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。;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.
