Symbolic computation of longitudinal impact waves Original Research Article

Wave propagation due to longitudinal impacts on thin rods is a classical problem of mechanics, but only few completely analytical results for longitudinal wave propagation are available in literature. In this paper, it is shown that even such complicated impact problems can nowadays be solved using symbolic computation. As an example, the wave propagation in a thin rod struck by a moving rigid body is discussed and analytical results describing the longitudinal wave propagation are given in detail so that these results may be used to validate some numerical programs for contact and impact analysis using the finite element methods or the boundary element methods, respectively. Further, from the obtained analytical results the duration of contact and the coefficient of restitution can be computed much more easily. Some numerical results for these important quantities in impact analysis are also listed.