- 學位論文
裂紋與移動質量對懸臂樑振動與疲勞之影響
Effect of a Crack and a Moving Mass on the Vibration and Fatigue of a Cantilevered Beam
摘要
在本文中，考慮在方形截面樑和圓形截面樑的小變形量下，樑的振動過程受到一具有簡諧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，因此對含裂紋軸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。
並列摘要
In this study, the small deformations of rectangular cross section beam and circular cross section beam are considered. Including the simple harmonic motion, the moving mass is considered during vibration procedure. 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 are without crack derived by Galerkin’s method. For opening and breathing crack, the stiffnesses are used to replace the stiffness without crack. The 4th order Runge – Kutta method to determine the relation of amplitude and time is used. Modified Forman equation is used to calculate the relation of fatigue crack growth and loading cycles. 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 vibration and fatigue crack growth is lacking in the literature and the commercial software of fatigue, providing a procedure of coupling analysis for the cracked beam is the major accomplishment. (Keywords: moving mass, beam, vibration, fatigue crack growth )