疲勞裂紋成長對含呼吸式裂紋樑的振動之影響

Effect of Fatigue Crack Growth on the Vibrational Response of a Beam with Breathing Crack

郭銅城(Tung-Cheng Kuo)

指導教授 ： 施延欣

中原大學/工學院/機械工程研究所/碩士(2002年)

https://doi.org/10.6840/cycu200200551

摘要

摘要
在本文中探討一直裂式裂紋圓形截面及方形截面樑在不同的邊界條件之下，受一週期性集中力之小變形振動。在振動過程中，考慮非保守力之影響並使用漢米爾頓(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強度則採用Galerkin’s method推導。在振動的部份則使用Runge-Kutta的方法來描述振幅對負載週期的關係。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。在振動和疲勞裂紋的分析中本文採用呼吸式裂紋模型代替傳統使用開放式裂紋模型。對於頻率的變化、疲勞裂紋成長，使用呼吸式裂紋模型分析可以更客觀的描素振動的過程和裂紋成長的現象。

關鍵字

疲勞裂紋 ； 呼吸式 裂紋

並列摘要

ABSTRACT
In this study, the small deformations of rectangular cross section beam and circular cross section beam with different boundary conditions are considered. Including the alternating concentration force, the non – conservative force is considered during vibration procedure. The equation of motion, and boundary conditions are derived by Hamilton’s principle. Opening crack stiffness are derived by fracture mechanics. Mathieu equation and no crack stiffness are derived by Galerkin’s method. Using 4th order Runge – Kutta method to determined the relation of amplitude and time. The modified Forman equation are used to calculate the relation of fatigue crack growth and loading cycles. The effects of damping and exciting frequency on amplitude and fatigue life, the effect of vibration on fatigue life and the interaction between vibration and fatigue are analyzed by breathing crack theory. While using breathing crack model to describe the phenomenons of frequency response and fatigue crack growth are more realistic.

並列關鍵字

fatigue crack ； breathing crack

參考文獻

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