Waves in the reduced elastic Cosserat medium with transversal anisotropy of the coupling between linear rotational and translational deformations: Linearization near natural and axisymmetric prestressed state. Special directions

We consider elastic reduced Cosserat medium, a continuum where each point body possesses independent translational and rotational degrees of freedom, but no stresses can be induced by gradient of turn. We consider two cases: linear perturbation near a natural state, with axisymmetric coupling between translational and rotational deformation of general kind, and linear perturbation near a nonlinear axisymmetric prestressed state. We consider special directions of the wave propagation, parallel or orthogonal to the axis of symmetry. In the first case, we see that the waves demonstrate strong dispersion and have a band gap depending on the elastic parameters. In the second case, it is true for shear waves, but compression waves in these special directions are non-dispersive.