Fractional visco-elastic systems under normal white noise

In this paper an original method is presented to compute the stochastic response of singledegree- of-freedom structural systems with viscoelastic fractional damping. The key-idea stems from observing that, based on a few manipulations involving an appropriate change of variable and a discretization of the fractional derivative operator, the equation of motion can be reverted to a coupled linear system involving additional degrees of freedom, the number of which depends on the discretization adopted for the fractional derivative operator. The method applies for fractional damping of arbitrary order a (0 < α < 1). For most common input correlation functions, including a Gaussian white noise, it leads to closed-form expressions of the response second-order statistics that can be readily implemented in any symbolic package. Numerical applications show that a limited number of additional degrees of freedom is requested, in general, to achieve accurate results.