Grazing impact oscillations

An impact oscillator is a periodically driven system that hits a wall when its amplitude exceeds a critical value. We study impact oscillations where collisions with the wall are with near-zero velocity (grazing impacts). A c haracteristic feature of grazing impact dynamics is a geometrically converg ing series of transitions from a nonimpacting period-1 orbit to period-M or bits that impact once per period with M=1.2,.... In an experiment we explor e the dynamics in the vicinity of these period-adding transitions. The expe riment is a mechanical impact oscillator with a precisely controlled drivin g strength. Although the excitation of many high-order harmonics in the exp eriment appeared unavoidable, we characterize it with only three parameters . Despite the simplicity of this description, good agreement with numerical simulations of an impacting harmonic oscillator was found. Grazing impact dynamics can be described by mappings that have a square-root singularity. We evaluate several mappings, both for instantaneous impacts and for impact s that involve soft collisions with a yielding wall. As the square-root sin gularity appears persistent in the reduction of the dynamics to mappings, a nd because impact dynamics appears insensitive to experimental nonidealitie s, the characteristic bifurcation scenario should be observed in a wide cla ss of experimental systems.