Reflection of an inhomogeneous wave at the plane boundary of initially stressed fiber-reinforced viscoelastic medium

Abstract

The reflection phenomenon of attenuated waves is considered at the stress-free boundary of an initially stressed fiber-reinforced medium. An arbitrary arrangement of fibers is taken into account. The slowness vectors of reflected waves are associated with the incident wave slowness vector by generalized Snell’s law. The associated slowness vector of a particular reflected wave is resolved to yield its properties, i.e., phase velocity, attenuation angle, propagation direction and attenuation coefficient. A 4 × 4 energy matrix represents the energy fluxes of reflected waves and interaction energy. The effect of inhomogeneity and incidence angle on reflected wave characteristics are analyzed by a numerical example.