博碩士論文 110323122 詳細資訊




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姓名 蔡定羽(Ting-Yu Tsai)  查詢紙本館藏   畢業系所 機械工程學系
論文名稱 以雙向耦合離散元素法與有限元素法模擬顆粒體在矩形板振動下產生的克拉尼圖與反克拉尼圖
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摘要(中) 板殼振動與克拉尼圖在近百年內已被科學家們大量研究與應用,然而在過去的研究
中模擬平板振動特性大多採用 FEM 方法,而對於克拉尼圖的探討大多採用物理實驗,
本研究第一次提出採用雙向耦合離散元素法(DEM)與有限元素法(FEM),模擬顆粒體在
彈性矩形板上的動態行為,探討顆粒體在不同無因次加速度(Γ)下的顆粒聚集情況,並與
對應實驗比較。研究中採用粒子面積佔有率、粒子平移速度、粒子旋轉速度、粒子擾動
速度及粒子溫度,進一步分析顆粒體在矩形板上運動時的內部物理行為。本研究也有考
慮各種不同參數對顆粒體聚集圖樣造成的影響,包括矩形板有無受重力效應影響、顆粒
楊氏係數及顆粒恢復係數。
本研究結果摘要如下:
(1)不考慮矩形板的重力效應,當無因次加速度(Γ)小於 1 時,顆粒體往腹點聚集,形成
反克拉尼圖,當無因次加速度(Γ)大於等於 1 時,顆粒體往節線聚集,形成克拉尼圖,
且在無因次加速度(Γ)甚大於 1 時,形成克拉尼圖所需時間大幅減少,Γ值越大,圖樣
形成時間越短。
(2)考慮矩形版的重力效應,矩形板受重力影響,易於產生預變形,使顆粒體滾向變形較
大位置,較難形成反克拉尼圖,但當無因次加速度(Γ)值超過某個筏值時,仍會形成克
拉尼圖。
(3)隨著無因次加速度(Γ)的增加,顆粒體平移速度增加速率較快,形成克拉尼圖的時間
較短。
(4)形成反克拉尼圖時,顆粒體會朝波腹滾動,形成克拉尼圖時,顆粒體會朝節線滾動。
(5)形成反克拉尼圖時,顆粒體間碰撞現象較微弱,形成克拉尼圖時,顆粒碰撞現象較劇
烈,且碰撞多集中於腹點,無因次加速度(Γ)越大,碰撞趨勢越劇烈。
關鍵字:克拉尼圖,反克拉尼圖,雙向耦合離散元素法與有限元素法,無因次加速
度,顆粒體內部物理性質
摘要(英) Vibration of plate structures and the phenomenon of clustering and inversion of Chladni
patterns have been extensively studied by scientists in the past century. However, prior
investigations predominantly employed the Finite Element Method (FEM) to simulate plate
vibration characteristics and relied on physical experiments for chladni patterns. This study
pioneers the application of a bidirectional coupled Discrete Element Method (DEM) and Finite
Element Method (FEM) to simulate the dynamic behavior of particles on an elastic rectangular
plate. The proposed coupled model was validated against corresponding experimental
observations. The aggregation behavior of particles was explored under various dimensionless
accelerations (Γ). Particle area fraction, particle translational velocity, particle rotational
velocity, particle perturbation velocity, and granular temperature are employed to further
analyze the internal physical behavior of particles on the rectangular plate. Various parameters
are considered in this study to understand their impact on the patterns of particle aggregation,
including the influence of gravity on the rectangular plate, particle Young′s modulus, and
particle restitution coefficient. The main findings are summarized below
(1) Disregarding the effect of gravity on the rectangular plate, when the dimensionless
acceleration (Γ) is less than 1, particles aggregate towards the nodal lines, forming an
inverse Chladni patterns. When Γ is greater than or equal to 1, particles aggregate towards
the anti-nodal line, forming a Chladni patterns. Moreover, as Γ significantly exceeds 1, the
time required to form a Chladni patterns substantially decreases. Larger values of Γ reduce
formation time for Chladni patterns.
