Effect of the stiffness and inertia of a rib reinforcement on localized bending waves in semi-infinite strips

This paper reports an analytical and numerical study of localized bending waves in a thin elastic isotropic semi-infinite strip with a rib reinforment. Such waves can be considered as spatially non-uniform bending perturbations localized near free edges, similar to Rayleigh waves decaying exponentially with the distance. From the analysis of localized bending waves in thin elastic structures it may be possible to infer the presence of imperfections, cracks or inclusions, in the structure. In this study, a semi-infinite strip, simply supported on two edges and reinforced on the free one, is considered. A general solution is presented and the conditions under which localized bending waves exist are derived. The mathematical model, accompanied by numerical simulations, reveals that the presence of a reinforcement rib can suppress localized bending waves. This effect is mainly due to the stiffness coming from the rib, rather than from its added inertia terms.