Response and stability of a SDOF strongly nonlinear stochastic system with light damping modeled by a fractional derivative

A stochastic averaging procedure for a single-degree-of-freedom (SDOF) strongly nonlinear system with light damping modeled by a fractional derivative under Gaussian white noise excitations is developed by using the so-called generalized harmonic functions. The approximate stationary probability density and the largest Lyapunov exponent of the system are obtained from the averaged Itô stochastic differential equation of the system. It is shown that the approximate stationary solutions obtained by using the stochastic averaging procedure agree well with those from the numerical simulation of original systems. The effects of system parameters on the approxiamte stationary probability density and the largest Lyapunov exponent of the system are also discussed.