# 臺灣博碩士論文加值系統

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 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 11.1替代土壤之簡易模式 11.2系統化集中參數模式 21.3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 52.1基礎動力勁度函數與柔度函數 52.2靜力極限與高頻極限 62.3以多項式分式近似動力柔度函數 72.4參數之正規化 8第三章 巢式除法分解 103.1一回合連續兩次前除運算 113.2一回合連續兩次後除運算 123.3一回合同時前後除運算 153.4巢式分解 17第四章 部份分式分解 194.1高次型多項式分式之部份分式展開 194.2低次型多項式分式之部份分式展開 224.3綜合巢式除法與部份分式分解 26第五章 等效電路模擬 285.1基本力學與電路元件 285.2力學與電路類比之串聯與並聯問題 295.3基本離散元素模式之電路模擬 305.4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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Barros, F.C.P., Luco, J.E., 1990, “Discrete models for vertical vibrations of surface and embedded foundations,” Earthquake Engineering and Structural Dynamics, Vol.19, pp.289-303.24.Jean, W.Y., et al., 1990, “System parameters of soil foundations for time domain dynamic analysis,” Earthquake Engineering and Structural Dynamics, Vol.19, pp.541-553.25.Paronesso, A., and Wolf, J.P., 1995 “Global lumped-parameter model with physical representation for unbounded medium,” Earthquake Engineering and Structural Dynamics, Vol.24, pp.637-654.26.Wolf, J.P., 1997, “Spring-dashpot-mass models for foundation vibrations,” Earthquake Engineering and Structural Dynamics, Vol.26, pp.931-949.27.Wolf, J.P., 1991, “Consistent lumped-parameter models for unbounded soil: physical representation,” Earthquake Engineering and Structural Dynamics, Vol.20, pp.11-32.28.Wolf, J.P., 1991, “Consistent lumped-parameter models for unbounded soil: frequency-independent stiffness, damping and mass matrices,” Earthquake Engineering and Structural Dynamics, Vol.20, pp.33-41.29.Wu, W.H., and Chen, C.Y., 2001, “Simple lumped-parameter models of foundation using mass-spring-dashpot oscillators,” Journal of the Chinese Institute of Engineers, Vol., 24, pp. 681-697.30.Wu, W.H., and Chen, C.Y., “Simplified soil-structure interaction analysis using efficient lumped-parameter models for soil,” Soils and Foudations, Vol. 42, pp. 41-52, 2002..31.Wu, W.H., and Lee, W.H., 2002, “Systematic lumped-parameter models for foundations based on polynomial-fraction approximation,” Earthquake Engineering and Structural Dynamics, Vol.31, pp.1383-1412, 2002.32.Wu, W.H., and Lee, W.H., “Nested lumped-parameter models for foundation vibrations,” Earthquake Engineering and Structural Dynamics, Vol.33, pp.1873-1902, 2004.33.曾文昌，以多項式分式簡化基礎振動所對應之各型系統化集中參數模式及其在地震分析之應用，國立雲林科技大學，碩士論文，2002。34.Konagai, K. and Nogami, T., “Analog Circuit to Simulate Dynamic Soil-structure Interaction in Shake Table Test,” Soil Dynamics & Earthquake Engineering, Vol. 17, pp. 279-287, 1998.35.Konagai, K., et al., “Real Time Control of Shaking Table for Soil-structure Interaction Simulation,” Structural Engineering /Earthquake Engineering, JSCE, Vol. 16, pp. 45-54, 1999.36.OrCAD PSpice A/D V9.2電路分析軟體，美國Cadence公司，台灣代理商映陽科技股份有限公司。
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 1 以多項式分式簡化基礎振動所對應之各型系統化集中參數模式及其在地震分析之應用 2 利用系統化集中參數模式替代基礎振動之等效電路模擬與實驗 3 同時考慮水平和翻轉向振動及其耦合效應之簡易土壤集中參數模式 4 完整土壤─結構互制系統之等效電路模擬與實驗

 1 33. 蔡益超、洪振銘 (1980)，「台北市鋼筋混凝土高樓動力特性測析及應用」，科學發展月刊，第八卷，第十二期。

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