Waves propagation in elastic solids with microstructure having a symmetric stress tensor (Q1087042)

In this paper the propagation of plane waves in an isotropic and homogeneous infinite elastic solid with microstructure having a symmetric stress tensor is studied. It is shown that in any space direction there are both longitudinal and transversal plane waves, two progressive and two regressive ones, whose phase velocities depend only on the material constants. Monochromatic plane waves in such an infinite elastic space are also considered and it is proved that they are not dispersive. Finally, it is shown that the harmonical vibrations of the considered elastic space are expressed as a sum of both progressive and regressive longitudinal and transversal monochromatic plane waves.