Investigation of dynamic Saint-Venant's principle in a cylindrical waveguide – Analytical results

• Exact solutions of the end effects have been derived.
• Stress wave form is not significantly different after a distance from the end.
• The length of the affected zone is approximately 2.2 times bar radius.
• The analytical results agree well with the experimental and numerical observations.
• The study validates the dynamic Saint-Venant's principle.

An analytical approach has been carried out to analyze the wave propagation in the cylindrical waveguide which was hit by four impactors with different head shapes. The Pochhammer–Chree solution, including evanescent wave modes, was applied to describe the stress field in the vicinity of the proximal end of the waveguide. Two strategies were used to derive the Pochhammer–Chree equation convergent at the vicinity of the loaded end, i.e., 1) Fast Fourier Transformation of the loading boundary condition, and 2) derivation of complex wave-numbers for the evanescent modes. The length of the affected zone, which confirms a dynamic Saint-Venant's principle (DSVP), was about 2.2 times of radius based on the analytical results, which coincide with the experimental and numerical results. Parametric study has also been conducted with respect to different frequency ranges of the pulse wave.