Waves in Linear Elastic Media with Microrotations: Isotropic Full Cosserat Model

In this study, we discussed solutions for longitudinal and transverse bulk waves, Rayleigh wave and surface transverse wave in a half-space as well as Lamb wave and transverse wave in a thin layer within the framework of the isotropic Cosserat continuum. The medium deformation in this model is described not only by the displacement vector, but also by kinematically independent rotation vector. Problems on bulk wave propagation are rather interesting from the viewpoint of interpretation of new parameters introduced for the dimensionless notation of wave solutions. However, these problems have no prospects from the standpoint of experimental implementation. In contrast to bulk waves, surface waves for the elastic half-space have a considerable experimental potential. These waves can be divided into two groups, one of which corresponds to the well-investigated elliptical wave and the other - to the transverse wave with depth-dependent decay, which does not have any analogy in the classical theory of elasticity. The results obtained in this study can be used for the preparation and interpretation of seismic experiments, which could validate the importance of asymmetric theories of elasticity in earthquake and exploration seismology, and for experimental determination of the material constants of the Cosserat media. Firstly, the dispersion analysis of experimental three-component seismograms allows constructing experimental dispersion curves and comparing them with theoretical ones. Secondly, rotation sensors make it possible to trace a relation between displacement and rotation components according to relations. Thirdly, the presence of a transverse surface wave in the Cosserat continuum can also be the subject of experimental study with the use of sensors imbedded at different depths.