Passive control of fractional viscoelastic structures by Fractional Tuned Mass Dampers

In this paper, Fractional Tuned Mass Damper device is proposed in order to reduce the vibrations of structures with inherent fractional viscoelastic behaviour. The Fractional Tuned Mass Damper consists of an oscillating mass connected to the main structure using viscoelastic links. The damper device can be tuned with the main structure taking advantage of the Damped Fractional Frequency of the fractional oscillator, i.e. the frequency at which its transfer function attains a maximum value, and of optimal tuning ratios proposed in literature for classic Tuned Mass Dampers. Numerical simulations on fractional single degree of freedom structures excited by stochastic loads are presented by solving the fractional differential equations of motion of the system equipped with the damper device in the time domain and evaluating the statistics of the response by stochastic analysis in the frequency domain. For each structure, the effectiveness of the Fractional Tuned Mass Damper is measured by an opportune performance index defined in terms of reduction of the standard deviation of the main structural response. Sensitivity analysis with respect to the mass ratio between the primary mass and the Fractional Tuned Mass Damper and with respect to the damper parameters is reported in terms of performance index.