高速移動質量對樑的振動與疲勞裂紋成長之影響

Effect of High-Speed Moving Mass on the Vibration and Fatigue Crack Growth of Beams

張弘(Hung 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/cycu200400692

摘要

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

關鍵字

高速移動質量 ； 疲勞 ； 裂紋

並列摘要

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.

並列關鍵字

fatigue ； crack ； high speed moving mass

參考文獻

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