既有橋梁的損傷診斷是近期國內外工程界所關切的，其中如何能 夠快速又準確的進行橋梁損傷診斷，更是現在許多研究追求的目標， 本論文以量測結構自然頻率配合破壞力學及旋轉彈簧的概念進行損 傷位置與劣化程度診斷之計算，相較於傳統以載重實驗進行損傷診 斷，橋梁自然頻率的量測較為經濟與便捷，因此可達到快速損傷診斷 之目的。 本論文首先結合Anifantis 所提出的破壞力學及旋轉彈簧的損傷 模型概念，再來進一步的延伸至Liang 提出的損傷指標的計算。文中 搭配SAP2000 的數值模擬以及實際的鋁梁敲擊實驗進行此損傷診斷 方法的驗證，實驗中的自然頻率是藉著頻率域分解法(FDD)去的計算 由互易定理量測到的加速度訊號所得到的。最後更進一步的探討以理 論的模態振形及實際量測到的模態振形所計算的損傷位置與劣化程 度的結果，以及損傷產生前後可能面臨到的系統邊界條件改變之問 題。 Damage assessment of existing bridge is currently concerned by most engineers in the world, especially those techniques with accuracy and efficiency. In this thesis, a fast damage diagnosis technique by means of measuring natural frequency and modal shapes is proposed. Compared with the damage diagnosis process by loading test, the vibrational type testing method is more economical and efficient. The rotational spring modal for defect based on fracture energy theory proposed by Anifantis (1983) is applied into the damage index calculation method developed by Liang (1992) to form the damage diagnosis process of this thesis. The accuracy and reasonableness of this newly proposed technique on detecting damage location and severity are verified by numerical simulations and laboratory tests on beams with various types of damage state. Those natural frequencies and modal shapes of structures are obtained from the reciprocal theorem of elastodynamics and the frequency domain decomposition (FDD) method. Some signal processing techniques on field measured data and the adjustment of boundary conditions in the structure modal are also addressed.