Existence and stability of the grazing periodic trajectory in a two-degree-of-freedom vibro-impact system |
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Authors: | Jieqiong Xu Qunhong LiNan Wang |
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Institution: | a The Department of Dynamics and Control, Beijing University of Aeronautics and Astronautics, Beijing 100091, China b College of Mathematics and Information Science, Guangxi University, Nanning 530004, China |
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Abstract: | This paper investigates the existence and stability of the grazing periodic trajectory in a two-degree-of-freedom vibro-impact system. The criterion for existence of grazing period-n motion is presented. A local analysis based on the discontinuity-mapping approach is employed to derive a normal form Poincaré mapping near the grazing trajectory. Based on the above approach, a condition of stability can be formulated, such that a grazing trajectory will be discontinuous if the condition is unfulfilled. The predicted grazing bifurcations are in agreement with the numerical results. In particular, comparison of the grazing bifurcation diagrams of the normal form Poincaré mapping and the simulation diagrams of the original differential equation illustrates the validity of the discontinuity-mapping approach. |
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Keywords: | Grazing bifurcations Discontinuity-mapping approach Local analysis Stability Existence |
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