臺灣博碩士論文加值系統

摘要
首先由無拘束(即未附帶任何懸吊系統和簡支撐跨距)的均勻樑之運動方程式，吾人可得含有五個積分常數的特徵函數，將此特徵函數代入每一個懸吊系統和簡支撐跨距之附著點的四個相容方程式、懸吊系統與樑之間的力交互作用方程式，則得一組五個聯立方程式。同樣的，將特徵函數分別代入樑之左端與右端的邊界條件方程式中，吾人亦可分別得到另一組聯立方程式。將上述所有的聯立方程式寫成矩陣的形式，則得一特徵值方程式。因此一均勻樑附帶 n 個懸吊系統和簡支撐跨距的總係數矩陣 之階數為5n+4。求解 = 0可得有拘束的均勻樑附帶 n 個懸吊系統和簡支撐跨距的自然頻率 (j = 1,2,…)。將每一自然頻率代入特徵方程式後，可得其對應的積分常數值，將此積分常數值代入每一個懸吊系統和簡支撐跨距之附著點的特徵函數中，即得對應之振態。在現有文獻中，特徵方程式皆以數學展開顯示式之型式表示之，再利用解析法或數值法去求解。當一均勻樑附帶二個(含)以上之集中質量和簡支撐跨距時，因其數學展開顯示式過於冗長便難以操作，故本文使用數值組合法以克服此一困難。

關鍵詞：懸吊系統、簡支撐跨距、特徵函數、數值組合法

Abstract
From the motion equation of the “bare” uniform beam (without any number of spring-mass systems and in-span support), an eigenfunction consisting of five integration constants is obtained. Where the last eigenfunction is substituted into the four compatible equations, one force-equilibrium equation and incorporating with the equation of motion for each attaching point of the spring-mass system, and the boundary equations for the two ends of the beam, a matrix equation of the form is got. The solutions of = 0 (where denotes a determinant) give the “exact” natural frequencies of the “constrained” beam (carrying any number of spring-mass systems and in-span support) and the substitution of each corresponding values of into the associated eigenfunction for each attaching points will determine the corresponding mode shapes. Since the order of is 5n+4, where n is the total number of spring-mass systems and in-span support, the “explicit” mathematical expressions for the existing approach becomes lengthy intractable if n > 2. The “numerical assembly method” introduced in this paper aims at improving the last drawback of the existing approach. The “exact” solutions in this paper refer to the numerical results obtained from the “continuum” models for the classical analytical approaches rather than from the “discretized” ones for the conventional finite element methods.
Keyword：spring-mass system, in-span support, eigenfunction, numerical assembly method

目錄
頁次
摘要 I
ABSTRACT II
誌謝目錄 III
目錄 III
圖目錄………………………………………………………………….VII
表目錄…………………………………………………………….......VIIII
第一章 緒論
1-1 研究背景 1
1-2 文獻回顧 2
1-3 研究動機與目的 3
1-4 本文架構 3
第二章
2-1拘束均勻樑之特徵函數................................................................4
2-2拘束均勻尤拉樑在第 個附著點之矩陣係數 …………….7
2-3拘束均勻樑在左端之矩陣係數 ………………...…………11
2-4拘束均勻樑在右端之矩陣係數 …………………………..12
2-5整個拘束均勻樑之全部矩陣係數 及頻率方程式…………14
2-6決定各種支橕條件下之 及 矩陣係數………………..16



第三章 結果與討論
3-1 均勻樑附帶n個懸吊系統與附帶n個簡支撐跨距之結果與討論.18
3-1-1與現存有之結果比較 18
3-1-2一均勻樑附帶多個簡支跨距未附帶懸吊系統 22
3-1-3一均勻樑附帶多個簡支跨距(Span)和附帶多個懸吊系統 24
第四章 結論與未來展望
4-1 結論 43
4-2未來展望 43
參考文獻………………………………………………………………..44
附錄..........................................................................................................46

圖目錄
頁次
圖2-1一均勻懸臂樑附帶n個懸吊系統與附帶n個簡支撐跨距………4
圖3-1 一均勻樑在邊界條件為簡支-簡支跨距-簡支…………………19
圖3-2一均勻樑在邊界條件為簡支-簡支跨距-簡支附帶一個懸吊系統………………………………………………………………19
圖3-3一均勻樑在邊界條件為夾住-簡支跨距-夾住附帶一個懸吊系統………………………………………………………………..20
圖3-4一均勻樑在四種邊界條件………………………………………27
圖3-5一均勻樑在邊界條件為簡支-簡支跨距-簡支跨距-簡支………23
圖3-6一均勻樑在四種邊界條件………………………………………31
圖3-7一均勻樑在四種邊界條件……………………………………錯誤! 尚未定義書籤。…35
圖3-8一均勻樑在邊界條件為簡支-簡支跨距-簡支跨距-簡支附帶三個懸吊統…………………………………………………………..26
圖3-9一均勻樑在四種邊界條件………………………………………39








表目錄
頁次
表3-1一均勻樑在邊界條件為簡支-簡支跨距-簡支下(如圖3-1所示)未附帶懸吊系統(spring-mass system)所得之前五個最低的特徵值係數…………………………………………………………..21
表3-2 一均勻樑在邊界條件為簡支-簡支跨距-簡支附帶一個懸吊系統所得之前五個最低的特徵值係數……………………………..21
表3-3一均勻樑在邊界條件為夾住-簡支跨距-夾住附帶一個懸吊系統所得之前五個最低的特徵值係數……………………………..22
表3-4一均勻樑在四種邊界條件下：CSC(夾住-簡支跨距-夾住)、SSS(簡支-簡支跨距-簡支)、CSF(夾住-簡支跨距-自由) 及CSS(夾住-簡支跨距-簡支)下未附帶懸吊系統(spring-mass system)所得之前五個最低的自然率…………………………..23
表3-5一均勻樑在四種邊界條件下：CSSC(夾住-簡支跨距-簡支跨距- 夾住)、SSSS(簡支-簡支跨距-簡支跨距-簡支)、CSSF(夾住-簡支跨距-簡支跨距-自由) 及CSSS(夾住-簡支跨距-簡支跨距-簡支)下(如圖3-5所示)未附帶懸吊系統(spring-mass system)所得之前五個最低的自然頻率……………………………………………24


表3-6 一均勻樑在四種邊界條件下：CSC(夾住-簡支跨距-夾住) 、SSS(簡支-簡支跨距-簡支)、CSF(夾住-簡支跨距-自由) 及CSS(夾住-簡支跨距-簡支)下附帶一個懸吊系統所得之前五個最低的自然頻率………………………………………………..25
表3-7 一均勻樑在四種邊界條件下：SSSS(簡支-簡支跨距-簡支跨距-簡支)、CSSC(夾住-簡支跨距-簡支跨距-夾住)、CSSS(夾住-簡支跨距-簡支跨距-簡支)及CSSF(夾住-簡支跨距-簡支跨距-自由)下附帶三個懸吊系統所得之前五個最低的自然頻率……………26

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