Tuned mass damper with fractional derivative damping

A tuned mass damper with a viscoelastic damping element applied to a single-degree-of-freedom system excited by white noise is considered. The viscoelastic damping is modelled as a force proportional to the fractional derivative of the relative displacement between the structure and the secondary mass.

Optimal parameters for the tuned mass damper are obtained numerically by optimizing the effective damping ratio of the system. It is shown that the structural damping has very little influence on the optimal parameters. Furthermore, it is demonstrated that the effect of the damper is the same for different values of the fraction in the fractional derivative.

This implies that this tuned mass damper with a fractional derivative damping element introduces the same reduction in the structural vibration as a conventional tuned mass damper if properly tuned. Simple approximate analytical expressions for optimal parameters are obtained by a frequency domain approach, in which the force acting between the structure and the secondary mass is assumed to be equal to the force of a conventional tuned mass damper at resonance.