Fractional damping Induced by a slave system attached to a master oscillator

This paper illustrates a class of mechanical systems exhibiting a damping mechanism based on fractional derivatives. In particular it is shown how a set of small oscillators of appropriate characteristics attached to an oscillator of larger mass produces an effect that globally can amount to a fractional derivative dissipation mechanism. More precisely the fractional derivative model depends on the choice of frequency distribution selected within the set of the attached small oscillators. On this basis a general theory that provides a link between fractional damping and damping induced by a slave system attached to a primary structure is presented.