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研究生:陳繼峰
研究生(外文):Ji-Feng Chen
論文名稱:三維剛架結構之迴傳波射動力分析
論文名稱(外文):Dynamic Analysis of Three-Dimensional Framed Structure by the Method of Reverberation-Rays
指導教授:王彥博鮑亦興
指導教授(外文):Yen-Po WangYih-Hsing Pao
學位類別:碩士
校院名稱:國立交通大學
系所名稱:土木工程系
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:120
中文關鍵詞:迴傳波射法入射波出射波迴傳矩陣靜力分析
外文關鍵詞:method of reverberation-raysarrival wavedeparture wavemethod of reverberation matrix
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本文承襲Pao、Howard和Keh等人的研究成果,以彈性波理論為基礎,分析結構構件中的軸向波、扭轉波和撓曲波等三種應力波,依應力波之傳播、折射和反射追蹤計算波形之變化,將到達觀測點之所有波形疊加,求出結構之動態反應,稱為迴傳波射法。文中特別針對結構構件各種邊界條件之處理加以說明,並詳述計算三維空間構架動態歷時反應之數值方法。此外,並由就物理上的觀點,探討入射波和出射波之因果關係,並修正了理論公式的誤差。目前迴傳波射法的理論發展已臻完整,此一概念若應用於結構靜力分析時,則稱之為迴傳矩陣靜力分析,其逐次疊加之過程即相當於彎矩分配法。

This study follows the previous research of Pao, Howard and Keh, to analyze the stress waves of axial, torsional, and bending waves propagating in structural members, based on the theory of elastic waves. The overall transient response of the structure at any observing point can be obtained by superposing the arriving waves via scattering, refraction and reflection traced in time. This process is referred to as the method of reverberation-ray. In this thesis, treatments of various boundary conditions of the structural members are presented in details, along with the numerical procedure for dynamic analysis of 3-D space frame. Moreover, the causality between the arrival and departure waves is explored, and the previous derived formula is modified accordingly for improved accuracy. Theoretical development of the method of reverberation-ray has been completed. Similar technique has been developed for static analysis of structures and referred to as the method of reverberation matrix. The process of summing the solutions term by term is physically equivalent to the classical moment distribution method.

