Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/1618
DC FieldValueLanguage
dc.contributor.advisor林仕亭zh_TW
dc.contributor.advisorShih-Tin Linen_US
dc.contributor.author王文志zh_TW
dc.contributor.authorWang, Wen-Chihen_US
dc.date2000zh_TW
dc.date.accessioned2014-06-05T11:41:15Z-
dc.date.available2014-06-05T11:41:15Z-
dc.identifier.urihttp://hdl.handle.net/11455/1618-
dc.description.abstract本文的目的在解決受拘束(constraint)條件下,多體(multibody)機械系統數值積分的穩定性問題。多體系統之運動方程式是一個包含外力、拘束力、加速度的混合微分、代數方程式(mixed differential-algebraic equations,簡稱DAE)。在使用數值積分法解開微分方程式同時,其位置及速度必須滿足拘束運動方程式及速度運動方程式外尚有能量拘束方程式需被滿足,也就是說積分的變數是相關的。然而一般的數值積分法並不考慮其中的相關性,直接求解而造成數值的偏差。 為了解決此問題,Baumgarte提出拘束穩定方法(constraint stabil-ization method),使得數值積分獲得正確的解。不過此方法唯一的缺點在於係數的選擇,並無規則可循。本文將利用數位控制理論中的系統穩定分析,提供不同數值積分法在使用拘束穩定法時係數的選擇。zh_TW
dc.description.abstractThe objective of this thesis is to resolve the stability problem for the numerical integration of constrained multibody mechanical systems. The dynamic equations of motion of the constrained multibody mechanical system is a mixed differential-algebraic equation(DAE) which contains external forces, constraint reaction forces as well as acceleration of the generalized coordinates of the system. In applying numerical integration methods to solve the mixed differential- algebraic equation, the constraint equation and its first and second derivatives and energy constraint must be satisfied. That is, the generalized coordinates are dependent. Direct integration methods do not consider this dependency and constraint violation occurs. This problem was seemingly resolved by Baumgarte's Constraint Violation Stabilization Method. But this solution had some ambiguity in selecting the feedback parameters. In this thesis, the digital stability theory for integration formulas is applied to determine the stability region of the stabilized constraint equations.en_US
dc.description.tableofcontents目錄 中文摘要 I 英文摘要 II 目錄 III 圖目錄 VI 表目錄 VIII 第一章 緒論 1 1.1 前言 1 1.2 文獻回顧 3 1.3 論文大綱 5 第二章 運動方程式與數值積分法 6 2.1 多體機械系統拘束方程式簡介 6 2.1.1 運動拘束方程式簡介 6 2.1.2 能量拘束方程式簡介 8 2.2 DAE方程式的求解 10 2.2.1 直接積分法 10 2.2.2 廣義座標分隔法 11 2.2.3 拘束穩定法 13 2.2.4 混合法 15 2.3 數值積分法之介紹 16 2.3.1 Adams-Bashforth, Adams-Moulton, Predictor-Corrector數值積分法 16 2.3.2 Backward Differentiation Formulae數值積分法 19 2.3.3 Hybrid 數值積分法 21 2.3.4 Runge-Kutta數值積分法 22 第三章 系統穩定區域分析 24 3.1 離散系統之穩定度分析 24 3.2 假積分的應用 25 3.2.1 Adams-Bashforth積分法 27 3.2.2 Adams-Moulton積分法 28 3.2.3 Runge-Kutta積分法 29 3.3 Adams-Bashforth數值積分法 30 3.4 Adams Predictor-Corrector數值積分法 39 3.4.1 一階predictor配合二階corrector 39 3.4.2 二階predictor配合三階corrector 41 3.4.3 三階predictor配合四階corrector 44 3.5 Backward differentiation數值積分法 52 3.5.1 一階BDF 52 3.5.2 二階BDF 54 3.5.3 三階BDF 55 3.5.4 四階BDF 55 3.6 Runge-Kutta數值積分法 57 第四章 實例模擬與驗證 62 4.1 曲柄滑塊之實例 62 4.2 Adams-Bashforth法 65 4.3 Predictor-Corrector法 68 4.4 Runge-Kutta法 72 4.5 Hybrid法之實例模擬 75 第五章 結論與未來展望 110 參考文獻 112zh_TW
dc.language.isoen_USzh_TW
dc.publisher機械工程學系zh_TW
dc.subjectEnergy constrainten_US
dc.subject能量拘束方程zh_TW
dc.subjectMultibody Mechanical Systemsen_US
dc.subjectNumerical Integrationen_US
dc.subjectDifferential -algebraic equationen_US
dc.subject多體機械系統zh_TW
dc.subject數值積分zh_TW
dc.subject微分代數方程zh_TW
dc.title具能量拘束方程之多體機械系統使用數值積分穩定法時參數選擇之研究zh_TW
dc.titleParameters Selection of the Constraint Stabilization Method for Numerical Integration of Multibody Mechanical Systems with Energy Constrainten_US
dc.typeThesis and Dissertationzh_TW
item.openairetypeThesis and Dissertation-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.grantfulltextnone-
item.fulltextno fulltext-
item.cerifentitytypePublications-
item.languageiso639-1en_US-
Appears in Collections:機械工程學系所
Show simple item record
 

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.