GENERATION OF PERTURBATIONS BY A FOCUSED SOURCE DRIVING WITH CONSTANT DOWN SPEED ALONG THE BORDER OF THE GRADIENT-ELASTIC HALF-SPACE
Within the mathematical model of the gradient-elastic continuum, i.e. medium, the stress-strain state of which is described by the strain tensor, the second gradients of the displacement vector, the asymmetric stress tensor and the couple-stress tensor, the problem of generating perturbations by a moving source is considered. The model under study belongs to the class of generalized continua, its appearance is associated with the names of J.-M. Le Roux and T. Jaramillo. The well-known model of the Cosserat continuum reduces to the model of a gradient-elastic medium when the dependence of the rotation vector on the displacement rotor (constrained rotation) is rigidly fixed in it. It is assumed that the source moves at a constant velocity along the boundary of the half-space. The problem is considered in a two-dimensional formulation, when all the processes are homogeneous along the horizontal transverse coordinate axis. The displacement vector contains two components: longitudinal and vertical transverse. The velocity of the source does not exceed in its magnitude the velocity of the shear elastic wave (subsonic motion). As a result of analytical studies it is shown that a moving source will generate waves propagation along the boundary of a half-space and exponentially decreasing in its depth. The transverse component of the displacement vector always exceeds the longitudinal component, and the rotation of the particles during the propagation of the perturbation occurs along an elliptical trajectory. Such a wave, unlike the classical Rayleigh surface wave, has dispersion, since its phase velocity is not a constant, but depends on the frequency. The amplitudes of displacements vary depending on the magnitude of the load of the moving source and its speed. As the velocity of the source approaches the velocity of the shear wave, the perturbation amplitudes increase without limit.