大振幅振動對具表面裂紋簡支樑疲勞裂紋成長之影響

Effect of large Amplitude Vibration on Fatigue Crack Growth for Simply-Supported Beam with Surface Crack

李子揚(Tzu-Yang Lee)

指導教授 ： 施延欣

中原大學/工學院/機械工程研究所/碩士(2015年)

https://doi.org/10.6840/cycu201500688

摘要

在本文中探討的大變形自由振動的長方形截面簡支樑 ，並在樑的正中央
具有一直裂式裂紋。在振動過程中，不考慮非保守力影響並依據漢米爾頓
(Hamilton)準則來求出系統的運動方程式、邊界條件和形狀函數。文中，利用Galerkin's method將統御方程式化簡為一個以時間為變數的Mathieu方程式和無裂紋之勁度方程式。在振動部分是使用Runge-Kutta 的方法來描述振幅與時間的關係；裂紋模型上，同時討論呼吸式裂紋與傳統開放式裂紋模型，並在求取開放式裂紋與呼吸式裂紋的勁度時，提出不同的方法。
最後對於在大振幅振動的情況下，探討呼吸式裂紋樑和開放式裂紋樑的頻
率變化與裂紋深度關係。在疲勞裂紋成長上，採用Modified Forman model方程式來計算出疲勞裂紋成長與次數之間的關係，而得有關振動對疲勞裂紋的影響，裂紋成長對振動的關係也同時被描述及探討，並且在最終的分析結果求得大振幅振動與一般振動的差異，當裂紋長度增加大振幅振動比小振動壽命還要減少。

關鍵字

大振幅 ； 疲勞裂紋成長 ； 簡支樑

並列摘要

In this study, the large amplitude free vibration of a simply supported beam with a straight-edge crack at mid-span is considered.
The equation of motion and boundary conditions are derived by Hamilton's principle. The stiffness with opening crack is derived by fracture mechanics.
The Mathieu equation and the stiffness of the beam without a crack are derived by Galerkin's method.
And then using Runge-Kutta method to determine the relationship between amplitude and time.
About the crack model, both of the opening crack and the breathing crack are considered. And the different way to calculate the stiffness of the opening and breathing crack is provided. In addition, under the premise of large amplitude vibration, with the crack depth ratio in change, the relationship of frequency ratio and crack depth ratio with the opening crack and the breathing crack are discussed in this study.
Modified Forman equation is used to calculate the relation of crack growth and loading cycles.
Vibration on the crack, and crack growth related vibrations have also been described and discussed.

並列關鍵字

Large Amplitude ； Fatigue Crack Growth ； Simply-Supported Beam

參考文獻

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