WAVE PROPAGATION IN A COSSERAT ELASTIC HALF-SPACE: DISPERSION ANALYSIS OF SURFACE AND BULK WAVES

The paper investigates the propagation of harmonic waves in an elastic half-space whose material is described by a simplified two-dimensional Cosserat continuum (micropolar medium). The equations of motion of the Cosserat medium are reduced, by means of the Green–Lamb (scalar–vector potential) transformation, to a system of ordinary differential equations with complex coefficients. The complex character of the coefficients is due to the viscoelastic properties of the medium, modelled by the three-parameter weakly singular relaxation kernel of Rzhanitsyn–Koltunov. The general solution of the system is constructed, volume wave velocities are determined, and a dispersion equation for a layered Cosserat structure is derived. It is shown that a Rayleigh-type surface wave in a Cosserat half-space is dispersive, in contrast to the classical case: the "phase velocity–frequency" plane contains two dispersion branches, a lower ("acoustic") and an upper ("optical") one. The phase velocity of the surface wave exceeds the phase velocity of the bulk displacement wave over the whole frequency range; the wave propagates in the horizontal direction and decays with depth. From the same system, solutions describing Lamb waves (symmetric and antisymmetric plate modes) and Stoneley waves at the interface of two half-spaces are obtained. Numerical results show that the normal stress moment in the Cosserat medium exceeds the classical value by approximately 24 %, and the displacement-amplitude trajectory is elliptical.

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