Steady vibration problems in the theory of elasticity for materials with double voids

In the present paper, the linear theory of elasticity for materials with double voids is considered. Some basic properties of plane harmonic waves of this theory are established. The internal boundary value problems (BVPs) of steady vibrations are formulated. On the basis of Green's tensors, the internal BVPs are reduced to the equivalent Fredholm's integral equations of the second kind with symmetrical kernel. The existence of eigenfrequencies of the internal BVPs of steady vibrations is proved. Finally, the formula of the asymptotic distribution of these eigenfrequencies is obtained.