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首页> 外文期刊>new journal of physics >Coupling between rotational and translational motions of a vibrated polygonal disk
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Coupling between rotational and translational motions of a vibrated polygonal disk

机译：振动多边形圆盘的旋转和平移运动之间的耦合

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摘要

We investigate experimentally the dynamics of a single polygonal disk (regular n-gon with 3 <= n <= 8) confined in a closed container under vertical vibrations against gravity. The disks tend to precess continuously upon vibrations, transferring mechanical energy into rotational and lateral translational degrees of freedom (DoF). An analysis of the velocity distribution functions in both DoF suggests that the mobility in both DoF are coupled with each other, exhibiting a characteristic angular velocity that depends on confinement and disk shape. The characteristic angular velocity can be captured with an analytical model considering sustainable precession due to continuous driving. Depending on confinement, translational and rotational kinetic energy fluctuations within one vibration cycle can be synchronized with each other and there exists a regime where injected energy is equally distributed in different DoF. Depending on n, the tendency for the disk to precess varies and there exists a regime (n <= 6) where persistent rotation of the disk rarely lasts longer than one vibration period. Our results suggest the possibility of tuning energy injection into different DoF in vibrated granular disk mono-layers via shape design and confinement.
机译：我们通过实验研究了单个多边形圆盘（规则 n-gon，3 <= n <= 8）在垂直振动下被限制在封闭容器中的动力学。圆盘倾向于在振动时连续前进，将机械能传递到旋转和横向平移自由度 （DoF）。对两个景深中速度分布函数的分析表明，两个自由度中的迁移率是相互耦合的，表现出取决于约束和圆盘形状的特征角速度。特征角速度可以通过考虑连续行驶导致的可持续进动的解析模型来捕获。根据约束的不同，一个振动周期内的平移和旋转动能波动可以相互同步，并且存在注入能量均匀分布在不同自由度中的状态。根据 n 的不同，圆盘的先动趋势会发生变化，并且存在一个状态 （n <= 6），其中圆盘的持续旋转很少持续超过一个振动周期。我们的研究结果表明，通过形状设计和约束，可以调整能量注入到振动颗粒盘单层中的不同自由度。

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