Dispersion and polarization of surface Rayleigh waves for the Cosserat continuum

In the framework of the nonsymmetric theory of elasticity (the Cosserat contimum), we consider the problem of propagation of a surface acoustic Rayleigh wave in the half-space. The wave is represented as a wave packet of arbitrary form bounded both in the time space and the Fourier space. We assume that the material strain is described by not only the displacement vector but also an independent rotation vector. The general analytic solution of this problem is obtained in displacements. We perform comparative analysis of the obtained solution and the corresponding solution for the classical elastic medium. We introduce and analyze macroparameters characterizing the difference between the stress-strain state and the state predicted by the classical theory of elasticity: the elasticity coefficient, the wave number, and the phase and group velocities. It should be noted that these parameters can be measured experimentally.