具有多處斷面驟變之半無限長瑞利– 洛夫桿受衝擊桿加載下之應力波傳播

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Nguyen Ngoc Thang(Nguyen Ngoc Thang) 查詢紙本館藏

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土木工程學系

論文名稱

具有多處斷面驟變之半無限長瑞利– 洛夫桿受衝擊桿加載下之應力波傳播
(Stress Wave Propagation in a Semi-Infinite Rayleigh–Love Rod with Multiple Sudden Cross-Sectional Area Variations Excited by a Striker Rod)

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至系統瀏覽論文 (2025-9-30以後開放)

摘要(中)

本論文研究了在不同橫截面積和不同一般阻抗條件下，側向慣性和泊松比對瑞利-洛夫桿中縱向波的影響，並探討了應力波在有突變橫截面的桿中的傳播情況，導出了反射波和透射波的解析解。通過有限元分析驗證了解析解之正確性。此外，本論文提出了一種基於沖擊回聲技術的新型非破壞檢測（NDT）方法，可用於檢測具有突變橫截面結構中的缺陷位置及劣化程度。
這項研究探討了在一個包括移動擊錘桿和靜止的半無限長瑞利-洛夫桿系統中，不同阻抗對應力波傳播的影響。在這項研究中，使用拉普拉斯變換的數值逆轉換是處理與瑞利-洛夫桿中應力波傳播方程相關的複雜數學模型的關鍵技術。這種數值方法的可將複雜的微分方程從拉普拉斯域轉回時間域，提供了一個清楚且可行的波動行為展示。拉普拉斯變換的數值逆轉換有助於更深入地探索在阻抗變化的界面處發生的波動傳播。這種功能非常重要，因為它有助於預測材料屬性和幾何配置的變化如何影響波的特性，這對於設計有效的測試系統至關重要。它揭示了這些桿件之幾何不連續性如何顯著改變波的幅度和傳播模式，導致波形的放大或衰減。這一關鍵的理解有助於改善分離式霍普金森壓力桿（SHPB）測試的設計和校準，以獲得更好的測試結果。
最後，本研究開發了一個正算及反算分析方法，用於評估土木工程中的後張錨固系統中鋼腱的完整性。通過模擬擊錘沖擊並利用瑞利-洛夫桿理論，該模型評估張力鋼腱的完整性，通過波幅、波形和時序的變化識別腐蝕和其他缺陷的位置及尺寸。這項研究加深了對截面變化如何影響波動行為的理解，從而促進了結構健康監測方法的發展。

摘要(英)

This dissertation studies the stress wave propagation in Rayleigh–Love rods considering the effects of lateral inertia and Poisson’s ratio on longitudinal waves in the rods under varying conditions of cross-sectional areas and different general impedances. The study explores the propagation of stress waves in rods with abrupt changes in cross-sectional area, deriving analytical solutions for reflected and transmitted waves. Theoretical findings are substantiated through finite element analysis, confirming the analytical solutions. Additionally, the research proposes a novel nondestructive testing (NDT) method based on impact echo techniques for detecting defects in structures with sudden cross-sectional changes.
This study simultaneously investigates the effects of different impedances on stress wave propagation in a system comprising a moving striker rod and a stationary semi-infinite Rayleigh–Love rod. The utilization of the numerical inversion of Laplace transformations in this research is a pivotal technique for handling the complex mathematical models related to the equation of stress wave propagation in Rayleigh–Love rods. The convenience of this numerical method allows for the transformation of complicated differential equations from the Laplace domain back to the time domain, providing a clear and actionable depiction of wave behaviors over time. The numerical inversion of Laplace transformations facilitates a deeper exploration into the wave propagation that occurs at the interfaces where general impedances vary. This capability is crucial because it helps in predicting how changes in material properties and geometrical configurations influence the wave′s characteristics, which are essential for designing effective testing setups. It reveals how these discontinuities can significantly alter wave amplitude and propagation patterns, leading to either wave amplification or attenuation. This crucial understanding is instrumental in refining the design and calibration of Split-Hopkinson Pressure Bar (SHPB) tests, optimizing them for better response under test conditions.
Lastly, the research develops both forward and backward analysis methods to assess the integrity of post-tension anchorage systems in civil engineering. By simulating striker impacts and leveraging the Rayleigh–Love rod theory, this model assesses the integrity of anchorage blocks, identifying corrosion and other defects through variations in wave amplitude, waveform, and timing. This research provides a deeper understanding of how cross-sectional variations influence wave behavior, thereby facilitating the development of methodologies in structural health monitoring.

