Nonstationary Displacements in an Axisymmetric Problem for an Elastic Half-Space Under Mixed Boundary Conditions*

The strain state of an elastic half-space under a non-stationary normal load acting on its boundary is determined. A mixed boundary-value problem is stated. Its the solution is found using Laplace and Hankel integral transforms. The exact inversion of transforms is performed. As a result, an analytical solution that determines the normal displacement at any point in the half-space at any time is obtained. Specific numerical calculations are given for displacement on the axis of symmetry of the problem when loads are homogeneous and inhomogeneous.