On the steady vibrations of elastic materials with voids

This paper is concerned with the linear elastodynamics of homogeneous and isotropic materials with voids. First, the singular solutions corresponding to concentrated forces in the case of steady vibrations are established. Then, representations of Somigliana type for the displacement field and the change in the volume fraction field are presented. Radiation conditions of Sommerfeld type are derived. The potentials of single layer and double layer are used to reduce the boundary value problems to singular integral equations for which Fredholm's basic theorems are valid. Existence and uniqueness results for exterior problems are established.