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Double impact orbits of periodically forced impact oscillators. (English) Zbl 0885.70019

The authors treat periodic motions with double impacts against a rigid constraint of a periodically forced single-degree-of-freedom oscillator. The forcing is a combination of the first and second harmonics of a Fourier series. The main goal is to show that, by constructing a proper mapping, under certain conditions concerning the forcing frequency and the eigenfrequency of the oscillator, solutions can be found in analytic form which can be used for a bifurcation analysis. The authors show that under a quasistatic variation of the forcing frequency three mechanisms of bifurcations occur, namely saddle node, period doubling and grazing bifurcations where for the latter an intervening impact of zero velocity occurs. The grazing bifurcation analysis requires global estimates of the flow. Some results are also checked by numerical simulations.
Reviewer: H.Troger (Wien)

MSC:

70K40 Forced motions for nonlinear problems in mechanics
70F35 Collision of rigid or pseudo-rigid bodies
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