Stress wave propagation in a rectangular bar

Abstract

The process of propagation of nonstationary waves in a rectangular bar is studied from the viewpoint of three-dimensional elasticity. The motion arises owing to the action of normal impact forces applied at the end face of a half-infinite bar all of whose four lateral surfaces are force-free. Precisely these one-type conditions complicate the solution of this problem. The already known solutions were obtained under the assumption that conditions of mixed type are partially or completely posed on the lateral sides, and precisely this fact permits separating the boundary values of distinct waves on these surfaces. In the absence of this simplifying factor, it is rather problematic to construct a solution satisfying all free lateral conditions.

In the paper, the solutions in integral transforms are guessed for a constant distribution of the impact load and then analytic solutions are constructed at the initial stages of the process.