A study on type II structures. Part I:: a modified one-dimensional mass–spring model

Most impact energy-absorbing structures can be classified into one of two types in terms of the shape of the overall quasi-static load–displacement curve in the early stages of deformation. Type I has a relatively “flat-topped” curve, while type II has an initial peak load followed by a “steeply falling” curve. The previous work showed that the deformation of type II specimens is much more sensitive to the impact velocity than that of type I specimens. That is, when the total kinetic energy remains the same for all specimens, smaller final deformations result from higher impact velocities; and this phenomenon is much more significant for type II specimens than for type I specimens. In order to explain this characteristic of type II structures, a one-dimensional mass–spring model with variable mass is proposed for a typical type II structure (i.e., a pair of pre-bent plates), and used to examine the effects of the lateral inertia of the structure under impact. Unlike conventional mass–spring models, our system contains an equivalent variable mass, which is a function of the rotational angle at plastic hinges and comes into effect during the second phase of the dynamic response. Predictions of this analytical model agree very well with an ABAQUS FE simulation of the dynamic response of the pre-bent plates to impact; and this verifies the validity of the mass–spring model proposed.