以多體動力學與離散元素法雙向耦合模擬探討具阻尼顆粒機構的能量損失機制

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翁健紘(Chien-Hung Weng) 查詢紙本館藏

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機械工程學系

論文名稱

以多體動力學與離散元素法雙向耦合模擬探討具阻尼顆粒機構的能量損失機制

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至系統瀏覽論文 (2027-1-5以後開放)

摘要(中)

本研究採用採用多體動力學(Multi-body dynamics, MBD)與離散元素法(Discrete element method, DEM)雙向耦合模擬具阻尼顆粒箱體彈簧系統的自由振動行為與減振效果，透過七個基準測試與三個具阻尼顆粒不同中空體積箱體的實驗結果驗證數值模型的正確性，進一步探討顆粒間摩擦係數、牆壁摩擦係數、顆粒間恢復係數、牆壁恢復係數與顆粒剪力模數等參數對箱體減振效益的影響，並分析顆粒體與箱體在振動過程中的能量變化與能量損失的機制。研究結果顯示：(1) 顆粒體總能量為箱體對顆粒體的作功量、摩擦機制的作功量與碰撞機制的作功量之和，箱體損失能量為顆粒體對箱體作功量、線性滑軌摩擦損失能量與系統阻尼損失能量之和，且箱體對顆粒體的作功量等於顆粒體對箱體的作功量，前者為正功，後者為負功；(2) 顆粒體對箱體的作功量是在振動初期顆粒體與箱體接觸而作負功，接著顆粒體與箱體發生多次正面碰撞損失能量；(3) 改變顆粒體參數性質的情況下，箱體的位置與能量變化差異甚小，且顆粒體摩擦損失能量與顆粒體碰撞損失能量變化的趨勢相反；(4) 顆粒體摩擦損失能量隨著顆粒間摩擦係數與顆粒剪力模數的增加而減少，隨著牆壁摩擦係數的增加而增加；(5) 顆粒體碰撞損失能量隨著顆粒間與牆壁恢復係數的增加而減少。

摘要(英)

The purpose of this study is to investigate the damping effect of a mass-spring-damper-slider system with a particle damper by coupled Multi-body dynamics (MBD) and Discrete element method (DEM). Seven numerical benchmark tests and free vibration experiments for a mass-spring-damper-slider system with a particle damper were adopted to validate the proposed coupled MBD–DEM model. Subsequently, the validated coupled MBD–DEM model was used to further investigate the effects of the friction coefficient, restitution coefficient, and shear modulus of particles on the suppression of box vibration, and further analyze the energy dissipation of the particles and the box during the vibration process. The main findings are highlighted below: (1) The particles system energy is the sum of the work done by the box, the energy loss from friction, and the energy loss from collision. The energy loss of the box consists of the work done by the particles, the energy loss from the slider, and the energy loss from the damper. The work done by the box to the particles is equal to the work done by the particles to the box. The former is positive work, whereas the latter is negative work; (2) The work done by the particles to the box is induced by the contacts between the particles and the box at the initial stage of vibration, and then by multiple frontal collisions between them; (3) The effects of the particle properties have little influence on the dynamic characteristics of the box. The energy loss from friction has an opposite trend with that from collision; (4) The energy loss from friction decreases with the increase of the inter-bead friction coefficient and shear modulus of particles, but increases with the wall friction coefficient; (5) The energy loss from collision decreases with the increase of the inter-bead and wall restitution coefficients.

關鍵字(中)

★ 阻尼顆粒
★ 多體動力學
★ 離散元素法
★ 雙向耦合
★ 能量損失機制
★ 顆粒參數分析

關鍵字(英)

★ Particle damper
★ Multi-body dynamics
★ Discrete element method
★ Two-way coupling
★ Mechanism of energy dissipation
★ Parametric analysis of particle properties

論文目次

摘要 i
Abstract ii
目錄 iii
附表目錄 vi
附圖目錄 vii
第一章緒論 1
1-1 研究背景 1
1-2 文獻回顧 1
1-2-1 顆粒阻尼器應用相關文獻 1
1-2-2 顆粒阻尼器性質相關文獻 2
1-2-3 MBD-DEM雙向耦合模擬相關文獻 5
1-3 研究動機與目的 7
1-4 研究架構 7
第二章研究方法 9
2-1 物理模型 9
2-2 數學模型 10
2-3 離散元素法 11
2-3-1 離散元素法之架構 12
2-3-2 三維剛體運動方程式 12
2-3-3 接觸力模型 14
2-3-4 臨界時間步 15
2-4 離散元素電腦模擬 16
2-4-1 模型建模 16
2-4-2 模擬輸入參數 16
2-4-3 顆粒體自然沉積 16
2-4-4 多體動力學與離散元素法雙向耦合模型 17
2-5 Runge-Kutta數值解法 18
2-6 能量計算 18
2-6-1 動能 18
2-6-2 位能 19
2-6-3 摩擦損失能量 20
2-6-4 顆粒間碰撞損失能量 21
2-6-5 箱體系統阻尼損失能量 21
2-6-6 箱體對顆粒體的作功量及顆粒體對箱體的作功量 22
2-6-7 總能量 22
第三章結果與討論 24
3-1 Runge-Kutta模型基準測試 24
3-1-1 基準測試Ⅰ 24
3-1-2 基準測試Ⅱ 25
3-1-3 基準測試Ⅲ 26
3-1-4 基準測試Ⅳ 26
3-2 能量基準測試 27
3-2-1 基準測試Ⅰ 28
3-2-2 基準測試Ⅱ 29
3-2-3 基準測試Ⅲ 30
3-3 模擬與實驗驗證 31
3-3-1 1/4箱體 31
3-3-2 1/8箱體 33
3-3-3 1/16箱體 35
3-4 顆粒體參數的影響 38
3-4-1 顆粒間摩擦係數 39
3-4-2 顆粒與牆壁間摩擦係數 41
3-4-3 顆粒間恢復係數 43
3-4-4 顆粒與牆壁間恢復係數 45
3-4-5 顆粒剪力模數 46
第四章結論 49
參考文獻 51
附表 56
附圖 58

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指導教授

鍾雲吉(Yun-Chi Chung)

審核日期

2021-12-30

推文