EXTENDED ENERGY APPROACH TO CHAOTIC ELASTIC PLASTIC RESPONSE TO IMPULSIVE LOADING

The paper supplements and extends an energy approach which helps to interpret elastic-plastic dynamic responses of a two-degree-of-freedom beam model whose ends are fixed, so that shallow arch action prevails, and chaotic as well as quasi-periodic vibrations may occur. For a problem of short pulse loading, a characteristic diagram is derived in which the energies at the stationary points (equilibria) of the elastic strain energy function V(w1, w2) are plotted against the pulse force, taken as the single loading parameter of the problem. Here w1, w2 are the displacements, and the function V contains the set of plastic strains as parameters, generated during the response. An alternative viewpoint is also introduced in which the plastic strains and the total available energy are regarded as specified parameters, and the problem is one of elastic response to arbitrary initial values of displacements and velocities.