Chaotic and asymmetrical beam response to impulsive load

Both symmetrical and asymmetrical final displacements are observed for elastic-plastic beams under symmetrical impulsive loading. A three-degree-of-freedom Shanley-type model is developed in this study, which is capable of revealing chaotic and asymmetrical responses of an elastic-plastic beam by introducing initial imperfections. To identify the asymmetrical displacement, the beam response is decomposed into three vibration modes. Corresponding modal participation factors are derived based on the displacement of the three-degree-of-freedom beam model. Phase plane trajectories, Poincaré maps and power spectral density diagrams are derived to illustrate both the symmetrical and asymmetrical chaotic vibrations. Numerical simulations using a general-purpose FE code LS-DYNA are carried out for an elastic-plastic beam subjected to impulsive load. The simulation results indicate that the elastic-plastic beam demonstrates chaotic and asymmetrical vibration when the applied impulsive load exceeds a critical value, which agrees with experimental observations.