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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
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dc.contributor.advisor | 劉進賢(Chin-Hsien Liu) | |
dc.contributor.author | Huan-Cheng Hsu | en |
dc.contributor.author | 許桓誠 | zh_TW |
dc.date.accessioned | 2021-05-13T08:36:57Z | - |
dc.date.available | 2016-08-24 | |
dc.date.available | 2021-05-13T08:36:57Z | - |
dc.date.copyright | 2016-08-24 | |
dc.date.issued | 2016 | |
dc.date.submitted | 2016-08-03 | |
dc.identifier.citation | [1] Al-Khatib MJ, Grysa K, Maciag A (2008) The method of solving polynomials in the beam vibration problems. Journal of Theoretical and Applied Mechanics, 46(2),(347–366).
[2] Barcilon V (1986). Inverse eigenvalue problems.In G. Talenti (Ed.), Inverse problems. Lecture Notes in Mathematics, 1225 (1–51). [3] Cannon JR, Duchateau P (1998). Structural identification of an unknown source term in a heat equation. Inverse Problems, 14, (535–551). [4] Chang J-D, Guo B-Z (2007). Identification of variable spatial coefficients for a beam equation from boundary measurements. Automatica, 43, (732–737). [5] Ciałkowski MJ, Fr¸ackowiak A, Grysa K (2007) Solution of a stationary inverse heat conduction problems by means of Trefftz non-continuous method. International Journal of Heat and Mass Transfer, 50,(2170–2181). [6] Ciałkowski MJ, Futakiewicz S, Ho˙zejowski L (1999) Heat polynomials applied to direct and inverse heat conduction problems. Proceedings of the international symposium on trends in continuum physics, (79–88). [7] Gladwell GML (1986). The inverse problem for the Euler-Bernoulli beam. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 407(1832), (199-218). [8] Guo B-Z (2002). On boundary control of a hybrid system with variable coefficients. Journal of Optimization Theory and Applications, 114(2), (373–395). [9] Hasanov, A. (2009). Identification of an unknown source term in a vibrating cantilevered beam from final overdetermination. Inverse Problems, 25. [10] Hasanov A, Baysal O (2015). Identification of an unknown spatial load distribution in a vibrating cantilevered beam from final overdetermination. Journal of Inverse and Ill-posed Problems, 23(1), (85–102). [11] Hodges DH, Rutkowski MJ (1981). Free-Vibration Analysis of Rotating Beams by a Variable-Order Finite-Element Method. American Institute of Aeronautics and Astronautics, 19(11), (1459-1466). [12] Hurlebaus S, Gaul L (2006). Uniqueness in the identification of asynchronous sources and damage in vibrating beams. Inverse Problems, 30. [13] Krstic M, Smyshlyaev A (2008). Boundary Control of PDEs: A Course on Backstepping Designs. Philadelphia: SIAM. [14] Krstic M, Guo B-Z, Balogh A, Smyshlyaev A (2008). Control of a tip-force destabilized shear beam by observer-based boundary feedback. SIAM Journal on Control and Optimization, 47, (553–574). [15] Kuo C-L, Chang J-R, Liu C-S (2013). The modified polynomial expansion methodfor solving the inverse heat source problems. Numerical Heat Transfer, Part B: Fundamentals, 63, (357–370). [16] Lagnese JE (1991). Recent progress in exact boundary controllability and uniform stabilizability of thin beams and plates. Lecture Notes in Pure and Applied Mathematics, 128, (61–111). [17] Lesnic L, Elliott L, Ingham DB (1999). Analysis of coefficient identification problems associated to the inverse Euler-Bernoulli beam theory. IMA Journal of Applied Mathematics, 62, (101–116). [18] Lesnic L, Hasanov A (2008). Determination of the leading coefficient in fourth-order SturmLiouville operator from boundary measurements. Inverse Problems in Science and Engineering, 16(4), (413–424). [19] Liu C-S, Atluri SN (2008). A novel time integration method for solving a large system of non-linear algebraic equations. Computer Modeling in Engineering and Sciences, 31(2), (71-83). [20] Liu C-S (2009). A two-stage LGSM to identify time-dependent heat source through an internal measurement of temperature. International Journal of Heat and Mass Transfer, 52, (1635–1642). [21] Liu C-S (2012). A Lie-group adaptive differential quadrature method to identify unknown