PERIODIC MOTIONS AND BIFURCATIONS OF A SMALL VIBRO-IMPACT PILE DRIVER

Dynamics of a small vibro-impact pile driver is represented using three-dimensional mapping,which is of piecewise property and singularities.Existence and stability of period-n single-impact motions of the pile driver are analyzed by theoretical and numerical methods,and the characteristic of period-n single-impact motions is described.The singularity of the Poincaré mapping,caused by the grazing contact of driver and pile,is considered.The influence of singularities on global bifurcations and transitions to chaos is elucidated.These transitions are not regular bifurcations but arise from piecewise property and singularity of the impact mapping.Transitions of two kinds of period-n single-impact motions and routes to chaos are analyzed by numerical simulation.