臺灣博碩士論文加值系統

摘 要
就一攜帶任意個數之集中元素(concentrated elements)(如固定集結質量、彈性懸吊集結質量、線性彈簧、螺旋彈簧或彈簧-阻尼器-質量系統等)的均勻樑(uniform beams)之自由振動或強迫振動分析而言，除了傳統的有限元素法(finite element method, 簡寫為FEM)外，解析與數值混合法(analytical-and-numerical-combined method, 簡寫為ANCM)係較為簡單，且具有高準確度的方法之一。雖然在現存文獻中，已有不少利用ANCM來探討均勻樑「撓曲振動」(flexural vibration)之例子，但尚未見有人利用ANCM，來進行一攜帶多個集中元素(如螺槳、皮帶輪或聯軸器等)的旋轉軸之「扭轉振動」(torsional vibration)分析。故本文之第一個目的是，嘗試利用ANCM，來探討船舶推進軸系之自由與強迫扭轉振動特性。
此外，未攜帶任何集中元素之「不均勻樑」(non-uniform beams)的撓曲振動分析之文獻，本來已經很少，而攜帶任意個數集中元素之「不均勻樑」的撓曲振動分析之文獻，則尚未發現。故本文之第二個目的是，嘗試利用ANCM，來進行一攜帶多個集結質量之「不均勻樑」的自由撓曲振動分析。
就一多節的樑形格狀桁架(multi-bay beam-like lattice girder)而言，設計者所需要的動態分析資料，主要的是整個桁架的自然頻率與振態(natural frequencies and mode shapes for global structure)，但以傳統的有限元素法所求得的動態分析資料中，常因夾雜著許多局部構件(local structural members)的自然頻率與振態．而給設計者帶來莫大的困擾。因此早有許多學者專家，從事此類樑形格狀桁架簡化法(structural-simplification method,簡寫為SSM)之研究，以節省動態分析所需之電腦運算時間，並排除局部構件的自然頻率與振態。但就一多節的三維樑形格狀桁架而言，現有簡化法之準確度，並尚未能今人滿意，故本文之第三個目的是，提出一集結質量模型(lumped-mass model)來配合根據剛性平面假設所求得的勁度矩陣，以改善現存三維樑形格狀桁架簡化法之缺陷。

Abstract
For the free or forced vibration analysis of a uniform beam carrying any number of concentrated elements (such as fixed lumped masses, elastically-mounted lumped masses, linear springs, rotational springs, or spring-damper-mass systems), the analytical-and-numerical-combined method (ANCM) is one of the most simple and accurate approaches in addition to the conventional finite element method (FEM). From the existing literature one finds that the ANCM has been used in the "flexural vibration" analysis of the uniform beams, but use of the ANCM to the "torsional" vibration analysis of the rotating shafts carrying multiple concentrated elements (such as propellers, pulleys, or couplings) is not found yet. Hence, the first objective of this thesis is to investigate the free and forced torsional vibration characteristics of a propulsive shafting system by means of the ANCM.
Besides, the literature relating to the dynamic analysis of the "non-uniform" beams without carrying any concentrated elements is rare and the study on the flexural vibration analysis of the "non-uniform" beams carrying any number of concentrated elements is not found yet. Therefore, the second objective of this thesis is to deal with the latter problem with the ANCM.
For a multi-bay beam-like lattice girder, one of the main information required by the designers is the natural frequencies and mode shapes for the "global" (or whole) structure. But the dynamic analysis results obtained from the conventional FEM are composed of the natural frequencies and mode shapes for the "global" structure and those for the "local" structural members. These results often trouble the designers very much. Hence, a lot of researchers devoted themselves to the study of the structural-simplification method (SSM) of such kind of lattice girders to save computer time and to exclude the natural frequencies and mode shapes for the "local" structural members during the dynamic analysis. However, for the "three-dimensional" multi-bay beam-like lattice girders, the accuracy of the existing SSM is still not satisfactory. This is one of the reasons why the third objective of this thesis tries to present a lumped-mass model to incorporate with the stiffness matrix derived based on the rigid-plane assumption to improve the accuracy of the existing SSM.

封面
中文摘要
英文摘要
誌謝
目錄
表目錄　　　
圖目錄　　　
符號說明　　
第一章 緒 論
1.1 研究動機
1.2 文獻回顧
1.2.1 旋轉軸之扭轉振動　　　
1.2.2 「不均勻樑」之撓曲振動
1.2.3 樑形格狀桁架之結構簡化法　　　
1.3 研究方法
第二章 具有阻尼軸系之扭轉振動分析　　
2.1 解析與數值混合法(ANCM)　
2.1.1 「無拘束的」旋轉軸系之自然頻率及正規振態　　　
2.1.2 一根「有拘束的」旋轉軸之運動方程式　　
2.1.3 強迫振動分析　
2.1.4 自由振動分析　
2.2 數值分析結果與討論　　　
2.2.1 FEM及ANCM與正確解之比較　　　　
2.2.2 有限元素個數( )對精確度的影響　
2.2.3 一個特例的自由振動分析
2.2.4 一般實例的自由振動分析
2.2.5 含阻尼器且「有拘束的」旋轉軸系之強迫振動　　　
2.2.5.1 時間歷程圖　
2.2.5.2 頻率反應曲線
2.3 結 論　　
第三章 攜帶多個集結質量的不均勻樑之自由振動分析　　　
3.1 不均勻樑的自然頻率及正規振態之閉式解　　
3.1.1 「夾支-鉸支」的邊界條件　　　　
3.1.2 「鉸支-夾支」的邊界條件　　　　
3.2 攜帶多個集結質量的不均勻樑之解　
3.3 數值分析結果與討論　　　
3.3.1 與FEM及現有文獻結果的比較　　　
3.3.2 「無拘束的」不均勻樑之自由振動分析　　
3.3.3 攜帶一個集結質量的不均勻樑　　
3.3.4 攜帶三個集結質量的不均勻樑　　
3.3.5 攜帶五個集結質量的不均勻樑　　
3.4 結 論　　
第四章 空間樑形格狀桁架動態分析之集結質量模型　　　　
4.1 「節」等值樑的勁度矩陣　
4.2 集結質量模型及其相關的質量矩陣之推導　　
4.2.1 X-braced型桁架
4.2.2 Pratt型桁架　　
4.2.3 Warren型桁架　
4.3 自由振動分析　　
4.4 數值分析結果及討論　　　
4.4.1 總節數多寡的影響　　　
4.4.2 邊-長比 的影響
4.4.3 較高階自然頻率的精確度
4.4.4 最低的六個自然頻率所對應的振態
4.5 結 論　　
第五章 總結論　　　　
參考文獻　　
附錄一 以為轉換函數的不均勻樑之自然頻率及正規振態的閉式解　　
A1.1 「夾支-自由」(clamped-free)(CF)的樑　　　　
A1.2 「自由-夾支」(free-clamped)(FC)的樑　　　　
A1.3 「鉸支-鉸支」(hinged-hinged)(HH)的樑　　　
附錄二 X-braced型、Pratt型及Warren型桁架最低的六個振態
A2.1 12節的X-braced型桁架之邊-長比為 時之最低的六個振態
A2.2 12節的Pratt型桁架之邊-長比為 時之最低的六個振態　　
A2.3 12節的Warren型桁架之邊-長比為 時之最低的六個振態　
自述

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