Stochastic response of fractional oscillators subjected to non-stationary random excitations via hybrid pseudo-force approach

In this paper, a novel “hybrid pseudo-force approach” is proposed for evaluating the stochastic response of fractional oscillators subjected to non-stationary input processes. The fractional oscillator analysed here is a secondorder linear system that includes a term with a fractional derivative, capable of capturing the dissipative properties of viscoelastic materials. The convolution integral method is adopted to evaluate the response. The fractional term in the equation of motion is then treated as a pseudo-force, allowing for a decomposition of the convolution integral into two distinct parts. The first part, related to the modulating function, is solved analytically in closed form using “classical” stochastic dynamics techniques. The second part, which involves the pseudoforce contribution of the fractional term, requires the discretization of the fractional derivative using the Grünwald-Letnikov approximation and a piecewise linear interpolation. Finally, the stochastic response statistics are obtained via numerical integration in the frequency domain. Numerical examples validate the stability, accuracy and applicability of the proposed method through comparisons with Monte Carlo simulation.