臺灣博碩士論文加值系統

敲擊回音法為目前廣泛應用於土木工程領域，用以檢測混凝土結構內部損傷位置、裂縫範圍、評估完整性等之非破壞檢測設備。然而對於材料性質的檢測，常見是在試驗室中完成，根據ASTM 試驗規範，試體體積必須十分細長且試驗結果不易獲得。

本研究以共振理論、試驗及數值模擬三者為核心，針對實心圓柱與平板進行分析。首先，對於橫截面採不同材料性質以guided-wave 法進行解析，發現第二至六共振頻率與基礎頻率的比例僅與卜松比有關，藉由線性回歸得到一適合檢測各式材料橫截面完整性之公式。次者，由細長桿件一維縱向波傳理論所得之基礎共振頻率，結合與橫截面基礎共振頻率二者關係，提出一對桿件縱向及橫向各進行一次敲擊，即可檢測材料卜松比與彈性模數之計算公式。此外，對於標準圓柱方面，分析Love 彈性波理論後發現，縱向基礎頻率與第二頻率的比例亦僅與卜松比有關，據此發展出一套只需對桿件縱向一次敲擊即能檢測標準圓柱材料性質的公式。最後，解析Lamb wave 方程式過程中同樣地發現第一與第二頻率的比例僅與卜松比相關，進而推導出對混凝土平板表面一次敲擊即可測定板材料性質之公式。

藉由試驗結果以及2D、3D 模態與暫態分析之數值模擬的印證，證明敲擊回音法設備可應用於不僅可以檢測混凝土，其他包括石膏、金屬、合金金屬、塑膠等圓柱相關材料均可測定其橫截面完整性以與材料性質。對於混凝土平板的材料性質亦可藉由簡單的敲擊即可獲得。相較於ASTM 規範的操作程序，本研究的檢測過程是相對精簡與可靠，可於方便工地現場及時進行材料性質的測定。

The impact-echo method is a nondestructive technique and has been widely used in civil engineering to determine the location of the internal defect, extent of flaws, and the integrity of concrete structures, etc. However, the procedures of evaluation of material properties are always finished in laboratory. According to the manual of American Society for Testing and Materials (ASTM), the dimension of specimen must be very slender and test results are hard to attain.

Base on resonant theories, experiments, and numerical simulation, this research focuses on solid cylinder rod and concrete plate. First, the guided-wave method is used to analyze cross-sectional resonant frequency with different material properties, and frequency coefficients for the 2nd to 6th frequencies only relate with Poisson’s ratio. The curve-fitting technique is used to obtain the best fit equations to determine the integrity of a cross-section. The second, according to the longitudinal fundamental frequency from one-dimensional wave equation and cross-sectional fundamental frequency from guided-wave method of slender rod, a new equation for evaluation Poisson’s ratio and modulus of elasticity is led out. The experimental procedures only need one impact respectively on the center of one end and the middle surface of rod. Furthermore, the elastic wave theory for standard cylinder given by Love is solved and the ratio of the 2nd to 1st longitudinal frequency also only concerns with Poisson’s ratio. The equations are developed to determine material properties and the test process is to impact once with one end of cylinder. Finally, The Lamb wave equations are analyzed and similarly the ratio of the 2nd to 1st longitudinal frequency only corresponds with Poisson’s ratio. New equations for evaluation of material properties of concrete plate are led out and the new test procedure proposed in the paper just needs only one impact to surface of plate.

Via verification of test results and 2D/3D of modal and transient analyses of numerical simulation, the impact-echo equipment is suitable for determination of material properties and evaluation of cross-sectional integrity. The applied scope of materials is including concrete, gypsum, metal, alloy metal, plastic, etc. The material properties of concrete plate will also be obtained by a simple impact. Comparison with the manual of ASTM, the experimental procedures of this search are relative simple, reliable, convenient and immediate to determinate the material properties at field.

