Transverse decay of solutions in an elastic cylinder

In a semi-infinite cylinder composed of anisotropic linearised elastic material, loaded on the base and clamped along the lateral surface, it is known that the solution as measured, for example, by the strain-energy flux through a plane cross-section decays longitudinally at most exponentially with respect to the axial distance from the base. There is, however, also a transverse radial decay of the solution, again measured for example by the strain-energy, occurring from the region close to the cylinder's axis to the region near the lateral surface, where the energy vanishes. This problem is considered in the present paper which discusses a circular semi-infinite cylinder and derives an estimate for the strain-energy contained in a cylindrical annulus at a given distance from the base and of variable height, and whose outer surface coincides with the lateral surface of the cylinder. It is shown that the strain-energy decays at most algebraically to zero as the inner radius of the annulus increases to that of the cylinder.