CHAOTIC PHENOMENA IN THE DYNAMIC BUCKLING OF AN ELASTIC-PLASTIC COLUMN UNDER AN IMPACT

The present study is concerned with the dynamic anomalous response of an elastic-plastic column struck axially by a mass m with an initial v elocity upsilon(0). This simple example is considered in order to clar ify the influence of the impact characteristics and the material plast ic properties on the dynamic buckling phenomenon and particularly on t he final vibration amplitudes of the column when it shakes down to a w holly elastic behaviour. The material is assumed to have a linear stra in hardening with a plastic with a plastic reloading allowed. These ma terial properties are the reason a number of elastic-plastic cycles to be realized prior to any wholly elastic stable behaviour, which cause s different amounts of energy to be absorbed due to the plastic deform ations. The column exhibits two types of behaviour over the range of t he impact masses - a quasi-periodic and a chaotic response. The chaoti c behaviour is caused by the multiple equilibrium states of the column when any small changes in the loading parameters cause small changes in the plastic strains which result in large changes in the response b ehaviour. The two types of behaviour are represented by displacement-t ime and phase-plane diagrams. The sensitivity to the load parameters i s illustrated by the calculation of a Lyapunov-like exponent. Poincare maps are shown for three particular cases.