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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 | 陳振山(Jen-San Chen) | |
dc.contributor.author | Hsing-Ying Chen | en |
dc.contributor.author | 陳星穎 | zh_TW |
dc.date.accessioned | 2021-06-16T05:14:40Z | - |
dc.date.available | 2020-08-04 | |
dc.date.copyright | 2020-08-04 | |
dc.date.issued | 2020 | |
dc.date.submitted | 2020-07-29 | |
dc.identifier.citation | Achenbach, J.D., Sun, C.T., 1965. Moving load on a flexibly supported Timoshenko beam. International Journal of Solids and Structures 1, 353-370. Ansari, M., Esmailzadeh, E., Younesian,D., 2010. Internal-external resonance of beams on non-linear viscoelastic foundation traversed by moving load. Nonlinear Dynamics 61, 163–182 Bogacz, R., 1983. On dynamics and stability of continuous systems subject to a distributed moving load. Ingenieur Archiv 53, 243-255. Chonan, S., 1975. The elastically supported Timoshenko beam subjected to an axial force and a moving load. International Journal of Mechanical Sciences 17, 573-581. Den Hartog, J.P., 1952. Advanced Strength of Materials. Dover publication, New York. Denisov, G.G., Kugusheva, E.K., Novikov, V.V., 1985. On the problem of the stability of one-dimensional unbounded elastic systems. Journal of Applied Mathematics and Mechanics 49, 533-537. Duffy, D.G., 1990. The response of an infinite railroad track to a moving, vibrating mass. Journal of Applied Mathematics and Mechanics 57, 66-73. Froio, D., Moioli, R., Rizzi, E, 2016. Numerical dynamic analysis of beams on nonlinear elastic foundations under harmonic moving load. VII European Congress on Computational Methods in Applied Sciences and Engineering, Crete Island, Greece, 5–10. Jaiswal, O.R., Iyengar, 1993. Dynamic response of a beam on elastic foundation of finite depth under a moving point force. Acta Mechanica 96, 67-83. von Kármán, T., 1910. Festigkeitsprobleme im Maschinenbau. Encyklopädie der Mathematischen Wissenschaften IV, 311–385 Kenney, J.T., Jr., 1954. Steady-state vibrations of beam on elastic foundation for moving load. ASME Journal of Applied Mechanics, 21, 359-364. Kerr, A.D., 1972. The continuously supported rail subjected to an axial force and a moving load. International Journal of Mechanical Sciences 14, 71-78. Kononov, A.V., de Borst, R., 2002. Instability analysis of vibrations of a uniformly moving mass in one and two-dimensional elastic systems. European Journal of Mechanics A/Solids 2, 151–165 Mallik, A.K., Chandra, S., Singh, A.B., 2006. Steady-state response of an elastically supported infinite beam to a moving load. Journal of Sound and Vibration 291, 1148–1169. Metrikine, A.V., Dieterman, H.A., 1997. Instability of vibrations of a mass moving uniformly along an axially compressed beam on a viscoelastic foundation. Journal of Sound and Vibration 201, 567-576. Newland, D.E., 1970. Instability of an elastically supported beam under a travelling inertia load. Journal of Mechanical Science 12, 373-374. Steele, C.R., 1967a. The finite beam with a moving load. Journal of Applied Mechanics 111-118. Steele, C.R., 1967b. Nonlinear effects in problem of the beam on a foundation with a moving load. International Journal of Solids and Structures 3, 565-585. Timoshenko, S., 1926. Method of analysis of statical and dynamical stress in rail. Proceedings of the Second International Congress for Applied Mechanics, Zurich, 422-435 Younesian, D., Saadatnia, Z., Askari, H., 2012. Analytical solutions for free oscillations of beams on nonlinear elastic foundation using the variational iteration method. Journal of Theoretical and Applied Mechanics 50, 639-652. Zhang, Y., 2020. Steady state response of an infinite beam on a viscoelastic foundation with moving distributed mass and load. Science China: Physics, Mechanics Astronomy 63, 284611 | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/56073 | - |
