Dynamic characterization of fractional oscillators for Fractional Tuned Mass Dampers tuning

A novel formulation for Fractional Tuned Mass Damper (FTMD) devices is proposed in this paper. The FTMD is realized by connecting an oscillating mass to the main structure using a viscoelastic link, realized through elastomeric rubber bearings with fractional derivative constitutive model. A new function, labeled Damped Fractional Frequency, is defined for the fractional oscillator as the analogous of the damped frequency for classic single oscillators. Then, a critical value for the fractional order derivative involved in the damper constitutive law is defined as the limit value for which the DFF is real. It is shown that prevalent elastic or viscous dynamic behaviours are observed for the fractional oscillator when the fractional order derivative assumes values smaller or greater than the critical value, respectively. Finally, the DFF concept is utilized to opportunely tune the FTMD to its main structure, analogously to classic Tuned Mass Damper devices. Applications to a system excited by stochastic loads are presented, using the classic tools of stochastic analysis to determine the system response statistics and measure the performance of the FTMD.