板結構廣泛應用於各類工程結構中，平板在外力作用下的靜態與暫態行為直 接影響其設計與安全性。由於平板在載重下會同時呈現靜態應力場與暫態波傳行 為，如何有效分析兩者行為並掌握其影響機制，成為重要的研究課題。因此，本 研究採用模態展開法 (modal expansion method) 作為理論基礎，並搭配光彈法 (photoelastic method) 進行實驗量測，其可視化且能顯示全場應力分布變化的特 性，十分適合用於觀察板結構的靜態與暫態全場面內變形。以平板面內模態形狀 與自然頻率為基底，利用模態正交性質推導出各模態的貢獻係數，藉由疊加原理 建構出平板在不同受力條件下的理論解，包含面內位移、應變和應力場。實驗部 分分別施加固定載重與敲擊錘衝擊，透過光彈法觀察平板在靜態與暫態下的應力 分佈情形；同時利用有限元素軟體 (finite element software) 建立平板力學模型進 行數值模擬。藉由實驗量測之等色線條紋 (isochromatic fringes) 對應之應力差大 小分布，與理論推導及數值模擬結果進行比對，以確認三者之一致性。 本文的主要貢獻在於證實了以平板面內模態形狀為基底之疊加方法，具備同 時處理靜態載重與暫態敲擊問題之可靠性。藉由光彈法實驗技術，本研究成功直 觀地呈現並區辨了靜態載重下的穩定規則應力場，以及暫態敲擊下快速變化的波 動傳遞行為。經由理論解析、實驗量測與有限元素模擬三者的交叉比對，結果顯 示高度一致性，確立了此整合分析方法在探討平板面內變形行為上的準確度與實 用價值。;Plate structures are widely used in various engineering applications. The static and transient behaviors of plates under external forces directly affect their design and safety. Since plates under loading exhibit both static stress fields and transient wave propagation behaviors, effectively comparing their differences and understanding the underlying mechanisms has become a critical research topic. Therefore, this study adopts the Modal Expansion Method as the theoretical basis and combines it with the Photoelastic Method for experimental measurement. The ability of the Photoelastic Method to visualize full field stress distribution makes it highly suitable for observing the static and transient in plane deformations of plates. based on the in-plane mode shapes and natural frequencies of the plate, this study utilizes the orthogonality of modes to derive the contribution coefficients of each mode. Through the principle of superposition, theoretical solutions for the plate under different loading conditions—including in-plane displacement, strain, and stress fields—are constructed. In the experiments, fixed loads and hammer impacts were applied to observe the stress distribution of the plate under static and transient conditions using the Photoelastic Method. Simultaneously, Finite Element Software was used to establish a mechanical model of the plate for numerical simulation. The stress difference distributions corresponding to the experimentally measured isochromatic fringes were compared with the theoretical and numerical results to confirm the consistency among the three methods. The main contribution of this paper is demonstrating the reliability of the superposition method based on plate in-plane mode shapes to simultaneously handle static loading and transient impact problems. Using photoelastic experimental techniques, this study successfully visualized and distinguished the stable, regular stress fields under iii static loading from the rapidly changing wave propagation behaviors under transient impact. Cross-comparison of theoretical analysis, experimental measurement, and finite element simulation showed high consistency, establishing the accuracy and practical value of this integrated analysis method in investigating in-plane deformation behaviors of plates.
