臺灣博碩士論文加值系統

在本文中，考慮在方形截面樑的小變形量下，樑的振動過程受到一具有脈衝運動型態的移動質量影響。利用漢米爾頓原理（Hamilton’s principle）來推導其運動方程式與邊界條件，開放式裂紋的勁度則使用破壞力學的理論來推導，無裂紋狀態時的勁度與Mathieu方程式是運用Galerkin’s的方法，使用開放式裂紋與呼吸式裂紋的勁度來替代無裂紋時的勁度。關於振幅與時間關係的計算，是使用四階的Runge-Kutta方法。在疲勞裂紋成長的部分，關於疲勞裂紋成長與負載次數的關係，則是使用Modified Forman方程式來做計算。再利用呼吸式裂紋的理論來分析振動對疲勞壽命的影響以及振動與疲勞之間的互相影響。在選擇裂紋模型時，使用呼吸式裂紋來描述頻率響應的現象與疲勞裂紋成長是較接近現實的。由於現有文獻以及分析軟體對耦合分析的缺乏，因此對具高速移動質量對梁樑的振動與疲勞裂紋成長，提供完整的分析步驟是本研究主要的貢獻

In this study, the small deformations of rectangular cross section beam are considered. Including the pulse motion, the high speed moving mass is considered during procedure of andysis vibration. The equation of motion and boundary conditions are derived by Hamilton’s principle. The stiffness with opening crack is derived by fracture mechanics. Mathieu equation and the stiffness without crack are derived by Galerkin’s method. For models of opening and breathing cracks, the stiffnesses are replace of by the definitions. The 4th order Runge – Kutta method is used to determine the relation of amplitude and time. Modified Forman equation is used to calculate the relation of fatigue crack growth and loading cycles. Since the stiffness depends on the crack length, the corrected of stiffness is determined cycle by cycle. The effect of vibration on fatigue life and the interaction between vibration and fatigue are analyzed by breathing crack theory. That the breathing crack model is applied to describe the phenomenon of frequency response and fatigue crack growth is more realistic. The Coriolis and Centrifugal force effect the vibration and fatigue crack growth and this kinds of literature and the commercial software of fatigue is lacking, providing a procedure of coupling analysis for the cracked beam is the major accomplishment.

CONTENTS
摘 要…………………………………………………………………..…i
ABSTRACT……………………………………………………………...ii
誌 謝……………………………………………………………………iii
第一章 前言…………………………………………………………….iv
第二章 運動方程式…………………………………………………….vi
第三章 裂紋模型……………………………………………………….xi
第四章 分析程序……………………………………………………...xiii
第五章 疲勞裂紋成長…………………………………………...…..xviii
第六章 結果與討論……………………………………………….....xxiv
第七章 結論…………………………………………...…………….xxvii
CONTENTS…………………………………………………………..xxix
LIST OF TABLES…………………………………………….………xxxi
LIST OF FIGURES…………………………………………………..xxxii
NOMENCLATURE……………………………………………..…xxxviii

CHAPTER 1. INTRODUCTION………………………………………..1

CHAPTER 2. EQUATION OF MOTION……………………………….5
2.1 PROBLEM DESCRIPTION AND ASSUMPTIONS………….....5
2.2 HAMILTON’S PRINCIPLE……………………………………...6

CHAPTER 3. THE CRACK MODEL………………………………….10

CHAPTER 4. ANALYTICAL PROCEDURE………………………….12
4.1 DETERMINING THE ADDITIONAL COMPLIANCE OF RECTANGULAR CROSS SECTION…..……………………..12
4.2 DETERMINING THE OPENING, BREATHING, AND NO CRACK STIFFNESS…………………………………………..15

CHAPTER 5. FATIGUE CRACK GROWTH………………………….20
5.1 MODIFIED FORMAN EQUATION………………..…………..20
5.2 CRACK GROWTH ANALYSIS………………………………..22
5.3 FATIGUE FAILURE CRITERIA………………………………..24
5.4 FATIGUE CRACK GROWTH ANALYSIS STEPS…………….25

CHAPTER 6. RESULTS AND DISCUSSION…………………………26
6.1 TRANSIENT VIBRATION WITHOUT CRACK GROWTH…..26
6.2 CRACK DEPTH RATIO ………………………..…………....27
6.3 CORIOLS AND CENTRIFUGAL FORCES AFFECTED BY THE MOVING MASS………………………………………………...27
6.4 COUPLING ANALYSIS OF VIBRATION AND FATIGUE GROWTH…………………………………………………….….27

CHAPTER 7. CONCLUSION………………………………………….30

REFERENCES………………………………………………………….32

TABLES………………………………………………………………...35

FIGURES……………………………………………………………….36

簡 歷…………………………………………………………………....67

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