呼吸式裂紋產生的阻尼對樑的振動與疲勞裂紋成長之影響

The effect of Crack-Friction Damping on the Vibration and Fatigue Crack Growth of Beams with Breathing Crack

張肇殿(Chao-Tien Chang)

指導教授 ： 施延欣

中原大學/工學院/機械工程研究所/碩士(2004年)

https://doi.org/10.6840/cycu200400006

摘要

摘 要
本文中提出的理論模型，係由圓形截面及方形截面樑在不同邊界條件下，受到一週期性交變負荷集中力作用，產生小變形振動的尤拉樑（Euler’s beam），在振動過程中，考慮在此結構產生一直裂式裂紋，由於裂紋表面相互摩擦，產生摩擦阻尼，來定義摩擦模型，在此過程中能量之損失所產生非保守力，對此系統影響之探討。
首先使用漢米爾頓(Hamilton)準則，求取運動方程式、邊界條件和形狀函數，在振動和疲勞裂紋的分析中，採用呼吸式裂紋模型代替傳統開放式裂紋模型。開放式裂紋勁度的推導採用破壞力學的理論。而Mathieu方程式和無裂紋時之勁度則採用Galerkin’s method來進行推導。在振動的部份則使用四階Runge-Kutta method計算振幅對週期性負載的關係。在疲勞裂紋成長上，採用Modified Forman model計算出疲勞裂紋成長與次數之間的關係。刺激頻率和摩擦裂阻尼效應對疲勞壽命之影響，以及振動與疲勞之間的交互作用，在本文中將逐一討論。
對於本文中，採用摩擦模型理論結合呼吸式裂紋模型所產生阻尼的變化、疲勞裂紋成長及頻率變化等現象來進行分析，定義方型與圓型截面樑之裂紋表面產生的摩擦係數，再利用此一摩擦係數，配合各種邊界條件的變化，裂紋摩擦阻尼對振動與疲勞裂紋成長的影響。本研究結果顯示，刺激頻率在0.1 ~ 0.2 時，裂紋阻尼無顯著影響，但刺激頻率在0.5 ~ 2 時，裂紋阻尼的影響相當明顯。

關鍵字

呼吸裂紋阻尼

並列摘要

ABSTRACT
In this study, the beam of circular or square cross section subjected to a cyclic loading is considered as Euler’s beam.The straight-edge type of crack locates at the center of beam.The damping due to the friction of crack surface is considered in which the damping ratio or loss factor is simulated as the model provided by Sanliturk and Imregun.
The equation of motion is derived by Hamilton’s principle, and the shape function is applied to satisfy the boundary conditions. The equation of motion is simplified to Mathieu equation by Galerkin’s method. For the crack, the breathing model of crack is used, and the stiffness corrected. In a cycle of vibration , the fourth order of Runge – Kutta method is applied to determine the amplitude of vibration, and The modified Forman model is applied to determine the rate fatigue crack growth. Both vibration and fatigue analyses are coupled cycle by cycle.
The effects of crack-friction damping on the vibration and fatigue crack growth is determined and discussed in this study. The results can be concluded that the crack-friction damping does not influence at the excite frequency 0.1 ~0.2 ,.and does evidently influence at 0.5 ~ 2 .

keywords:damping, fatique crack, loss factor, breathing crack, exciting frequency, amplitude,vibration.

並列關鍵字

loss factor

參考文獻

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