Distributed-order fractional wave equation on a finite domain. Stress relaxation in a rod

Abstract

We study waves in a viscoelastic rod of finite length. Viscoelastic material is described by a constitutive equation of fractional distributed-order type with the special choice of weight functions. Prescribing boundary conditions on displacement, we obtain displacement and stress in a stress relaxation test. We use the Laplace transformation method in the time domain as a tool for solving system of differential and integro-differential equations, that describe the motion of the rod.