中文摘要 --------------------------------------------------------------------------- I
英文摘要 ------------------------------------------------------------------------- III
誌謝 -------------------------------------------------------------------------------- V
目錄 ------------------------------------------------------------------------------- VI
符號對照表 ----------------------------------------------------------------------- X
表目錄 -------------------------------------------------------------------------- XIII
圖目錄 -------------------------------------------------------------------------- XIV
第一章 緒論 -------------------------------------------------------------------- 1
1-1 研究背景 -------------------------------------------------------------------- 1
1-2 研究動機與目的 ----------------------------------------------------------- 2
1-3 範圍與方法 ----------------------------------------------------------------- 3
1-4 論文內容 -------------------------------------------------------------------- 3
第二章 文獻回顧 -------------------------------------------------------------- 7
2-1 應力波傳行為 -------------------------------------------------------------- 7
2-1-1 圓柱縱向波傳 -------------------------------------------------------- 7
2-1-2 半無限域應力波傳 -------------------------------------------------- 9
2-2 敲擊回音法 ---------------------------------------------------------------- 11
2-2-1 發展沿革------------------------------------------------------------- 11
2-2-2 檢測原理-時間域法 ------------------------------------------------ 13
2-2-3 檢測原理-頻率域法 ------------------------------------------------ 14
2-2-4 試驗參數：敲擊源、取樣間隔、取樣筆數與頻譜解析度 -- 15
2-3 敲擊回音法之應用 -------------------------------------------------------- 19
2-3-1 圓形截面之檢測 ---------------------------------------------------- 19
2-3-2 圓柱縱向之檢測 ---------------------------------------------------- 20
2-3-3 平板結構之檢測 ---------------------------------------------------- 22
2-4 ASTM 對動態彈性模數及卜松比之檢測方法 ------------------------ 24
第三章 試驗規畫 ------------------------------------------------------------- 38
3-1 試驗材料 ------------------------------------------------------------------- 38
3-2 試驗儀器與設備 ---------------------------------------------------------- 40
3-3 分析軟體 ------------------------------------------------------------------- 42
3-4 試驗項目與步驟 ---------------------------------------------------------- 43
第四章 數值分析方法 ------------------------------------------------------- 61
4-1 概述 ------------------------------------------------------------------------- 61
4-1-1 2D PLANE162 元素 ------------------------------------------------ 62
4-1-2 3D SOLID164 元素 ------------------------------------------------ 62
4-2 數值模型 ------------------------------------------------------------------- 63
4-2-1 2D 模型之平面應變與軸對稱 ------------------------------------ 63
4-2-2 網格劃分------------------------------------------------------------- 64
4-2-3 邊界條件與漂移問題 ---------------------------------------------- 67
4-3 圓形截面共振頻率 -------------------------------------------------------- 68
4-3-1 暫態分析------------------------------------------------------------- 68
4-3-2 模態分析------------------------------------------------------------- 70
4-4 細長柱與標準圓柱軸向共振頻率 -------------------------------------- 70
4-4-1 暫態分析------------------------------------------------------------- 71
4-4-2 模態分析------------------------------------------------------------- 72
4-5 平板共振頻率 ------------------------------------------------------------- 72
4-5-1 時間域法------------------------------------------------------------- 73
4-5-2 暫態分析------------------------------------------------------------- 73
4-5-3 模態分析------------------------------------------------------------- 74
第五章 圓形截面特徵頻率與動態卜松比 ------------------------------- 94
5-1 圓形截面之導波法 ------------------------------------------------------ 94
5-2 卜松比對形狀因子與頻率比例因子的影響 ------------------------- 95
5-3 形狀因子與頻率比例因子公式之建立 ------------------------------- 96
5-4 試驗與數值模擬印證 --------------------------------------------------- 98
第六章 圓柱與平板之動態卜松比與彈性模數公式推導與應用 ---- 116
6-1 長柱分析 ------------------------------------------------------------------ 116
6-1-1 動態卜松比 --------------------------------------------------------- 116
6-1-2 動態彈性模數 ------------------------------------------------------ 119
6-1-3 試體檢測與數值模擬 -------------------------------------------- 121
6-2 標準圓柱分析 ----------------------------------------------------------- 124
6-2-1 動態卜松比 -------------------------------------------------------- 124
6-2-2 動態彈性模數 ----------------------------------------------------- 126
6-2-3 試體檢測與數值模擬 -------------------------------------------- 127
6-3 平板動態卜松比與彈性模數推導 ------------------------------------ 130
6-3-1 平板藍姆波之解析方法 ----------------------------------------- 131
6-3-2 卜松比、形狀因子與彈性模數 -------------------------------- 133
6-3-3 試體檢測與數值模擬 -------------------------------------------- 137
第七章 結論與建議 -------------------------------------------------------- 177
7-1 結論 ----------------------------------------------------------------------- 177
7-1-1 圓形截面共振頻率與動態卜松比 ----------------------------- 177
7-1-2 細長圓柱動態卜松比與彈性模數 ----------------------------- 178
7-1-3 標準圓柱動態卜松比與彈性模數 ------------------------------ 180
7-1-4 平板動態卜松比與彈性模數 ----------------------------------- 181
7-2 建議 ----------------------------------------------------------------------- 182
參考文獻 ----------------------------------------------------------------------- 184
作者簡介 ----------------------------------------------------------------------- 194

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