PERTURBATION-METHODS FOR THE IMPACT PROBLEM OF A NONLINEAR ELASTIC STRING

The standard normal impact problem for a non-linear elastic string can essentially be solved analytically, on the assumption that the bounda ry conditions are constant, i.e. the impact velocity is sufficiently h igh so that it can be considered constant over the time span considere d. If variable boundary conditions occur, as in the case when the elas tic 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. The solutions obtained are compared with direct numerical methods and good agreement obtained, t hus providing a check on the numerical methods before proceeding to th e full finite deformation problem.