Perturbation methods for the impact problem of a nonlinear elastic string (Q1321889)

The standard normal impact problem for a nonlinear elastic string can essentially be solved analytically, on the assumption that the boundary conditions are constant, i.e. the impact velocity is sufficiently high so that it can be considered constant over the time span considered. If variable boundary conditions occur, as in the case when the elastic restoring force is included, this is no longer so. We propose here perturbation procedures to examine the problem in this case assuming that the deformations are small but finite.