Motion of the particles due to viscoelastic surface waves of an assigned frequency

The motion of the material particles due to viscoelastic properties of the half-space is considered when the propagating surface wave has an assigned frequency. The detailed examination shows that for Rayleigh waves in classical elasticity as well as for the viscoelastic Rayleigh-type surface waves the sense of the particle path along the ellipse is retrograde on the surface of the half-space and changes into direct only once at depth about one seventh to one quarter of the wavelength. When there is a viscoelastic surface wave that does not satisfy the adopted four criteria for behaviour at infinity (the case of viscoelastic Rayleigh-type surface wave) but only two of them, this additional wave is direct on the surface of the half-space and does not change or may change many times the sense of the particle path along the ellipse with the distance from the stress-free surface of the half-space. In contrast to the elastic case, the ellipse axes in the viscoelastic case are not parallel and orthogonal to the surface of the half-space, respectively. Their orientation depends on the magnitude of the viscous part of the Lamé moduli and tends to a constant at great depth. The numerical computations in the paper refer to some typical values of the complex Lamé moduli and to some real materials.