Strange dynamics of bilinear oscillator close to grazing

In this work strange behaviour of an impact oscillator with a one sided elastic constraint discovered experimentally [1, 2] is compared with the predictions obtained using its mathematical model. Particular attention is paid to the chaos recorded near grazing frequency when a non-impacting orbit becomes an impacting one under increasing excitation frequency. Extensive experimental investigations undertaken on the rig developed at the Aberdeen University [1, 3] reveal different bifurcation scenarios under varying excitation frequency near grazing which were recorded for a number of values of the excitation amplitude. It was found that the evolution of the attractor is governed by a complex interplay between smooth and non-smooth bifurcations. In some cases the occurrence of coexisting attractors is manifested through a discontinuous transition from one orbit to another through boundary crisis. One of those bifurcation scenarios is explained here based on numerical simulation.