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首页> 外文会议>International Conference on Mechanical Engineering and Mechanics vol.1; 20051026-28; Nanjing(CN) >Periodic Motions and Bifurcations of a Vibrating Impact System
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Periodic Motions and Bifurcations of a Vibrating Impact System

机译：振动冲击系统的周期性运动和分叉

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摘要

An inertial shaker is considered. Dynamics of the shaker is studied with special attention to periodic-impact stability and bifurcations. Dynamics of the shaker are analyzed by use of a mapping derived from the equations of motion. Each iterate of the mapping corresponds to the vibro-bench colliding with the cast each other once. The mapping is four dimensional in elastic impact case, three dimensional in inelastic impact case. The mapping, in inelastic impact case, is of piecewise property due to synchronous and non-synchronous motion of shaker and cast immediately after the impact, and singularities caused by the grazing contact motions of shaker and cast, so the inertial shaker exhibits two types of single-impact periodic motions. The influence of the piecewise property and singularities on global bifurcations and transitions to chaos is elucidated by numerical analyses. The single-impact periodic motion usually undergoes period doubling bifurcation with decrease in the forcing frequency. However, the period doubling cascades of the motion are discontinuous. Grazing contact of shaker and cast are likely to be a major cause of the discontinuous cascades of period doubling.
机译：考虑使用惯性振动筛。研究振动器的动力学时要特别注意周期性冲击的稳定性和分叉。通过使用从运动方程得出的映射来分析振动器的动力学。映射的每个迭代对应于振动台与铸模彼此碰撞一次。映射在弹性冲击情况下为三维，在非弹性冲击情况下为三维。在非弹性碰撞情况下，映射是分段的，这是由于振动器和撞击后立即进行铸造的同步和非同步运动，以及由振动器和铸造的掠入接触运动引起的奇异性，因此惯性振动器表现出两种类型的单次冲击的周期性运动。数值分析阐明了分段性质和奇异性对整体分叉和过渡到混沌的影响。单冲击周期性运动通常会经历周期加倍的分叉，而强迫频率会降低。但是，运动的周期倍增级联是不连续的。振动筛和铸件的掠食接触可能是周期加倍的不连续级联的主要原因。

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