The dynamic collapse of a column impacting a rigid surface

Abstract

An analytical investigation has been made of the dynamic collapse of an elastic periodically supported column having an attached mass at one end and impacting a rigid surface at the other end with prescribed velocity and angle of incidence. The investigation has been carried out using a first-order approximate nonlinear solution and a nonlinear finite element solution. The first-order approximate solution has led to the determination of four basic nondimensional parameters which govern the response. These parameters include mass, impact velocity, initial imperfection, and impact angle parameters. Three regions of these parameters have been identified in which the character of the column's response is markedly different. These regions have been designated as the linear, transition, and dynamic collapse regions. Threshold values of the parameters which separate these regions have been defined. Results obtained reveal that responses in the linear region are dominated by axial motion, those in the transition region exhibit some axial-flexural coupling, and those in the collapse region are dominated by flexure. The rebound velocity in the transition and dynamic collapse regions is shown to be less than that predicted by the linear dynamic solution. The dynamic peak axial compressive load in the transition region is shown to be the same as that predicted by the linear dynamic solution. In the collapse region, the peak load decreases to a value less than the linear dynamic value, but greater than the static Euler buckling load. Moreover, it is shown that whereas the peak axial compressive load predicted by the linear solution grows unbounded with increasing values of the mass parameter, an ultimate dynamic load value is approached in the collapse region.