Wave motion in a thick cylindrical rod undergoing longitudinal impact

• Longitudinal impact of thick elastic rods solved without the Skalak’s decomposition.
• Von Schmidt waves are crucial for stress peaks at the rod axis and its vicinity.
• The first longitudinal mode is sufficient to detect the wavefront of Rayleigh wave.
• For long times the 1D theory approximates 3D solution near the place of impact.
• Presented results give a deeper insight into the wave processes induced by impact.

The paper presents a new formulation and the comprehensive analytical solution to longitudinal impact of thick elastic rods. In contrast to previously published works, the solution is derived based on the exact three-dimensional theory without using the classic Skalak’s decomposition. This new direct approach makes the analytical solution more transparent and much easier to obtain. The resulting formulas for basic mechanical quantities are derived using the residue theorem and their evaluation is made in such a way that the accuracy of presented results is significantly higher than those previously published. Based on these results, the transient wave phenomena occurring in the rods are discussed in detail. Additionally, the solution in time domain is obtained also by semi-analytical approach making use of numerical inverse Laplace transform. It is shown that the selected FFT based algorithm is accurate and robust enough, such that the analysis of wave motion in spatial and time domain can be done effectively preserving the results precision. Presented solution can be used as a benchmark for verification of numerical and experimental methods applied to elastodynamics problems.