Waves in Viscoelastic Materials of Fractional‐Order Type

This chapter first presents the (one-dimensional) wave equation, which describes the motion, i.e. the change of displacement during time t at point x, of an elastic medium. It describes the wave equation for viscoelastic infinite media described by the fractional Zener and linear fractional models. The chapter then considers the wave equation for the non-local media of the fractional Eringen-type. It discusses stress relaxation, which corresponds to the case of the prescribed displacement, and creep, which corresponds to the case of the prescribed stress. These two effects, usually studied in the case of light rod, i.e. on the level of the constitutive equation, are investigated in the case of a rod of non-negligible mass. Also, the analysis is presented for solid and fluid-like viscoelastic bodies modeled by the constitutive equations of fractional derivative type. The chapter finally describes the displacement in the case of the forced oscillations of a rod.