Dynamics of the archetypal piecewise linear oscillator close to grazing

A linear oscillator undergoing impact with a secondary support is studied numerically. Smooth as well as nonsmooth bifurcations are observed. The bifurcations are explained with help from simulations based on mapping solutions between locally smooth subspaces. The obtained results are verified by comparison with previous experimental studies. Experimental stability analysis is also presented, justifying the normal form maps used to show the response close to grazing for systems with and without prestress of the secondary spring. The high degree of correspondence lends support to the modelling approach, as does the close match between experiments and simulations.