臺灣博碩士論文加值系統

考慮在週期性扭矩與彎矩、剪力及均佈負載的影響下，含裂紋懸臂軸的小變形振動。在振動過程中，懸臂軸受到扭矩與彎矩、剪力及均佈負載的作用，以漢米爾頓(Hamilton)原理求取運動方程式和邊界條件，並用Galerkin’s method推導出Mathieu方程式。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計算出裂紋成長，對於不同裂紋型式的應力強度因子，利用K-effect。而週期性扭矩與彎矩及剪力負載會有不同的疲勞壽命的幾個實例以及振動與疲勞間的交互影響，都會在本文中探討。結合振動與疲勞的研究可以更客觀地描述疲勞裂緩成長的現象。當動態不穩定的情況發生時，裂紋會快速成長並導致疲勞壽命的降低，由結果顯示振動與疲勞明顯地相互影響。

A small deformation vibration of a cantilever cracked shaft under alternating torsional moment、bending moment、shear force and uniform load is considered. Including torsional moment、bending moment、shear force and uniform load, the equations of motion and boundary conditions are derived by Hamilton’s principle. Mathieu equation is derived by Galerkin’s method. Using Runge-Kutta method, the relation between amplitude and loading cycles is determined. The modified Forman model is applied to calculate the crack growth. Using K-effect, Combining the different stress intensity factors (SIF) of crack mode. Several cases of vibration with torsional moment、bending moment and shear force applied on the shaft are considered, and the interaction between vibration and fatigue is discussed in this study. Combining the analysis of vibration and fatigue can describe the phenomenon of fatigue crack growth more realistically. When the dynamic instability occurs, the crack grows fastly and the life of fatigue reduces. The results show that the fatigue and vibration are obviously interactive.

CONTENTS
中文摘要…………………………………………………………………i
Abstract…………………………………………………………………ii
誌謝 ………………………………………………………………… iii
Contents…………………………………………………………………iv
List of tables……………………………………………………………vi
List of figures……………………………………………………………vii
Nomenclature……………………………………………………………xiii
Chapter 1Introduction…………………………………………………1
Chapter 2Equation of motion………………………………………5
Chapter 3Local flexibility matrix………………………………………11
Chapter 4Analytical procedure………………………………………14
Chapter 5 Fatigue crack growth………………………………………21
Chapter 6 Result and discussion………………………………………25
Chapter 7 Conclusion …………………………………………………29
References…………………………………………………………………30
Tables ………………………………………………………………… 33
Figures …………… …………………………………………………… 35

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