This paper is concerned with the linear elastodynamics of homogeneous
and isotropic materials with voids. First, the singular solutions corr
esponding to concentrated forces in the case of steady vibrations are
established. Then, representations of Somigliana type for the displace
ment 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 p
roblems to singular integral equations for which Fredholm's basic theo
rems are valid. Existence and uniqueness results for exterior problems
are established.