Free and forced modes of fractional-type torsional oscillations of a complex rod

Abstract

In this paper we study torsional oscillations of a complex rod made of material with viscoelastic properties. Free and forced modes of fractional-type torsional oscillations of a discrete system of a complex rod are described by a system of differential fractional order equations for a special case. The kinetic energy, deformation work, and generalized energy dissipation function of a fractional type system are identified for a special case. It has been shown that in the general case of such fractional type systems, with torsional oscillations, there are no independent modes, and that the system behaves as a nonlinear system.