dc.description.abstract | 隨著科技進步,軌道運輸的速度逐漸提升,而在高速移動後的軌道力學問題,可被模擬成質量於受彈性支撐無限長樑上移動之力學問題。其中動態反應所影響的真正幾何效應是我們深感興趣的,特別是在線性不穩定之臨界移動速度後的單點質量效應我們更加想探討。我們將無限長樑有效地取某一長度,並替換成有限長樑,並用和諧級數以及離散化的技巧使用在偏微分上,這個方法與解析解對比是驗證可行的。藉由特徵值技巧,我們可以找到線性不穩定之臨界速度後對於的指定質量,也就是說質量與速度將會影響線性穩定性。當移動速度超過線性不穩定之臨界速度時,以觀察者跟著施力點移動之移動座標觀看的話,非線性之動態反應會呈現穩定的週期運動,而穩定週期運動後的振幅與非線性參數成反比,也就是說非線性效應小時週期振幅會較大,非線性效應大時週期振幅會較小。這個結果與線性預測的沒有穩定振動是相反的。在週期運動中,樑上的每個點的相都是不同的,施力點會在週期振動的最大高度與最小高度中來回振動。在能量探討中,總能量包含了動能與位能,而能量會在週期運動中呈現週期變化,這些能量變化與水平施力做功抵消基底阻尼功後相同。 | zh_TW |
dc.description.abstract | We investigate the effect of the nonlinear terms arising from exact geometry on the dynamic response of the mass-beam-foundation system. In particular, we are interested in the case when the moving speed of the point mass exceeds the so-called critical speed. We replace the infinitely long beam with a sufficiently long finite beam and use a harmonic expansion method to discretize the partial differential equations of motion. The feasibility of this technique is verified by comparing our results with existing analytical solutions. By solving the eigenvalues of the linear problem, one can find the critical speed for a specified mass. When the moving speed of the mass is greater than the critical speed, the dynamic response eventually settles to a steady state of periodic motion as seen by an observer travelling along with the mass. This is contrary to the unbounded vibration predicted by the linear theory. During the periodic vibration, the phase of every point on the beam is different from each other. As a result, the location of maximum amplitude of vibration moves back and forth near the loading point. The total energy of the mass-beam-foundation, which includes all the kinetic and potential energy, fluctuates with time during the periodic vibration. The fluctuation of the total energy is balanced by the energy input from the horizontal pushing force and the energy dissipated by the damping in the foundation. The amplitude of the periodic vibration decreases as the geometric nonlinearity parameter increases. | en |
dc.description.provenance | Made available in DSpace on 2021-06-16T05:14:40Z (GMT). No. of bitstreams: 1 U0001-2807202010155500.pdf: 2821061 bytes, checksum: 814564f7f1e6a1a2d1e066c98ad51987 (MD5) Previous issue date: 2020 | en |
dc.description.tableofcontents | 目錄 摘要 i 英文摘要 ii 目錄 iii 圖目錄 v 表目錄 vi 有因次之符號表 vi 第一章 導論 1 第二章 統御方程式 3 2.1 空間固定座標系 3 2.2 無因次化 6 2.3 移動座標系 7 第三章 離散化 10 3.1 和諧級數展開 10 3.2 收斂測試 13 3.2.1 集中力線性靜態變形 13 3.2.2 穩定臨界以及臨界質量 14 第四章 非線性集中力分析 16 第五章 質量慣性動態分析 19 第六章 能量探討 24 第七章 結論 28 參考文獻 30 附錄目錄 33 附錄一 統御方程式推導 34 附錄二 集中力在彈性支撐長樑上移動時之靜態解 41 附錄三 Galerkin Method離散化過程 44 附錄四 Gamma推導 48 附錄五 線性不穩定之臨界速度與質量 54 附錄六 打靶法(Shooting Method) 58 附錄七 Newmark Method 60 附錄八 能量無因次推導 68 附錄九 Steele1967比較 74 | |
dc.language.iso | zh-TW | |
dc.title | 質量於受彈性支撐無限長樑上移動時樑的動態反應-幾何非線性效應 | zh_TW |
dc.title | Effects of geometric nonlinearity on the response of a long beam on viscoelastic foundation and under moving mass | en |
dc.type | Thesis | |
dc.date.schoolyear | 108-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 莊嘉揚(Jia-Yang Juang),劉建豪(Chien-Hao Liu) | |
dc.subject.keyword | 質量點在彈性基底之樑上等速移動,集中力在彈性基底之樑上等速移動, | zh_TW |
dc.subject.keyword | mass-beam-foundation,force-beam-foundation, | en |
dc.relation.page | 74 | |
dc.identifier.doi | 10.6342/NTU202001946 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2020-07-29 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 機械工程學研究所 | zh_TW |
顯示於系所單位: | 機械工程學系 |
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