Effect of the fractional foundation on the response of beam structure submitted to moving and wind loads

A particular attention is devoted to analyze the effect of the foundation having fractional order viscoelastic material on a response of a beam structure. Periodic responses are computed using the stochastic averaging method, and the effects of fractional order damping on the vibration reduction of the beam are analyzed. The analysis shows that, as the order of the derivative increases, the resonant amplitude of the beam vibration decreases. It means that high order of the fractional derivative appear to be beneficial for the beam vibration control. It is also observed that the multivalued solution only appears for the smallest order and suddenly disappears as the derivative order increases. Further, the additive and parametric wind turbulence contributes to decrease the chance for the beam to reach the resonance of the amplitude oscillations. The analytical predictions are confirmed by numerical simulations.