Non-stationary response of fractionally-damped viscoelastic systems

In this paper the non-stationary response of single-degree-of-freedom structural systems with fractional damping is addressed. By considering a proper variable transformation, the equation of motion is reverted to a set of equivalent coupled linear equations, the number of which depends on an appropriate discretization of the fractional derivative operator. It is shown that the additional equations correspond to a set of half oscillators with a fractal representation, whose Mandelbrot dimension is equal to the order α of the fractional derivative. Then, based on a preliminary eigenvector expansion, the response statistics are built in a closed form for stochastic inputs of relevant interest