force in an Euler–Bernoulli beam equation. Acta Mech, 223, (2207–2223). [22] Liu C-S (2015). A BIEM using the Trefftz test functions for solving the inverse Cauchy and source recovery problems. Engineering Analysis with Boundary Elements, 62, (177–185). [23] McLaughlin JR (1984). On constructing solutions to an inverse Euler-Bernoulli problem, Inverse Problems of Acoustic and Elastic Waves. Philadelphia: SIAM. [24] Nicaise S, Zair O (2004). Determination of point sources in vibrating beams by boundary measurements: identifiability, stability, and reconstruction results. Electronic Journal of Differential Equations, 20, (1–17). [25] Wang X, Bert C-W (1993). A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates. Journal of Sound and Vibration, 162, (566–572). [26] Yang L, Dehghan M, Yu J-N, Luo G-W (2011). Inverse problem of time-dependent heat sources numerical reconstruction. Mathematics and Computers in Simulation, 81, (1656–1672). [27] Zheng D-Y, Cheung Y-K, Au FTK, Cheng Y-S (1998). Vibration of multi-span non-uniform beams under moving loads by using modified beam vibration functions. Journal of Sound and Vibration, 212(3), (455-467). | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/3802 | - |
dc.description.abstract | 在梁的分析模型中,通常使用尤拉-伯努力梁方程理論,在正算尤拉梁問題其解決方法則不計其數。然而當問題的待求項變為系統參數之一時,其複雜度則非一般正算問題可比擬。本論文介紹了解決非齊性的尤拉梁方程反問題的一種數值方法,其目的為在梁上找回其外力(源識別問題)。本篇論文將邊界積分方程方法應用至尤拉梁上,以其振態作為伴隨測試函數,再以我們假設的試解帶入積分方程,以數值方法解此代數方程組,即可得到外力源之數值解。在論文中將以數值算例實際求解尤拉梁的反問題,其中包含四種不同邊界條件的梁以及使用傅立葉級數與振型函數兩種試解之基底,並分析其數值結果。 | zh_TW |
dc.description.abstract | Euler-Bernoulli beam theory is a typical beam theory when discussing the behavior of beams. There are several methods to obtain the behaviors of the Euler-Bernoulli beam under an external force, but without knowing the external force, the problem becomes an inverse source problem which is the subject of this thesis. Different from the direct problems, the inverse problems are considered more ill-posed. In this thesis, the boundary integral equations method will be adopted to solve the Euler-Bernoulli beam problem, with its mode shape as an adjoint test function. Then, we assume the trail solution of the integral equation. Finally, we can obtain the numerical solution of the external force. Six examples of Euler beam are used to test the performance of the present method. | en |
dc.description.provenance | Made available in DSpace on 2021-05-13T08:36:57Z (GMT). No. of bitstreams: 1 ntu-105-R03521208-1.pdf: 3029649 bytes, checksum: 45cc56c2f6a9f0ef81496785eef5ed4c (MD5) Previous issue date: 2016 | en |
dc.description.tableofcontents | 口試委員審定書 i
誌謝 ii 摘要 iv ABSTRACT v 目錄 vi 表目錄 viii 圖目錄 ix 第一章 緒論 1 1.1 前言 1 1.2 文獻回顧 2 1.3 研究動機與目的 3 1.4 論文架構 3 第二章 理論基礎 5 2.1 自我伴隨運算子(Self-Adjoint Operator) 5 2.2 Trefftz方法(Trefftz Method) 6 2.3 廣義格林第二定理(General Green's Second Identity) 6 2.4 尤拉法(Euler Method) 8 2.5 辛普森法(Simpson’s Rule) 9 2.6 龍格-庫塔法(Runge-Kutta Method) 11 2.7 高斯-克朗羅德法(Gauss–Kronrod Quadrature Formula) 12 2.8 擬時間積分法(Fictitious Time Integration Method) 15 2.9 共軛梯度法(Conjugate Gradient Method) 16 2.10 傅立葉級數(Fourier Series) 19 第三章 尤拉梁的邊界積分方程 21 3.1 反問題 21 3.2 尤拉梁的邊界積分方程推導 21 3.3 簡支梁分析 24 3.4 懸臂梁分析 26 3.5 兩端固定梁分析 28 3.6 一端固定與一端簡支梁 30 第四章 數值算例 34 4.1 數值算例一 34 4.2 數值算例二 36 4.3 數值算例三 38 4.4 數值算例四 39 4.5 數值算例五 40 4.6 數值算例六 43 第五章 結論與未來工作 63 參考文獻 66 | |
dc.language.iso | zh-TW | |
dc.title | 以邊界積分方程方法求解尤拉梁的反算外力問題 | zh_TW |
dc.title | By Using Boundary Integral Equation Method to Solve the Inverse Problems of Forces of Euler-Bernoulli Beams | en |
dc.type | Thesis | |
dc.date.schoolyear | 104-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 張致文(Chih-Wen Chang),郭仲倫(Chung-Lun Kuo) | |
dc.subject.keyword | 尤拉梁,邊界積分方程方法,反問題,源識別問題,格林第二定理, | zh_TW |
dc.subject.keyword | Euler-Bernoulli beam,Boundary integral equations method,Inverse problem,Source identification problem, | en |
dc.relation.page | 68 | |
dc.identifier.doi | 10.6342/NTU201601667 | |
dc.rights.note | 同意授權(全球公開) | |
dc.date.accepted | 2016-08-04 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 土木工程學研究所 | zh_TW |
顯示於系所單位: | 土木工程學系 |
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