDOF) and a MDOF fractional-order system with various types of nonlinearity subjected to combined white/colored noise and harmonic excitation, demonstrate the accuracy of the proposed method.