具中心裂紋或雙邊裂紋之長方形平板的振動與疲勞裂紋成長耦合分析

Coupling Analysis of Vibration and Fatigue Crack Growth for Rectangular Plates with Central Crack or Cracks at Opposite Edges

莊鴻志(Hung-Chih Chuang)

指導教授 ： 施延欣

中原大學/工學院/機械工程研究所/碩士(2002年)

https://doi.org/10.6840/cycu200200548

摘要

摘 要

本研究探討中心裂紋或雙邊裂紋之長方形平板的振動與疲勞裂紋成長耦合的影響。依據von Karman 的大變形平板理論推導出運動方程式以及考慮modified Forman方程式去計算疲勞裂紋成長。運用 Galerkin的方法，將統御方程式化簡成一以時間為變數的Mathieu方程式。對於振幅、疲勞裂紋成長和自然振動頻率的關係，則利用Runge-Kutta的方法去求得再加以圖示出來。至於非線性自然頻率部分，也是運用Runge-Kutta的過程去先求得頻率比再去獲得非線性自然頻率。在動態不穩定方面，則以增量平衡調和法求得不穩定區域。
事實上，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，由結果可知振動與裂紋成長是互相影響的。在一般的文獻上對於振動與裂紋成長的耦合影響是不考慮的，因此本研究提供了一個對於中心裂紋或雙邊裂紋平板的完整分析步驟是主要的貢獻成果。
關鍵字：
中心裂紋、雙邊裂紋、振動、非線性自然頻率、動態不穩定、疲勞裂紋成長

關鍵字

中心裂紋 ； 雙邊裂紋 ； 振動 ； 非線性自然頻率 ； 動態不穩定 ； 疲勞裂紋成長

並列摘要

ABSTRACT
The coupling analysis of vibration and fatigue crack growth for rectangular plate with central crack or cracks at opposite edges is presented. The equations of motion for generally isotropic plates based on von Karman’s theory are considered in vibration analysis, and the modified Forman’s equation is employed to fatigue crack growth. The governing equations are reduced to Mathieu equation that is nonlinear equation by assuming mode shapes and Galerkin’s procedure. The relationships of amplitude, fatigue crack growth, natural frequency and loading cycles on cyclic vibration are determined by Rung-Kutta procedure and the modified Forman’s equation for crack propagation. The nonlinear natural frequency for Mathieu equation is obtained by Rung-Kutta scheme with corrected frequency ratio. The incremental harmonic balance method is applied to determine the region of dynamic instability. The results for square and rectangular cracked plates are provided in this study.
The interactive of vibration and fatigue crack growth in loading cycles for cracked plates are determined and discussed. Since the coupling analysis of vibration and fatigue crack growth is lacking in the literature, this study provided an analytical procedure for the cracked plate is the major contributions.
Keyword: central crack, crack at opposite edges, vibration, nonlinear natural frequency, dynamic instability, fatigue crack growth

並列關鍵字

crack at opposite edges ； fatigue crack growth ； dynamic instability ； central crack ； nonlinear natural frequency ； vibration

參考文獻

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5. K. Neku. “Free vibration of a simply supported rectangular plate with straight through-notch”, Bull. of JSME., 25, pp. 16-23, 1982.

6. R. Solecki. “Bending vibration of a simply supported rectangular plate with a crack parallel to one edge”, Engrg. Frac. Mech., 18(6), pp. 1111-1118, 1983.