關鍵字(中)

★ 應力波傳播
★ 瑞利-洛夫桿理論
★ 非破壞檢測（NDT）
★ 橫截面面積變化
★ 沖擊回聲技術
★ 結構健康監測
★ 拉普拉斯變換的數值逆轉換法
★ 反射波和透射波
★ 幾何不規則性
★ 後張錨固系統
★ 側向慣性和泊松比的影響

關鍵字(英)

★ Stress wave propagation
★ Rayleigh–Love rod theory
★ nondestructive testing (NDT)
★ cross-sectional area variation
★ impact echo techniques
★ structural health monitoring
★ post-tension anchorage systems
★ effects of lateral inertia and Poisson’s ratio

論文目次

中文摘要 I
ABSTRACT II
ACKNOWLEDGEMENTS III
Table of Contents V
List of Tables VIII
List of Figures IX
List of Abbreviations XVI
Chapter 1. Introduction 1
1.1 Overview and Motivation 1
1.3 Research Methods 7
1.4 Organization of Dissertation 7
Chapter 2. Fundamental of Traditional Wave Theory in a rod 10
2.1 Introduction to One-Dimensional Traditional Wave Theory 10
2.2 Derivation of One-Dimensional Traditional Wave Equation 10
2.3 Analytical Solutions for Solving the Traditional Wave Equation 11
2.4 Reflection and Transmission at Boundaries 22
2.5 Applications of One-Dimensional Traditional Wave Theory 23
Chapter 3. Fundamental of Rayleigh–Love Wave Theory in a Rod 25
3.1 Introduction to Rayleigh–Love Longitudinal Wave Theory in a Rod 25
3.2 Derivation of Rayleigh–Love Wave Equation under Tension Force 26
3.3 Applications of Rayleigh–Love Wave Theory 34
3.4 Methods for Solving the Rayleigh–Love Wave Equation 35
Chapter 4. Numerical Inversion of Laplace Transformation 37
4.1 Introduction to Laplace Transform 37
4.2 Basic Conditions and Theorems of the Laplace Transform 38
4.3 Inverse Laplace Transform Using an Approximation Formula 41
4.4 Applications of Laplace Transform 45
4.5 Examples 46
Chapter 5. Analysis of Stress Wave Propagation in a Rayleigh–Love Rod Under the Collinear Impact of a Striker Rod with Sudden Cross-Sectional Area Variations 51
5.1 Model Description 51
5.2 Solution of the Stress Wave Propagation Equation in a Rayleigh–Love Rod with Sudden Cross-Sectional Area Variation 52
5.3 Analysis of the Stress Wave Propagation in a Rod with A1  A2 56
5.3.1 Verification of the analytical solution from Eqs. (5.11) to (5.15) with the FEM solution 56
5.3.2 Investigation of stress wave propagation in a rod at various positions 60
5.4 Analysis of the Stress Wave Propagation in a Rod with A1  A2 64
5.5 Identification of Locations with Sudden Cross-Sectional Area Changes in the Rod 66
5.5.1 Reflection and transmission of stress wave in a rod with single sudden cross-sectional area variation 66
5.5.2 Reflection and transmission of stress wave in a rod with double sudden cross-sectional area variations 71
5.6 Identification of the Corresponding Model for Sudden Cross-Sectional Area Variations in the Rod 77
Chapter 6. Analysis of Stress Wave Propagation in a Semi-Infinite Rayleigh–Love Rod Under the Collinear Impact of a Striker Rod with Different General Impedances 82
6.1 Model Description 82
6.2 The Fundamental Theory of Wave Propagation in the Rayleigh–Love Rod Under the Collinear Impact of a Striker Rod of Different General Impedances 82
6.3 Investigation of Wave Propagation in a Rayleigh–Love Rod Under the Collinear Impact of a Striker Rod with the same Impedances 88
6.4 Investigation of Wave Propagation in a Rayleigh–Love Rod Under the Collinear Impact of a Striker Rod with Different Impedances 93
6.4.1 Investigation of stress wave propagation in a semi-infinite rod and a striker rod at the interface x = 0 m 96
6.4.2 Investigation of stress wave propagation in a semi-infinite rod at x = 0.5 m 98
6.2.3 Investigation of stress wave propagation in a striker rod at x = ?0.1 m 100
6.5 Investigation of Strain Rate’s Effect on the Material of the Striker Rod and Semi-Infinite Rod Under Collinear Impact 103
6.6 Travel Time History 106
Chapter 7. Detection of Defect in a Semi-Infinite Rayleigh–Love Rod Under Tensile Force 110
7.1 Model Description 110
7.2 The Fundamental Theory of Wave Propagation in a Semi-Infinite Rayleigh–Love Rod under Tensile Force Excited by a Striker Rod 110
7.3 Example and Discussion 121
7.4. Identification of Locations with Sudden Cross-Sectional Area Changes in the Rod 127
7.4.1. Formulation of method 127
7.4.2. Validation of formula 130
7.4.3. Identification of the locations and sudden cross-sectional area variations 132
Chapter 8. Conclusions 139
Chapter 9. Future Work 141
References 146
Appendixes 154
Appendix A. Derivation of the relationship between stress and velocity in a rod. 154
Appendix B. Integration of equations for determining incident, reflected, and transmitted stresses without considering Poisson’s ratio effect. 156
Appendix C. Derivation of the wave velocity taking into account the effect of Poisson′s ratio. 158
List of Publication 160

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指導教授

王仲宇(Chung-Yue Wang)

審核日期

2024-10-8

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