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研究生: 劉夙錡
Liu, Su-Chi
論文名稱: 考慮軸向負荷效應之浸水平台的動態分析
Dynamic Analysis of an Immersed tower with Effect of Axial Load Considered
指導教授: 吳重雄
Wu, Jong-Shyong
學位類別: 碩士
Master
系所名稱: 工學院 - 系統及船舶機電工程學系
Department of Systems and Naval Mechatronic Engineering
論文出版年: 2007
畢業學年度: 95
語文別: 中文
論文頁數: 68
中文關鍵詞: 浸水均勻樑軸向負荷位移函數特徵方程式自然頻率振態臨界挫曲負荷
外文關鍵詞: critical buckling loads, mode shapes, displacement functions, characteristic equation, natural frequencies, axial load, uniform immersed beam
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  • 本文之目的在探討一浸水均勻樑,於承受軸向壓縮(或拉張)負荷情況下的振動特性。為達上述目的,吾人先從一軸向負荷的均勻樑求得其浸水與露水兩部分的位移函數,接著,考慮該樑上端與具有偏心距及轉動慣量的集結質量有關的邊界條件、該樑下端與彈性支撐彈簧有關的邊界條件、以及該樑浸水與露水兩部分之位移在自由液面處的匹配條件,吾人可得整個振態系統的特徵方程式,此時,承受軸向負荷的浸水均勻樑之自然頻率與振態,便可由求解該程式而獲得。由於在上述的方程式推導過程中,吾人並沒有做任何有關於振態系統離散化的假設,故本文所得的結果是屬於正解。
    為了驗證本文理論及電算程式的可靠性,吾人以調整樑上端所附帶集中元素、以及樑的下端所安裝移動與旋轉彈簧勁度之大小的方式,來模擬一根兩端自由的(F-F)、一端栓住另一端自由的(P-F)或一端夾住另一端自由的(C-F)樑,然後,根據上述三種不同支撐情況均勻樑的臨界挫曲負荷及相關自然頻率,與現有文獻資料的一致性,來驗證本文理論及電算程式的可靠性。最後,軸向負荷、支撐彈簧勁度、以及樑的上端集結質量之偏心距與轉動慣量等因素的大小,對均勻浸水樑動態特性的影響,是本文探討的重點。

    The objective of this thesis is to investigate the vibration characteristics of a uniform immersed beam under axial load. To this end, the displacement functions of the immersed part and emerged part of the beam are determined from the equation of motion of the axial-loaded uniform beam. Next, the boundary conditions at the upper end relating to the tip lumped mass with eccentricity and rotary inertia, those at the lower end relating to the elastic support spring, and the matching conditions relating to the immersed and emerged parts of the beam at free water surface are imposed to the last two displacement functions to yield the characteristic equation for the entire vibrating system. From which the natural frequencies and mode shapes of the axial-loaded immersed beam are determined. Because no assumptions concerning discretization of the vibrating system are made for the formulations of problem, the solutions obtained in this thesis are the exact ones.
    In order to confirm the reliability of the theory presented and computer program developed for this thesis, the beam is modeled to an axial-loaded free-free (F-F) beam, pinned-free (P-F) beam or clamped-free (C-F) beam, by adjusting the magnitudes of the concentrated elements at its upper end and the stiffness of the translational and rotational springs at its lower end. Based on the good agreements between the critical buckling loads and the associated natural frequencies of the last F-F, P-F and C-F beams obtained from this thesis and the corresponding ones obtained from the existing literatures, the reliability of the theory and computer program for this thesis is confirmed. Finally, the influence of axial load, spring stiffness of the elastic support, and eccentricity and rotary inertia of the tip mass on the vibration characteristics of the immersed beam is studied.

    摘 要................................................ .I Abstract .............................................III 誌 謝..................................................V 目 錄................................................. VI 表 目 錄 ..............................................VIII 圖 目 錄.............................................. X 符 號 說 明........................................... XI 第一章 緒論........................................... 1 1.1研究動機........................................ 1 1.2文獻回顧........................................ 2 1.3研究方法.........................................8 第二章 浸水樑之自然頻率及振態..........................9 2.1基本假設........................................ 9 2-2浸水樑之自然頻率及振態.......................... 9 第三章 數值分析結果與討論............................. 19 3.1理論與電腦程式的可靠性........ ................. 20 3.2底端彈性支撐浸水樑之彈簧勁度(kT=kR)的影響....... 28 3.3頂端質量偏心距(eccentricity)的影響.............. 34 3.4浸水長度的影響.................................. 37 3.5頂端集結質量及轉動慣量的影響.................... 39 第四章 結論........................................... 43 參考文獻.............................................. 44 附錄A: F-F、C-F及P-F樑的頻率方程式.................... 49 附錄B:電腦程式使用說明................................ 60 自述.................................................. 68

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