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研究生:黃士賓
研究生(外文):Shih-Pin Huang
論文名稱:基礎振動之廣義系統化集中參數模式及其等效電路模擬初探
論文名稱(外文):General Systematic Lumped-parameter Models for Foundation Vibration and Preliminary Study on Their Equivalent Electric Circuit Simulation
指導教授:吳文華
指導教授(外文):Wen-Hwa Wu
學位類別:碩士
校院名稱:國立雲林科技大學
系所名稱:營建工程系碩士班
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:64
中文關鍵詞:土壤結構互制等效電路多項式分式簡化基礎
外文關鍵詞:Foundation VibrationSSIEquivalent Electric Circuitpolynomial-fraction
相關次數:
  • 被引用被引用:3
  • 點閱點閱:108
  • 評分評分:
  • 下載下載:11
  • 收藏至我的研究室書目清單書目收藏:0
根據多項式分式的近似概念,本研究廣義應用不同的數學方法來探討將其分解以對應至集中參數模式的各種可能性,並藉由綜合整理不同的分解分法發展出各型系統化的集中參數模式,用以有效替代無限域土壤之動力行為。在利用特殊設計的兩個多項式之比值來近似正規化的基礎柔度函數,並解出此多項式之最佳化係數後,本研究首先從兩類數學分解方法出發。第一類乃是根據巢式除法歸納出三種不同的分解,並且定義出高次與低次兩型多項式分式間的轉換,從而對代表基礎動力勁度的原始多項式分式進行系統化的巢式分解。第二類分解則是利用部份分式展開的技巧將多項式分式化為許多實係數一階及二階分式之組合。這一類方法也可根據柔度高次型及勁度低次型兩種多項式分式的型態,分別對應出串聯與並聯兩種不同的物理配置。同時,經由巢式除法分解的探討,每一個分解完成的二階分式也可各自發展出三種不同的離散元素模式來對應。最後,統合上述兩類多項式分式分解,便可在任一回合分解運算都有四種分解模式可以選擇,從而系統化地建構出各型集中參數模式。此外,本研究另一個重點則希望能開拓利用等效電路來模擬系統化集中參數模式的方向。對照部份電子元件運作的數學方程式,可發現力學元件均能完全類比於電路系統。應用這個觀念,本研究發展出兩型電路系統來類比集中參數模式所代表的力學系統。經由電路模擬軟體Orcad PSpice A/D的快速分析,這部分的初步探討可以充分驗證以電路模擬來處理基礎振動問題的可行性與精確度。
Based on the approximation by polynomial-fraction, different mathematical methods are applied in this study to investigate its various possible decompositions. These decompositions are further categorized to develop various types of systematic lumped-parameter models for efficiently representing the dynamic behavior of unbounded soil. Following the concise formulation employing a ratio of two polynomials to represent the normalized dynamic flexibility function of foundation and then solving the optimal coefficients of the polynomials, this research starts with two mathematical decomposition methods. The first method deduces three different decompositions according to nested division and also defines the transformation between the high-order type and low-order type of polynomial-fraction. Subsequently, systematic nested decomposition can be performed on the original polynomial-fraction representing the normalized dynamic stiffness function. The second method is to decompose the polynomial-fraction into the summation of numerous first-order and second-order partial fractions with real coefficients via partial-fraction expansion. This method can be corresponded to an “in-series” type and another “in-parallel” type of physical arrangement based on the high-order type of polynomial-fraction in flexibility formulation and the low-order type of polynomial-fraction in stiffness formulation. Moreover, applying the nested division decomposition, each decomposed second-order partial fraction can also be corresponded to three different discrete-element models. Finally, with the combination of the above two types of polynomial-fraction decomposition, four alternative decomposition options can be obtained in each round of decomposition operation and various systematic lumped-parameter models can be consequently constructed. Furthermore, another major phase of this study is to explore the possibility of using equivalent electric circuits to simulate systematic lumped-parameter models. With the mathematical correspondence between certain electronic elements and mechanical elements, this research develops two types of electric circuit systems to simulate the dynamic system represented by a lumped-parameter model. Applying the electric circuit simulation software OrCAD PSpice A/D, this part of preliminary investigation sufficiently verifies the feasibility and accuracy in utilizing electric circuit simulations to study the foundation vibration problems.
目 錄

中文摘要 i
英文摘要 ii
誌謝 iv
目錄 ii
表目錄 vii
圖目錄 viii
第一章 緒論 1
1.1替代土壤之簡易模式 1
1.2系統化集中參數模式 2
1.3研究目的與本文架構 3
第二章 應用多項式分式近似基礎動力柔度函數 5
2.1基礎動力勁度函數與柔度函數 5
2.2靜力極限與高頻極限 6
2.3以多項式分式近似動力柔度函數 7
2.4參數之正規化 8
第三章 巢式除法分解 10
3.1一回合連續兩次前除運算 11
3.2一回合連續兩次後除運算 12
3.3一回合同時前後除運算 15
3.4巢式分解 17
第四章 部份分式分解 19
4.1高次型多項式分式之部份分式展開 19
4.2低次型多項式分式之部份分式展開 22
4.3綜合巢式除法與部份分式分解 26
第五章 等效電路模擬 28
5.1基本力學與電路元件 28
5.2力學與電路類比之串聯與並聯問題 29
5.3基本離散元素模式之電路模擬 30
5.4完整集中參數模式之電路模擬 31
第六章 結論 33
參考文獻 35
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