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研究生:許君平
研究生(外文):Chun-Ping Hsu
論文名稱:應用Chebyshev偽譜法調合共振梁及高加速度衝擊試驗
論文名稱(外文):Use of Chebyshev Pseudospectral Method to Tune Resonant Beam for High-g Shock Test
指導教授:洪振發洪振發引用關係
口試委員:王偉輝廖建義梁卓中宋家驥吳重雄關百宸邱進東
口試日期:2019-07-24
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:工程科學及海洋工程學研究所
學門:工程學門
學類:綜合工程學類
論文種類:學術論文
論文出版年:2019
畢業學年度:107
語文別:中文
論文頁數:209
中文關鍵詞:Chebyshev偽譜法零空間轉換共振梁操作模態分析高加速度衝擊試驗衝擊響應譜
DOI:10.6342/NTU201902613
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本文以彈擊式高加速度衝擊試驗裝備的研製為主軸,提出以改良式的Chebyshev偽譜法求解尤拉-伯努利梁模型自由振動模態問題,其次,應用操作模態分析與共振梁等實驗設計,配合部分夾持邊界之尤拉梁解析法,提出一套減少試誤次數的共振梁邊界調整試驗與分析流程。
一般梁結構自由振動問題可使用解析與數值方法求解其自然頻率與模態振形,但遇到梁的邊界條件屬非典型邊界、端點質量、梁外形屬於非棱柱形、階段結構或求解甚高階的模態(大於10階以上)時,都必須採用個案的近似解或數值方法處理,否則容易造成系統矩陣求解精確度不足與高階模態參數發散等現象。本文提出Chebyshev偽譜法與零空間轉換法,針對非棱柱形且帶有邊界值問題的梁元素進行模態參數求解。Chebyshev偽譜法以微分化矩陣為基礎,搭配零空間轉換可將複雜的邊界、梁外形與高低階混合模態等條件所構成的系統矩陣,侷限在有界的數值內,進而搭配MATLAB與Chebfun等工具箱的使用,大大增加求解的面向與速度。此外,對部分夾持型態的棱柱形尤拉伯努利梁之高階模態參數也提出近似解,以上兩種求解過程不僅對目前梁問題都可得到高精度的模態參數,並可應用在本文後續探討彈擊式高加速度衝擊試驗裝備之共振梁模態參數估算。此外,本文針對操作模態分析提出理論說明與實際應用於結構補強或振動控制問題改善的實例,證實大型結構透過操作模態分析所獲得的操作模態參數或響應放大倍率等資訊,對結構設計、壽命評估或試驗再現性極有助益。
最後本文將提出多種不同型態的尤拉-柏努利梁模型,以本研究方法進行自由振動模態數值分析驗證其模擬之精確度,並以共振梁結構搭配彈擊式氣壓系統進行實際衝擊量測,以衝擊響應譜方式呈現規劃試驗流程的正確性,後續執行此型態高加速度衝擊試驗時,更能加速相關試驗參數調校與組件的選用,以期達成試驗高試驗重複性與規格要求。
In this paper, the main purpose is development of impact equipment with a pneumatic projectile launcher and a length adjustable resonant beam using for generating a high-g shock environment. The modified Chebyshev pseudospectral method is proposed to solve the free vibration of Euler-Bernoulli beam for modelling the resonant beam, and the experimental design of the operational modal analysis will be applied. Analytical method of beam element for clamping boundary, a set of resonance beam boundary adjustment test and analysis flow to reduce the number of trial and error times is proposed.
Free vibration modal analysis of the general Euler-Bernoulli beam can be solved by analytical and numerical methods for natural frequencies and mode shapes. For non-classical boundary conditions, non-prismatic or stepped shape, tip-massed at both end, and higher order modal solutions of Euler-Bernoulli beam, will cause an ill-conditioned system matrix of eigen-value problems, it must be treated by the approximate solution or numerical method case by case. A Chebyshev pseudospectral method with a null space approach is proposed for investigating the boundary-value problem of a non-prismatic Euler-Bernoulli beam with generalized boundary or interfacial conditions. It is shown that, with few vital improvements, the Chebfun toolbox introduced by Trefethen et al. can be systematically applied to modeling non-prismatic Euler-Bernoulli beams with eigenvalue embedded tip-massed boundary conditions as well as the jump conditions that appear at the stepped interfaces. This study also presents a numerical stable asymptotic modal solution for the higher-order modes of a partially clamped beam and show that the proposed approach validates the robust higher-order modal solutions. Through a sequence of four increasingly complicated examples, using the proposed approach with higher-order modes, generalized boundary conditions and interface jump conditions of non-prismatic beams, the results are in excellent agreement with those reported in the literature using various other approaches. Based on the presented analytical beam model, we apply our approach to a mechanical high-g shock machine by tuning the resonant frequencies and clamping stiffness of the beam. In addition, this paper presents theoretical examples and practical examples for the improvement of structural reinforcement or vibration control problems for operational modal analysis, and confirms the operational modal parameters or response magnification obtained by large-scale structures through operational modal analysis. Life assessment or test reproducibility is extremely helpful.
