The article deals with elastic homogeneous isotropic half-space filled with the Cosserat medium. A cylindrical coordinate system is used. A closed system of equations includes equations for the non-trivial components of the displacement and rotation potentials, as well as relations relating the displacements to the potentials and components of the stress and moment stress tensors with displacements and the angle of rotation. On the boundary plane, normal displacements are specified, and the angle of rotation and tangential displacements are absent. Initial conditions are zero. All components of the stress-strain state are assumed to be limited. A system of dimensionless quantities is used.
The solution is represented as a convolution with respect to time and a generalized convolution with respect to the radius of surface perturbations with influence functions. To construct them, Hankel transforms are applied along the radius and Laplace in time, as well as expansion in power series in a small parameter in the linear approximation. Found image of all surface influence functions. For example, the following function is considered corresponding to the normal voltage. Its original is on the border of a half-space using the connection of axisymmetric and plane problems, namely, taking into account the proportionality of the Hankel and Fourier images respectively. It uses the previously constructed solution of the planar problem. As a result, the desired function is represented as integrals, which are understood in the sense of regularized values. Analytic expressions for these integrals and the influence function itself are found.
Examples of calculations of the influence functions of a granular composite of aluminum shot in an epoxy matrix are given. Two variants of action on the half-space of surface normal displacements are also considered: the disturbance concentrated at the origin and distributed in a circle. Analysis of the results shows that the effect of the moment properties of the medium depends significantly on the value of the parameter characterizing the relationship of elastic displacements and rotational motions. For the material in question in quantitative terms it is not great. However, consideration of moment stress leads to qualitative changes. Namely, there is an additional wave front.
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