含裂紋長方形平板之振動與疲勞裂紋成長耦合分析

Coupling Analysis of Vibration and Fatigue CrackGrowth for the Cracked Rectangular Plates

吳貫遠(Guan-Yuan Wu)

指導教授 ： 施延欣

中原大學/工學院/機械工程研究所/博士(2001年)

https://doi.org/10.6840/cycu200100398

摘要

中文摘要

本文中主要對含邊緣裂紋平板分析其振動與疲勞裂紋成長的耦合影響。依據Von Karman的平板理論，推導含裂紋平板的運動方程式，其振動受平面向力的作用、不同裂紋長度和縱橫比(aspect ratio)影響。文中，運用Galerkin的方法，將統御方程式化簡為一個以時間為變數的Mathieu方程式、至於暫態振動的部份，則使用Runge-Kutta的方法，將振幅對時間及速度對振幅的圖表結果，分別繪出。而在動態不穩定方面，則以增量調合平衡法求得其動態不穩定區域。在疲勞裂紋成長上，則採用Forman 的方程式和振動時形成之應力關係同步進行計算，而得有關振動對疲勞裂紋的影響，裂紋成長對振動的關係也同時被描述及探討。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的相互影響。由於文獻及現有分析軟體對耦合分析的缺乏，因此對含裂紋平板的振動與疲勞裂紋成長的耦合分析，提供一個完整的分析步驟是本研究主要的貢獻。

關鍵字

疲勞裂紋成長 ； 平板裂紋 ； 邊緣裂紋 ； 振動

並列摘要

ABSTRACT

The coupling analysis of vibration and fatigue crack growth for the rectangular plate with an edge crack is presented. The modified Forman’s equation is employed to fatigue crack growth, and the plate equations of von Karman’s theory is considered in vibration analysis. The equations of vibration are reduced to an ordinary differential equation by assuming mode shapes and Galerkin’s procedure. The displacement ratio and natural frequency are determined by means of Runge-Kutta scheme. The incremental harmonic balance (IHB) method is applied to determine the region of dynamic stability. The results for square and rectangular cracked plates are provided in this study. The modified Forman’s equation for crack propagation and Runge-Kutta procedure for vibrating displacement ratio are simultaneously employed cycle by cycle. The effect of vibration on fatigue crack growth of the cracked rectangular plate is determined and discussed. The unsteady vibration affects to the fatigue life evidently. Since the coupling analysis of 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 plate is the major accomplishment.

並列關鍵字

cracked plate ； fatigue crack growth ； edge crack ； vibration

參考文獻

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