Release-type radial wall motion in a hollow rod–lumped mass system: A three-mode theory for axial impact

To address the dynamic response of hollow rods under axial impact, this study establishes a 3-mode model, incorporating axial displacement, overall radial motion of the rod wall, and thickness distortion, by introducing a radial-gradient-independent term into the Mindlin-Herrmann theory. The wave propagation of the hollow rod-lumped mass system under complex boundary conditions is solved using the Laplace transform. By calibrating the shear correction factor κ based on the circumferentially integrated signed radial reaction at the impact end, the proposed model achieves high accuracy in transient response prediction in impact. Through theoretical and numerical analyses, κ depends strongly on the rod wall thickness/outer radius ratio and the Poisson’s ratio. Besides, the radial boundary effects are localized near the impact end, leaving the remaining part weakly affected. The lateral inertia of the hollow rod can be decoupled into overall wall inertia and local thickness distortion inertia, dominating the double-peak characteristics and the dispersion effect of the strain waveform, respectively. Finally, the whole hollow rod-lumped mass system is studied. An increased lumped mass inertia amplifies the post-wave strain and introduces a delayed strain peak.