THE PROBLEM OF AN ELASTIC-PLASTIC BEAM DYNAMICS AND AN INCOMPLETE CODIMENSION 2 BIFURCATION

In this paper, a continuous fourth-order ordinary differential equatio n Shanley-type model is suggested for analytical analysis of the probl em of elastic-plastic beam dynamics. A codimension three bifurcation p roblem and its simplified case, an incomplete co-dimension two bifurca tion pf a pair of pure imaginary eigenvalues and a simple zero eigenva lue are presented and analyzed, and the normal form analysis and the u nfoldings of 2-jet and 4-jet cases of the incomplete normal forms are provided. Since elastic-plastic beam dynamics are of great non-linear complexity and the vector fields are multiple degeneracies, small diff erences of physical parameters cause dramatic essential changes of beh avior of the motion. Through these results the rich dynamical behavior s of the elastic-plastic beam dynamics, including the counterintuitive behavior and its sensitivity to small parameters of this problem, can be illustrated. Copyright (C) 1996 Elsevier Science Ltd.