Wave Propagation in a Stress-Relaxing Bar

An analysis of shock-induced wave propagation in a circular bar of stress-relaxing material is presented. The bar is subjected to a Motionless, elastic restraint to radial motion on the radial boundary. This boundary condition corresponds to an experimental configuration recently used to study the dynamic response of granular material confined in a thin, articulated shell. A solution is obtained by approximating the displacement components by early terms of Jacobi polynomials in the radial coordinate, resulting in equations that depend only on the axial coordinate and time. Final results are compared with a previous strictly one-dimensional analysis and with experimental results. The effects of radial motion are found to be relatively small because of the restraint produced by the radial boundary conditions.