One Approach to the Plane Problem on Impact of Timoshenko-Type Shells on Elastic Half-Space

Abstract

The article presents an attempt to solve the plane problem on the impact of an elastic Timoshenko shell on an elastic half-space using the method of reducing problems of dynamics to the solution of a Volterra's infinite system of integral equations (ISIE) of the second kind. It is shown that such an approach is not acceptable. When discretizing the reduced Volterra's ISIE of the second kind, a poorly defined system of linear algebraic equations is obtained: as the reduction order increases, the determinant of such a system tends to infinity. This circumstance shows the limitations of this approach.