中文摘要 i
英文摘要 ii
誌謝 iii
目錄 iv
表目錄 vi
圖目錄 vii
第一章 緒論 1
第二章 三維剛架結構之彈性波 5
2.1 軸向波的傳播 5
2.2 扭轉波的傳播 8
2.3 撓曲波的傳播 10
2.4 剛架節點和桿件的座標 18
第三章 彈性波在剛架節點之散射分析 22
3.1 節點的力平衡 22
3.2 節點的位移諧合 25
3.3 彈性波在剛性自由節點之散射 27
3.4 彈性波在鉸接節點之散射 28
3.5 彈性波在球型支承點之散射 32
3.6 彈性波在固定支承點之散射 33
第四章 空間構架之彈波射迴傳分析 36
4.1 傳播矩陣 35
4.2 轉列矩陣 39
4.3 結構之迴傳矩陣 39
第五章 迴傳波射法之實例分析 44
5.1離散化過程與數值方法 44
5.2 簡支樑以二力桿加勁時的迴傳波射動力分析 45
5.3 二維剛架之迴傳波射動力分析 47
第六章 試驗環境之建構與衝擊載重試驗結果 49
6.1 三維鋁模型剛架 49
6.2 加載機構 49
6.3 三維鋁模型構架之迴傳波射動力分析 50
6.4 三維鋁模型構架之衝擊載重試驗 51
第七章 結論與建議 55
參考文獻 56
附錄A 94
附錄B 104
表目錄
頁次
表5.1 複合型結構的材料參數與各斷面尺寸 59
表6.1 鋁材之材料性質 59
圖目錄
頁次
圖2.1 桿件中微小段元素的受力情形 5
圖2.2 樑中微小段元素的受力情形 10
圖2.3 白努利樑的撓曲波波速與頻率的關係 60
圖2.4 提摩盛科樑的撓曲波波數與頻率的關係(無阻尼) 60
圖2.5 提摩盛科樑的撓曲波波速與頻率的關係 61
圖2.6 提摩盛科樑的撓曲波波數與頻率的關係(有阻尼) 61
圖2.7 三維剛架結構 62
圖2.8 桿件的座標系統 62
圖5.1 簡支樑受一衝擊載重 63
圖5.2 簡支樑加勁後(複合型結構)受一衝擊載重 63
圖5.3 簡支樑在加勁前與加勁後中點垂直向位移歷時反應 64
圖5.4 二維剛架結構 64
圖5.5 二維結構5-7中點的軸向應變反應歷時圖 65
圖5.6 二維結構6-7中點的軸向應變反應歷時圖 65
圖5.7 二維結構5-7中點的撓曲應變反應歷時圖 66
圖5.8 二維結構6-7中點的撓曲應變反應歷時圖 66
照片6.1(a) 鋁模型剛架 67
照片6.1(b) 鋁模型剛架(短向) 67
照片6.1(c) 鋁模型剛架(長向) 68
圖6.1(a) 鋁模型剛架(上視圖) 69
圖6.1(b) 鋁模型剛架-側視圖(短向) 70
圖6.1(c) 鋁模型剛架-側視圖(長向) 71
照片6.2(a) 加載機構 72
照片6.2(b) 釣魚線固定於掛勾 72
照片6.2(c) 釣魚線跨過滑輪 73
照片6.2(d) 釣魚線懸吊質塊 73
照片6.2(e) 質塊 74
照片6.3 噴燈及釣魚線 74
照片6.4(a) 黏貼於鋁構架模型之應變計 75
照片6.4(b) 黏貼於鋁構架模型之應變計 75
照片6.5 衝擊載重試驗之儀器設備 76
照片6.6(a) 高頻示波器(前視) 76
照片6.6(b) 高頻示波器(後視) 77
照片6.7(a) 訊號調節放大器-惠斯敦電橋(前視) 77
照片6.7(b) 訊號調節放大器-惠斯敦電橋(後視) 78
照片6.8 應變計及軍用接頭 78
圖6.2(a) 軸向波產生之應變(梁桿件3-6-Right) 79
圖6.2(b) 彎矩波產生之應變(梁桿件3-6-Right) 79
圖6.2(c) 軸向波與彎矩波產生之應變(梁桿件3-6-Right) 80
圖6.3(a) 軸向波產生之應變(梁桿件3-6-Back) 80
圖6.3(b) 彎矩波產生之應變(梁桿件3-6-Back) 81
圖6.3(c) 軸向波與彎矩波產生之應變(梁桿件3-6-Back) 81
圖6.4(a) 軸向波產生之應變(梁桿件5-11-Front) 82
圖6.4(b) 彎矩波產生之應變(梁桿件5-11-Front) 82
圖6.4(c) 軸向波與彎矩波產生之應變(梁桿件5-11-Front) 83
圖6.5(a) 軸向波產生之應變(梁桿件5-11- Back) 83
圖6.5(b) 彎矩波產生之應變(梁桿件5-11- Back) 84
圖6.5(c) 軸向波與彎矩波產生之應變(梁桿件5-11- Back) 84
圖6.6(a) 軸向波產生之應變(梁桿件8-11-Top) 85
圖6.6(b) 彎矩波產生之應變(梁桿件8-11-Top) 85
圖6.6(c) 軸向波與彎矩波產生之應變(梁桿件8-11-Top) 86
圖6.7(a) 軸向波產生之應變(梁桿件8-11- Bottom) 86
圖6.7(b) 彎矩波產生之應變(梁桿件8-11- Bottom) 87
圖6.7(c) 軸向波與彎矩波產生之應變(梁桿件8-11- Bottom) 87
圖6.8(a) 軸向波產生之應變(柱桿件4-5-Front) 88
圖6.8(b) 彎矩波產生之應變(柱桿件4-5-Front) 88
圖6.8(c) 軸向波與彎矩波產生之應變(柱桿件4-5-Front) 89
圖6.9(a) 軸向波產生之應變(柱桿件4-5-Back) 89
圖6.9(b) 彎矩波產生之應變(柱桿件4-5-Back) 90
圖6.9(c) 軸向波與彎矩波產生之應變(柱桿件4-5-Back) 90
圖6.10(a) 軸向波產生之應變(柱桿件8-9-Front) 91
圖6.10(b) 彎矩波產生之應變(柱桿件8-9-Front) 91
圖6.10(c) 軸向波與彎矩波產生之應變(柱桿件8-9-Front) 92
圖6.11(a) 軸向波產生之應變(柱桿件8-9-Back) 92
圖6.11(b) 彎矩波產生之應變(柱桿件8-9-Back) 93
圖6.11(c) 軸向波與彎矩波產生之應變(柱桿件8-9-Back) 93

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