Wave Attenuation in Elastic Continuum with Attenuating Neighborhood

Abstract

Spatial wave attenuation in elastic material is investigated in light of attenuating neighborhood theory of continuum mechanics. The attenuating part of the constitutive equation is expressed by an integral function of strain over each point of the material. It is shown that the spatial attenuation can be determined independent of the temporal attenuation in the viscoelastic material with fading memory, discussed by the writers in their previous paper, where the nonelastic part of the constitutive equation is determined by a functional of strain rate. However, the functional expressions for constitutive law are similar. The linear theory of attenuating neighborhood is briefly introduced and the solution to plane wave equation is derived. Then the characteristics of spatial wave attenuation are investigated in wavenumber domain. The critical conditions for wave propagation are also discussed. The fading memory is utilized in the previous paper by the writers to express all the temporal characteristics of wave attenuation. The present study shows that the attenuating neighborhood theory can be advantageously utilized to express the characteristics of spatial attenuation, such as the wavenumber dependence of