https://scholars.lib.ntu.edu.tw/handle/123456789/80911
標題: | 整合連體力學與熱動力學之變分原理(1/3) | 作者: | 鮑亦興 | 關鍵字: | 連體力學;熱動力學;虛功率原理;特權座標;追蹤控制;Continuum Mechanics;Thermodynamics;Principle of Virtual Power;Privileged Coordinates;Tracking Control | 公開日期: | 31-七月-2004 | 出版社: | 臺北市:國立臺灣大學應用力學研究所 | 摘要: | 在處理各類物體,如質點、剛體、或變形體受有約束的力學問題時, 變分原理常能提供一適當的解決途徑。本計畫之主要課題,乃在已建 立的基礎上,繼續探討虛功率原理(Principle of Virtual Power)的可 能應用與推廣,以及是否可將該原理與熱力學定律整合成統一熱與力之 變分原理。經過近一年的研究,我們在確定速度及速梯度(velocity and velocity gradient) 為力學基本變數, 溫度或商(temperature or entropy)及熱通率(heat flux)為熱力學基本變數後,確可統合熱力學 與連體力學,完成統一虛功率原理,並據以導得變分方程,從而推出 連體動量平衡及角動量平衡原理(Cauchy’s laws of linear and angular momentum) 及新導出之連體變分組成率(variational constitutive law)。在選取適當的內能函數(internal energy)與耗散 函數(dissipating function)後,即可推出彈性固體、黏性流體之組成 律及熱力學組成律Fourier Law 及 Maxwell-Catteneo Equation。詳細 討論請參考本報告第一部份。此外,在追蹤控制方面,我們將系統座標 分成特權座標與非特權座標兩類,雖然各有其設計軌跡,但我們採取雙 迴圈控制策略,即先控制特權座標到其軌跡,再依特權座標與非特權座 標關係,調整特權座標設計軌跡,使得非特權座標亦能趨近於設計軌 跡。我們將此策略運用於三輪自走車的軌跡追蹤控制上,效果良好,請參考本報告第二部份。 In dealing with the mechanics of material bodies modeled by particles, rigid body, or deformable body subject to various types of constraint, variational principles can usually provide a suitable path to obtain the solutions. The main objective of this project is to seek additional applications and possible extensions on the basis of the Principle of Virtual Power, and to explore whether the proposed principle can be unified with the law of thermodynamics to form a unified variational principle. After nearly one-year term of endeavor, we are able to obtain the desired Principle by choosing the velocity and the velocity gradient as fundamental variables in mechanics, and the entropy and the hear flux as the fundamental quantities in theomodynamics. The Principle indeed unify the theory of thermodynamics and continuum mechanics, from which a variational equation can be established. The Cauchy’s laws of linear and angular momentum and the newly developed variational constitutive law are then deduced. By selecting appropriate internal energy function and dissipating function, we could derive the constitutive equations for elastic body or viscous fluid in mechanics, and Fourier law and Maxwell-Catteneo Equation, which are treated as the constitutive equation in thermodynamics. See Part I of this report for more detailed. On the other hand, to perform tracking control, we divide the system coordinates into two sets: privileged coordinates and non-privileged coordinates. While all the coordinates have their desired trajectory, two control loops are designed. The inner loop drives the privileged coordinates to their desired value. The relations between privileged coordinates and non-privileged coordinates are then used to change the desired values of privileged coordinates so that the non-privileged ones can be tracked. We apply the strategy to the trajectory tracking control of a three-wheeled vehicle and the performance is quite well. The results are shown in Part II of this report. |
URI: | http://ntur.lib.ntu.edu.tw//handle/246246/21710 | 其他識別: | 922212E002066 | Rights: | 國立臺灣大學應用力學研究所 |
顯示於: | 應用力學研究所 |
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922212E002066.pdf | 211.92 kB | Adobe PDF | 檢視/開啟 |
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