(2) Considering the gravitational effect on the rectangular plate, its susceptibility to gravity
leads to pre-deformation, causing particles to roll towards areas with higher deformation,
and making it difficult to form an inverse Chladni patterns. However, when the
dimensionless acceleration (Γ) exceeds a certain threshold, a Chladni pattern still emerges.
iii
(3) As the dimensionless acceleration (Γ) increases, the rate of increase in particle translational
velocity is faster, resulting in a shorter formation time for the Chladni patterns.
(4) When forming the inverse Chladni patterns, particles roll towards the anti-nodal regions,
while when forming the Chladni patterns, particles roll towards the nodal regions.
(5) When forming the inverse Chladni patterns patterns, there is a weaker occurrence of particle
collisions, while during the formation of the Chladni pattern, particle collisions are more
intense, concentrated largely around the nodal points. Moreover, with larger values of the
dimensionless acceleration (Γ), the tendency for collisions becomes more pronounced.
Keywords: Chladni patterns, inverse Chladni patterns, bidirectional coupled DEM and FEM,
dimensionless acceleration, internal physical properties of particles
關鍵字(中) ★ 克拉尼圖
★ 反克拉尼圖
★ 雙向耦合離散元素法與有限元素法
★ 無因次加速 度
★ 顆粒體內部物理性質
關鍵字(英) ★ Chladni patterns
★ inverse Chladni patterns
★ bidirectional coupled DEM and FEM
★ dimensionless acceleration
★ internal physical properties of particles
論文目次 摘要.............................................................................................................................................i
Abstract ............................................................................................................................ii
附表目錄...........................................................................................................................vi
附圖目錄..........................................................................................................................vii
第一章 緒論...................................................................................................................... 1
1.1 文獻回顧................................................................................................................. 1
1.2 研究動機.................................................................................................................. 6
第二章 雙向耦合 DEM-FEM 方法................................................................................. 7
2.1 有限元素模型......................................................................................................... 7
2.2 離散元素模型......................................................................................................... 8
2.3 離散元素模型與有限元素模型間的雙向耦合交互作用................................... 11
第三章 數值模型驗證.................................................................................................... 13
3.1 離散元素模擬基準測試....................................................................................... 13
3.1.1 兩個材質相同顆粒的彈性法向碰撞............................................................ 13
3.1.2 顆粒與剛性平面的彈性法向碰撞................................................................ 14
3.1.3 不同恢復係數下的正向碰撞............................................................................ 14
3.1.4 顆粒與剛性平面的斜向碰撞............................................................................ 14
3.1.5 兩個材料相同顆粒的非彈性法向碰撞 ............................................................. 16
3.2 數值模型元素 C3D8、C3D8R 與 C3D8I 選擇與網格收斂 .............................. 16
3.3 鋼珠撞擊可撓性懸臂板問題之解析解與數值解比較....................................... 17
第四章 顆粒系統物理模型建置 .................................................................................... 43
4.1 雙向耦合 DEM-FEM 模擬配置........................................................................... 43
4.2 雙向耦合 DEM-FEM 模擬的臨界時間步........................................................... 44
4.3 FEM 振動模態分析.............................................................................................. 45
4.3.1 兩端固定薄板............................................................................................... 45
v
4.3.2 四邊自由薄板............................................................................................... 45
第五章 結果與討論 ........................................................................................................ 55
5.1 顆粒體在四邊自由薄板振動下圖樣模擬結果與實驗結果比較....................... 55
5.2 顆粒體在兩端固定薄板振動下內部物理性質的探討....................................... 56
5.2.1 粒子面積佔有率.......................................................................................... 57
5.2.2 粒子平移速度.............................................................................................. 58
5.2.3 粒子旋轉速度.............................................................................................. 60
5.2.4 粒子擾動速度.............................................................................................. 62
5.2.5 粒子溫度...................................................................................................... 65
5.3 顆粒性質參數分析.............................................................................................. 66
第六章 結論................................................................................................................... 123
參考文獻........................................................................................................................ 125
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指導教授 鍾雲吉 廖展誼(Yun-Chi Chung Chan-Yi Liao) 審核日期 2024-1-25
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