Author： Ing James Pavlovskaia Ekaterina Wiercigroch Marian
Publisher： Springer Publishing Company
ISSN： 0924-090X
Source： Nonlinear Dynamics, Vol.46, Iss.3, 2006-11, pp. : 225-238
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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 predicted 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.
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