DYNAMICS OF A SIMPLE-MODEL FOR A WIND-LOADED NONLINEAR STRUCTURE - BIFURCATIONS OF CODIMENSION-ONE AND CODIMENSION-2

The motion induced by vortex shedding of a structure with nonlinear re storing force is investigated. In particular, a conclusion about nonex istence of bounded motions obtained for a similar problem in the previ ous study is improved by taking into account the nonlinear restoring f orce characteristic. The vortex shedding frequency is assumed to be cl ose to the natural frequency of the cross-wind oscillation and the alo ng-wind oscillation is not excited so that a single-degree-of-freedom model representing the cross-wind motions is obtained The averaging me thod is applied to the single-degree-of-freedom system, and the normal form and center manifold theories are used to discuss bifurcations of codimension one, saddle-node and Hopf bifurcations. Moreover, it is s hown that a multiple bifurcation of codimension two, called the Bogdan ov-Takens bifurcation, occurs in the averaged system. The implications of the averaging results on the dynamics of the original single-degre e-of-freedom system are described. Numerical examples are also given w ith numerical simulation results for both the averaged and original sy stems to demonstrate our theoretical predictions.