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研究生:呂岳峰
研究生(外文):Lu Yueh-Feng
論文名稱:水下爆震三維船體顫震分析
論文名稱(外文):3-D Analysis of Hull Whipping to Underwater Explosion
指導教授:洪振發洪振發引用關係
指導教授(外文):Hung C. F.
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:造船及海洋工程學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2000
畢業學年度:88
語文別:中文
論文頁數:142
中文關鍵詞:水下爆震船體顫震氣泡漲縮有限元素邊界元素模態疊加
外文關鍵詞:underwater explotionhull whippingbubble pulsationFEMBEMmode superposition
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摘要
當炸藥在水下引爆時,爆炸氣泡的脈衝現象具有週期性,而氣泡的脹縮運動會產生衝擊波與變化的壓力場引起水面船隻或潛艇剛體運動及撓曲運動的現象,這種全船週期性運動與撓曲振動稱為船體顫震現象。本研究採用模態疊加法,將每個模態的動態分量分別算出再合成整體的動態反應。本文整合三維有限元素結構分析、邊界元素流場分析以及爆炸氣泡脈衝分析,以推算船艦結構在水下爆炸的顫震反應。
首先,對於爆炸氣泡脈衝運動方程式,則從能量守恆定理並考慮流體壓縮效應進行推導,配合爆炸氣體狀態方程式與爆炸氣泡初始條件的設定,對爆炸氣泡運動進行模擬,同時以LS/DYNA進行模擬,與氣泡脈衝經驗公式加以比較。考慮爆炸中心離開船體有明顯距離的情況,採用模態疊加法,建立三維有限元素模型進行模態分析,在動態結構與水的交互作用方面,將船體振動與氣泡脹縮所引致流場之速度勢採用三維邊界元素法計算,將流體動力作用在船體的壓力轉換成模態附加船殼上的慣性力與氣泡體膨脹加速度的衝擊力兩部份,以潛水圓柱殼結構及漂浮圓柱殼結構為例進行分析。
Abstract
The hull whipping is the flexing motion of the whole hull structure. The pulsation of gas bubble can change the pressure field in its surrounding fluid, and induce the impact pressure on hull surface. In this paper, a mode superposition approach is used. The dynamic response for the significant mode is solved prior, the dynamic response of which structure is then approximated by linear superposition of these modes. The natural frequencies and mode shapes of structure in air are analyzed by 3-D FEM, the velocity potential of each vibration mode under bubble pulsation is solved by 3-D BEM.
First, a doubly asymptotic equation of motion (DA EOM) for bubble dynamics is adopted which is derived from the motion equation using the principle of energy conservation with the effect of fluid compressibility. A suitable initial condition for DA EOM is derived from the combination of DA EOM and empirical shock pressure function. We use LS/DYNA to simulate the motion of bubble to compare the results. The whipping response of ship structures caused by the bubble pulsation is then calculated by mode-superposition method. We build the 3-D FEM model for the modal analysis. The modal velocity potential function is calculated by 3-D BEM, in which the boundary condition on hull surface is adopted from mode shape analyzed by FEM. The pressure acting on hull surface is derived from velocity potential function, and transferred into two parts: an added modal mass and a bubble pulsation force.
A submerged cylindrical shell and a floating cylindrical shell are employed to illustrate the analysis procedure.
第一章 緒論
1.1 研究動機 .……………………………………………… 1
1.2 文獻回顧 …………………………………………….… 2
1.3 本文內容 ………………………………………………. 7
第二章 水下爆炸氣泡的脈衝運動
2.1 爆炸氣泡脈衝運動 ……………………………………. 9
2.2 氣泡脈衝運動方程式 …………………………………. 9
2.3 水下爆炸氣體狀態方程式 ……………………………. 13
2.4 氣泡脈衝運動方程式的初始條件 ……………………. 14
2.5 爆炸氣泡的移動現象 …………………………………. 17
2.6 氣泡運動分析範例 ……...…………………………….. 17
2.6.1 應用本章理論計算 ………………………………………18
2.6.2 應用LS/DYNA分析氣泡運動 …………………………… 18
2.6.3 氣泡脈衝經驗公式 ...………………………………… 20
2.6.4 討論 ………………………………………………………21
2.7 不同炸藥量引爆於相同深度 …………………………. 22
2.8 相同炸藥量引爆於不同深度 …………………………. 23
第三章 水下爆炸氣泡脈衝運動引發水面船艦顫震的基本理論分析
3.1 船樑結構垂向振動的正規模態 ………………………. 32
3.2 氣泡脈衝引致船樑顫震的模態運動方程式 …………. 34
3.3 邊界元素法求解拉普拉斯方程式 .…………………… 40
3.3.1 基本解 ………………………………………………… 41
3.3.2 邊界積分式 …………………………………………… 42
3.3.3 常數元素 ……………………………………………… 44
3.4 潛體的模態振動與浮體的模態振動的差別 …………. 45
第四章 圓柱體受爆炸氣泡脈衝現象引致振動之樑模型分析
4.1潛水圓柱殼結構在無限邊界流場受爆炸氣泡作用之樑
理論分析 …………………….………………………..... 50
4.1.1 樑模型圓柱結構在空氣中之模態與模態質量 …………51
4.1.2 浸水圓柱結構的模態附加質量矩陣 ……………………53
4.2 狀況A:爆炸位置在潛水圓柱殼正下方 ……………. 57
4.2.1 爆炸氣泡中心點的速度勢 ..………………………… 57
4.2.2 爆炸氣泡的體膨脹加速度 ………………………………58
4.2.3 正規化模態運動方程式 …………………………………58
4.3 漂浮圓柱殼結構受爆炸氣泡作用之樑理論分析 ……. 60
4.3.1 樑模型圓柱在空氣中之模態與模態質量 ………………60
4.3.2 漂浮圓柱結構的模態附加質量矩陣 ……………………62
4.4 狀況B:爆炸位置在漂浮圓柱殼正下方 ……………… 63
4.4.1 爆炸氣泡中心點的速度勢 ..………………………… 64
4.4.2 爆炸氣泡的體膨脹加速度 ………………………………64
4.4.3 正規化模態運動方程式 …………………………………64
4.5 計算結果討論 …………………………………………. 66
第五章 圓柱殼受爆炸氣泡引致振動之有限元素分析
5.1 潛水圓柱殼結構有限元素分析 ………………………. 92
5.1.1 有限元素模型 ……………………………………………92
5.1.2 模態分析 …………………………………………………93
5.2 狀況一:炸藥位置在潛水圓柱殼正下方 ..…………… 93
5.3 狀況二:炸藥位置不在潛水圓柱殼正下方 ..………… 95
5.4 漂浮圓柱殼結構有限元素分析 ………………………. 95
5.4.1 有限元素模型 ……………………………………………95
5.4.2 模態分析 …………………………………………………96
5.5 狀況三:炸藥位置在漂浮圓柱殼正下方 ..…………… 96
5.6 狀況四:炸藥位置不在漂浮圓柱殼正下方 ..………… 98
5.7 主爆震波對圓柱殼結構之衝擊 …………………….… 99
5.8 爆震係數 ..……………………………………………. 101
第六章 結論與展望
6.1 結論 …..………………………………………………. 136
6.2 展望 …..………………………………………………. 137
參考文獻 ..………………………………………………………. 139
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