SYMBOLICAL IMPACT ANALYSIS FOR A FALLING CONICAL ROD AGAINST THE RIGID GROUND

Longitudinal impact analysis for slender rods has fascinated many famous scientists for hundreds of years. For a rod with uniform cross-sectional area along its length, analytical results about the longitudinal wave propagation of the rod impacting a rigid wall or impacted by a rigid body are well known. However, for a rod with variable cross-sectional area, there exist only a few analytical results in the literature. Since the study of conical rods has recently attracted some interest in various fields, the impact analysis for a conical rod falling against the rigid ground is discussed in this paper in detail and some symbolical results computed by computer algebra are presented. These analytical results are exact and may be used to validate the numerical programs using the finite element method or the boundary element method, too. It is also shown that in contrast to rigid-body collision theory, the geometrical shape of rods plays an important role in impact dynamic.