Stability of periodic motions in an inclined impact pair
School of Mathematics and Statistics, Shandong Normal University, Ji’nan 250014, P.R. China
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Received in final form: 9 February 2019
Published online: 30 July 2019
Using the theory of the discontinuous dynamical systems, the dynamics of an inclined impact oscillator on the platform driven by periodic displacement excitation are investigated in this paper. To investigate periodic motions with simple impact sequences, four basic impact mappings are defined, and the mapping models of possible periodic motions without stick are developed. And then by the discrete mapping theory, the period-n periodic motions induced by period-doubling bifurcations are investigated analytically. The existence conditions of periodic motions with 2n alternate impacts on two sides and periodic motions with n impacts only on one side are obtained. By eigenvalue analyses the stability conditions of periodic motions with only impacts on one side are studied, the regions for stability, saddle-node bifurcation and period doubling bifurcation for periodic motion with one impact are developed in parameter space. Finally the numerical simulations of such periodic motion are given to demonstrate the analytical results. The stability conditions of periodic motions with impacts on two sides are being investigated in the inclined impact pair.
© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2019