Characteristic speeds and influences of cross-sectional warpings on high-speed beam-foundation structures

A railgun is a high-speed mechatronic system that is often modeled as an armature moving on a conductive elastic rail integrated with an elastic insulator. Three characteristic speeds (critical, shear, and bar speeds) play the key role in structural dynamics of such a beam-foundation structure, but their actual causes and physical implications have not clearly revealed in the literature. This paper proposes a generalized dynamic stiffness method for analysis, investigates the wave dynamics of beam-foundation systems, and provides detailed derivations, reasoning and numerical simulations to reveal the actual causes and physical implications of these characteristic speeds. A most-studied rail launcher is used in numerical simulations. We point out some errors in the literature about these speeds and reveal the important role of shear rotation in wave dynamics of beam-foundation structures. Moreover, two-dimensional sectional analysis is proposed and performed to reveal the influences of cross-sectional warpings on these characteristic speeds. Results show that cross-sectional warpings play important roles in dynamics of high-speed beam-foundation structures because they decrease the longitudinal wave speed and increase the torsional wave speed at high frequencies. Moreover, the elastic foundation causes each of the flexural wave and the torsional wave to have a critical speed.