Numerical solutions of the exact equations for axisymmetric wave propagation are obtained with continuous and discontinuous loadings at the impact end of an elastic bar. The solution for a step change in stress agrees with experimental data near the end of the bar and exhibits a region that agrees with the one-dimensional strain approximation. The solution for an applied harmonic displacement closely approaches the Pochhammer-Chree solution at distances removed from the point of application. Reflections from free and rigid-lubricated ends are studied. The solutions after reflection are compared with the elementary one-dimensional stress approximation.

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