An analytical model to predict the impact response of one-dimensional structures

Abstract

An analytical solution method is presented for the transient axial response of one-dimensional structures subjected to impact loading. The transient structural response is expressed as a series of the impact loading function and its progressive shifting values depending on both material position and time scale. The governing differential equation on the impact force is derived considering the general solution and constitutive equation of the contact interface. The analytical solution of differential equation yields a recursive function describing the impact force and displacement function of the total geometry. Depending on the contact surface roughness and the material properties, an impact function is introduced as a base function for impact response. The procedure is implemented to determine the shock waves generated at the collision of the elastic rod on the rigid surface and two elastic rods. The analytical solution also derives the steady-state response of the structure after the impact loading.