Dynamics of a viscoelastic rod of fractional derivative type

Abstract

We study dynamics of a viscoelastic rod with fractional derivative type of dissipation under time dependent loading. First the moment curvature relation for the rod from the generalized Zener model of a standard linear solid is derived. Then, we show that the dynamics of the problem is governed by a single linear differential equation with fractional derivative. The existence and uniqueness of solutions for this equation is studied in detail. The form of the solution for the case of periodic compressive force is also obtained. © WILEY-VCH Verlag Berlin GmbH.