Finally, this paper presents numerical solutions to verify the accuracy for free vibration analysis of different types of Euler-Bernoulli beam. Furthermore, with operational modal analysis of a shock machine, this study also builds the empirical curves for clamping position and stiffness, and shows an optimized procedure that may determine the feasible parameters to alleviate the need for trial and error. Finally, two experiments are conducted to verify the selected parameters, with a pneumatic projectile launcher and a length adjustable beam use for generating a high-g shock environment. With the proposed resontant beam tunning procedure, the measured shock responses are within the tolerance of required specification of shock serponse spectrum.
第一章 緒論 1
1.1前言 1
1.2 研究目的 2
1.3 研究方法 3
1.4 本文內容 4
第二章 文獻回顧 7
2.1 梁模型自由振動模態解析 7
2.2 模態試驗與操作模態分析 15
2.3 高加速度衝擊試驗環境、訊號量測與模擬裝備實現 18
第三章 應用矩陣化CHEBYSHEV偽譜法與零空間轉換解析EB梁模型自由振動模態 24
3.1部分夾持邊界非稜柱形EB梁之動力分析 24
3.2部分夾持稜柱形EB梁的高階振動模態分析解 26
3.3精進的CHEBYSHEV偽譜法與微分算子 32
3.4系統矩陣加入邊界條件之特徵值問題求解 35
3.4.1 列置換法與矩形偽譜配置法 35
3.4.2 零空間轉換法 37
3.5部分夾持邊界之均勻階段EB梁統域方程式推導 38
3.6 應用MATLAB結合CHEBFUN V5.1函式庫與零空間轉換過程求解特徵值問題 40
3.7 應用NSA 與CPSM求解部分夾持邊界非棱柱形EB梁兩端具有質量與部分夾持邊界棱柱形階段EB梁之自由振動模態問題 42
3.8數值分析實例說明與討論 45
3.8.1 簡單支撐邊界棱柱形EB梁高階模態確認 46
3.8.2 部分夾持棱柱形EB梁自由振動高階模態參數分析 50
3.8.3 部分夾持且兩端附加質量邊界非棱柱形EB梁模態求解 58
3.8.4階段棱柱形EB梁模態參數求解 69
第四章 動態環境結構模態分析與試驗 77
4.1 實驗模態分析理論 77
4.2. 操作撓度外形介紹 82
4.3. 操作模態分析理論 84
4.3.1. 頻域分析法 84
4.4.2. 時域分析法 88
4.4.3. 多頻道量測分析整合與諧頻訊號排除技術 89
4.5 振動機與控制系統 92
4.6. 操作模態試驗技術之執行實例 96
4.6.1應用OMA建立L型夾具結構特性資料庫 97
4.6.2 應用OMA執行大型60吋延伸台結構改善 98
4.6.3 阻尼材料與振動控制 101
第五章 高加速度衝擊環境 104
5.1 高加速度衝擊來源與定義 105
5.2高加速度衝擊的特性與可能造成損傷的效應 108
5.3高加速度衝擊環境量測技術 110
5.3.1高加速度衝擊相關術語 110
5.3.2衝擊量測規劃與儀具的需求 112
5.3.2.1 加速儀 112
5.3.2.2 訊號調節器 114
5.3.2.3訊號紀錄器 115
5.4 高加速度衝擊數據鑑別與分析技術 119
5.4.1 量測訊號零點飄移問題與處理 119
5.4.2 衝擊響應譜分析 120
5.4.3 衝擊量測分析鑑別 125
5.4.4 衝擊量測訊號記錄器取樣率與後置數位濾波器分析 130
5.5 高加速度衝擊環境試驗技術 132
5.5.1 電能啟動類裝備 133
5.5.2 位能轉換動能類裝備 134
5.5.3 共振夾具與其他高能類裝備 135
第六章 彈擊式高加速度衝擊試驗裝備之研製 138
6.1高加速度衝擊機設計概念 139
6.2共振梁系統設計與確認流程 141
6.3共振梁系統操作模態分析 143
6.4 共振梁邊界勁度優化程序 155
6.5共振梁系統應用於振動與跌落衝擊測試 158
6.6 投射氣壓系統與彈頭設計 166
6.7高加速度衝擊裝備全系統測試 170
第七章 結論與後續研究 179
參考文獻 183
附錄A 應用CPSM與NSA求解不同EB梁自由振動模態分析之程式碼 195
附錄B 操作模態試驗技術之案例 202
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