Dynamic asymmetrical instability of elastic–plastic beams

Dynamic instability of elastic–plastic beam is investigated by employing a three-degree-of-freedom (3-DoF) beam model. Especially, asymmetrical instability induced by symmetrical load is discussed. The asymmetrical instability is considered as a second-order buckling mode. Four types of perturbations, i.e., geometrical misalignment, material property mismatch, unsymmetry of applied load and disturbance of boundary conditions, are introduced to activate the asymmetrical responses. The asymmetrical response is characterized by a modal participation factor α₂ which corresponds to an asymmetrical mode shape. Phase plane trajectories and Poincaré map are used to illustrate the chaotic characteristics of the beam response. Results show that if the perturbations are small enough, the perturbation type has negligible influence on the critical load for the occurrence of the asymmetrical instability, which implies that the asymmetrical instability is an intrinsic feature of the beam system. However, with the increase of the magnitude of the perturbations, the influence of the asymmetrical vibration is expanded to a large extension of loading parameter.