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    Neimark-Sacker Bifurcations Near Degenerate Grazing Point in a Two Degree-of-Freedom Impact Oscillator

    Source: Journal of Computational and Nonlinear Dynamics:;2018:;volume( 013 ):;issue: 011::page 111007
    Author:
    Yin, Shan
    ,
    Ji, Jinchen
    ,
    Deng, Shuning
    ,
    Wen, Guilin
    DOI: 10.1115/1.4041236
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: Saddle-node or period-doubling bifurcations of the near-grazing impact periodic motions have been extensively studied in the impact oscillators, but the near-grazing Neimark-Sacker bifurcations have not been discussed yet. For the first time, this paper uncovers the novel dynamic behavior of Neimark-Sacker bifurcations, which can appear in a small neighborhood of the degenerate grazing point in a two degree-of-freedom impact oscillator. The higher order discontinuity mapping technique is used to determine the degenerate grazing point. Then, shooting method is applied to obtain the one-parameter continuation of the elementary impact periodic motion near degenerate grazing point and the peculiar phenomena of Neimark-Sacker bifurcations are revealed consequently. A two-parameter continuation is presented to illustrate the relationship between the observed Neimark-Sacker bifurcations and degenerate grazing point. New features that differ from the reported situations in literature can be found. Finally, the observed Neimark-Sacker bifurcation is verified by checking the existence and stability conditions in line with the generic theory of Neimark-Sacker bifurcation. The unstable bifurcating quasi-periodic motion is numerically demonstrated on the Poincaré section.
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      Neimark-Sacker Bifurcations Near Degenerate Grazing Point in a Two Degree-of-Freedom Impact Oscillator

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    contributor authorYin, Shan
    contributor authorJi, Jinchen
    contributor authorDeng, Shuning
    contributor authorWen, Guilin
    date accessioned2019-02-28T11:12:13Z
    date available2019-02-28T11:12:13Z
    date copyright9/12/2018 12:00:00 AM
    date issued2018
    identifier issn1555-1415
    identifier othercnd_013_11_111007.pdf
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4253784
    description abstractSaddle-node or period-doubling bifurcations of the near-grazing impact periodic motions have been extensively studied in the impact oscillators, but the near-grazing Neimark-Sacker bifurcations have not been discussed yet. For the first time, this paper uncovers the novel dynamic behavior of Neimark-Sacker bifurcations, which can appear in a small neighborhood of the degenerate grazing point in a two degree-of-freedom impact oscillator. The higher order discontinuity mapping technique is used to determine the degenerate grazing point. Then, shooting method is applied to obtain the one-parameter continuation of the elementary impact periodic motion near degenerate grazing point and the peculiar phenomena of Neimark-Sacker bifurcations are revealed consequently. A two-parameter continuation is presented to illustrate the relationship between the observed Neimark-Sacker bifurcations and degenerate grazing point. New features that differ from the reported situations in literature can be found. Finally, the observed Neimark-Sacker bifurcation is verified by checking the existence and stability conditions in line with the generic theory of Neimark-Sacker bifurcation. The unstable bifurcating quasi-periodic motion is numerically demonstrated on the Poincaré section.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleNeimark-Sacker Bifurcations Near Degenerate Grazing Point in a Two Degree-of-Freedom Impact Oscillator
    typeJournal Paper
    journal volume13
    journal issue11
    journal titleJournal of Computational and Nonlinear Dynamics
    identifier doi10.1115/1.4041236
    journal fristpage111007
    journal lastpage111007-8
    treeJournal of Computational and Nonlinear Dynamics:;2018:;volume( 013 ):;issue: 011
    contenttypeFulltext
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