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Dynamics of a nearly symmetrical piecewise linear oscillator close to grazing incidence: Modelling and experimental verification

Abstract:

Experimental studies and mathematical modelling have been carried out for a nearly symmetrical piecewise linear oscillator to examine the bifurcation scenarios close to grazing. Higher period responses are found after grazing, although the period adding windows pbkp_redicted as a generic feature of one-sided impacting systems are not observed. It appears that the presence of the second high stiffness spring stabilises additional periodic orbits. The global solution for a piecewise smooth model is developed by stitching locally valid maps. For the symmetrical case the highest period of response is three, if asymmetry in the gap and/or stiffness is introduced then higher periodic orbits are observed. Only small asymmetries are required to achieve a good correspondence with experiments. Further examination shows that many attractors are not stable to even small changes in the symmetry of the system. © Springer Science+Business Media, Inc. 2006.