Rayleigh Wave on the Boundary of Gradient-Elastic Semi-Space

In recent years, Rayleigh waves of the ultrasonic range have found wide application. By means of these waves, it is possible to monitor the state of the surface layer of a sample (revealing surface and near surface defects in samples of metal, glass, plastic and other materials — ultrasonic surface flaw detection). The influence of the properties of the surface layer of the sample on velocity and damping of Rayleigh waves allows using the latter to determine the residual stresses of the surface layer of the metal, the thermal and mechanical properties of the surface layer of the sample. Along with the model of the classical continuum, the models of generalized continua are widely used in the mechanics of a deformed rigid body. In particular, the gradient-elastic medium belongs to the number of generalized continua. The article focuses on the mathematical model of the generalized continuum called gradient-elastic medium, whose stress-strain state is described by the deformation tensor, second gradients of the displacement vector, the asymmetric stress tensor and the couple stress tensor. In the two-dimensional formulation, the problem of propagation of an elastic surface wave on the boundary of the gradient-elastic semi-space is considered. The solution of the equations is sought in the form of a sum of scalar and vector potentials, and the vector potential has only one component different from zero. It is shown that such a wave, unlike the classical Rayleigh wave, has dispersion. The dependence of phase velocity of the surface wave on the wave number is calculated and compared with the dispersion characteristic of phase velocity of the sheer volume wave. The stresses and displacements arising in the zone of surface wave propagation are calculated

This work was supported by the Russian Science Foundation (grant no. 14-19-01637)

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