Deformation mechanism and defect sensitivity of notched free-free beam and cantilever beam under impact

This paper studies the dynamic behavior of pre-notched free-free beam and pre-notched cantilever beam subjected to step loading at a free end, as typical structures with defects. Special attention is paid to the deformation mechanism and the defect sensitivity in the plastic energy dissipation. By employing the rigid, perfectly plastic material idealization, complete solutions are obtained for combinations of the notch size, notch position and the magnitude of load. Apart from a one-hinge mode, two- and three-hinge modes are observed and analyzed. It is revealed that the first hinge, which is the one closest to the loading point, dissipates most of the input energy. If the first hinge forms at the notched section, the energy dissipation is highly sensitive to the notch; otherwise, it is insensitive. It is also noted that when the load increases, the defect sensitive region shrinks to a narrower region close to the loading point, indicating that under a large load, the notch may affect the energy dissipation remarkably, only if it is very close to the loading point. To reveal the interaction between the traveling hinges and the notched section, a pre-notched cantilever beam subjected to a rigid striker on its free end is analyzed. It is found that for a heavy striker, the stationary hinge either on the root or on the notched section dissipates most of energy and only when the notched section is sufficiently close to the impact point, the traveling hinge can move across the notch, indicating that the energy dissipation is insensitive to the notch. However, for a very light striker, the defect sensitivity is influenced by the traveling distance of the hinge and the deformation mechanism in the modal phase.