短顆粒鍊在振動系統下的狀態研究

Abstract

我們研究短珠鍊在振動系統下的狀態隨振動強度的改變，發現珠鍊的狀態會反應在珠鍊的形狀上，因此在此論文中主要探討珠鍊的形狀來描述其不同的運動型態。我們將金屬製顆粒鍊放置在準二維(quasi-2D)的通道中，由側邊觀察珠鍊隨底板振動的運動。定性上看到在25Hz的振動條件之下，對適當長度範圍(N=5~8)之內的珠鍊都可以觀察到行為轉變(transition)的發生。隨著振動強度的增加，珠鍊的運動型態從整條珠鍊都平上平下逐漸趨向於不穩定而產生彎曲。 我們進行長時間的統計分析，藉由運動型態的平均持續時間以及比例分佈隨振動強度Г的變化來量化珠鍊狀態的轉變，以N=8的珠鍊為例，其行為轉變發生在Г≈1.65左右。我們也發現當珠鍊長度縮短時，會在比較低的振動強度就發生行為轉變。我們進一步發現，珠鍊甚至在固定的振動強度之下也會自發性地在不同狀態間轉變。因此藉由追蹤每一顆金屬珠隨底板振動的運動，以微觀分析的方式試著理解珠鍊狀態發生轉變的機制。同時我們以理論預測質點在簡諧振動底板上的自由拋體行為，並和實驗結果進行比較，初步地推測行為轉變發生的原因。而珠鍊的狀態除了反應在形狀上之外，也會表現在水平方向的運動特性，我們也試著找出珠鍊的形狀和水平運動之間的關聯性，並且有一些初步的討論。

We study experimentally the dynamics of a short granular chain under vibration, and find that the shape of chain can reflect the state of chain. In this master thesis, we use the shape of chain to define different motion modes. We confine the chain in a quasi-2D vertical channel and observe the shape of chain under vibration with side view. At the condition of 25Hz, we see qualitatively the chain (N=5~8) undergoes transitions from a uniform response (flat) to unstable behavior (with bending) as the vibrational strengths increase. With long time experiment and statistical analysis, we quantify the transition by how the mean duration and fraction of each motion mode change with vibration strength. Using N=8 as an example, the transition occurs about Г≈1.65. We also find that, the transition occurs at lower value of vibration strength when N decreases. In addition, the unexcited and excited states exhibit bistability and switch spontaneously even at a fixed value of vibration strength. Therefore, we track the motion of each bead, and use these analyses to understand the reason why the chain can switch its states spontaneously. Also, we make theoretical predictions on the parabolic flight of a particle over a substrate with sinusoidal vibration, and compare predictions with experiments to preliminarily explain the values of the vibration strength for transitions. In addition, we find that each state of chain has its characteristics of displacement and try to find the correlation between the shape of chain and the movement.