本文主要利用有限元素法分析含裂縫移動樑的振動行為。首先利用漢米爾頓原理與有限元素法推導軸向移動樑的運動方程式，並將裂縫視為一種扭轉彈簧，推導裂縫造成之局部可撓性和限制關係，結合兩者關係式，得到含裂縫移動樑的運動方程式。在動態穩定方面，本文採用Bolotin法則來分析含裂縫移動樑的動態穩定問題，最後利用狀態空間方法求得移動樑的不穩定區域。
由結果顯示不同裂縫深度與裂縫位置對結構的自然振動頻率會有不同的影響，由未含裂縫樑的模態斜率分佈圖可看出其影響程度，模態斜率絕對值越大，裂縫位於此處對自然振動頻率影響越大，而移動的速度也會造成自然振動頻率、臨界速度的下降與動態穩定區域的向下偏移。

The objective of this dissertation is to study the vibration of a traveling crack beam. The Hamilton’s principle and the finite element method are employed to derive the finite-element equations of motion for the traveling crack beam. The governing matrix equation for vibrations of the crack beam is constructed from the basic standard beam elements combined with the modified line-spring model. The regions of dynamic instability are determined by Bolotin’s method and the state space method.
From numerical calculations, the results show that the natural frequencies can be affected by the crack depth and location. The effect of crack position is found to be the most significant, when the crack is at the point with the steepest slope of the uncrack mode shape. The speed of the traveling beam can reduce the natural frequencies and the critical speed.

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