Elastic impact of Rayleigh–Love bar on half space

The elastic impact of a bar on a half-space, accounting for the lateral inertia effect of the bar, is investigated theoretically in this study. An analytical model is developed by coupling a quasi-static contact model with the Rayleigh–Love (RL) equation. The RL model can be degenerated to obtain the classic 1D model based on the classic 1D wave equation and bar impacting a rigid flat. Based on the RL model and the classical 1D model, three key dimensionless parameters and one governing dimensionless parameter are proposed, respectively. The effects of the three dimensionless parameters under the RL model on the lateral inertia effects during bar impact are investigated, and the evolution of contact force and contact duration with the governing dimensionless parameter within the framework of the classic 1D model is examined. Finally, based on the difference between the contact duration and the length of the corresponding perfect square-wave pulse, a quantitative equivalence criterion is provided for when the half-space can be treated as a rigid body.