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標題: 利用模態方程式與頻率比等高線圖檢測樑裂縫之研究
Crack identification of cracked beam with mode shapes and frequencies ratio contours
作者: 王志雄
Wang, Chih-Shiung
關鍵字: cracked beam;裂縫樑;Sectional flexibility factor;Identification;斷面彈性因子;檢測
出版社: 應用數學系所
引用: 1. G.C. Sih, Method of fracture analysis and solutions of crack problems, Noordhoff International Publishing, Leyden, Netherlands, 1973. 2. H. Tada, P.C. Paris and G.R. Irwin, The Stress Analysis of Cracks Handbook, Second edition, Paris Productions, Missouri, 1985. 3. L. Nobile, “Mixed mode crack initiation and direction in beams with edge crack,” Theoretical and Applied Fracture Mechanics, vol. 33, no. 2, pp. 107-116, 2000. 4. A.D. Dimarogonas and S.A. Paipetis, Analytical Methods in Rotor Dynamics, Applied Science Publishers Ltd, New York, 1983. 5. T.G. Chondros, A.D. Dimarogonas and J. Yao, “A continuous cracked beam vibration theory,” Journal of Sound and Vibration, vol. 215, no. 1, pp. 17-34, 1998. 6. N. Anifantis and A. Dimarogonas, “Stability of columns with a single crack subjected to follower and vertical loads,” International Journal of Solids and Structures, vol.19, no. 4, pp. 281-191, 1983. 7. W. M. Ostachowitz and M. Krawczuk, “Analysis of the effect of cracks on the natural frequencies of a cantilever beam,” Journal of Sound and Vibration, vol. 150, no. 2 , pp. 191-201, 1991. 8. H. P. Lin, S. C. Chang and J.D. Wu, “Beam vibrations with an arbitrary number of cracks,” Journal of Sound and Vibration, vol. 258, no. 5, pp. 987-999, 2002. 9. H. P. Lin and S. C. Chang, “Force response of cracked cantilever beams subjected to a concentrated moving load,” International Journal of Mechanical Sciences, vol. 48, no. 12, pp. 1456-1463, 2006. 10. A. S. Y. Alsabbagh, O. M. Abuzeid and M. H. Dado, “Simplified stress correction factor to study the dynamic behavior of a cracked beam,” Applied Mathematical Modelling, vol. 33, no. 1, pp. 127-139, 2007. 11. H. P. Lin, “Direct and inverse methods on free vibration analysis of simply supported beams with a crack,” Engineering Structures, vol. 26, no. 4, pp.427-436, 2004. 12. R. J. Lin and F. P. Cheng, “Multiple crack identification of a free-free beam with uniform material property variation and varied noised frequency,” Engineering Structures, vol. 30, no. 4, pp. 909-929, 2008.
這項研究提出一個新的裂縫樑結構斷面彈性因子來模擬單一裂縫樑之剛度。裂縫位置結構比擬為一扭轉彈簧,彈簧之彈性係數與裂縫深度比 有關。單一裂縫樑結構運動方程式遵守Euler-Bernoulli樑函數。本篇研究推導出的彈性係數中之修正因子 在裂縫深度與樑斷面深度比小於0.5時和近期學者研究結果相比較,達到良好的近似效果。應用修正因子 可計算出裂縫樑自然振動頻與相對應之mode shapes圖,並建立不同裂縫位置與深度的自然振動頻率比資料庫。利用頻率比資料庫建立裂縫樑前三個mode不同裂縫位置與深度的自然頻率比等高線圖,並可藉由自然頻率比等高線圖資料庫檢測出裂縫位置與深度。這個裂縫樑數值模式可作為檢測裂縫樑位置與深度的反算法。
關鍵字: 裂縫樑; 斷面彈性因子; 檢測

This research presents a new sectional flexibility factor to simulate the reduction of the stiffness of a single-edge open cracked beam. The structural model for crack of the beam is considered as a rotational spring which is related to the ratio of crack depth to the beam height, . The mathematical model of this single-edge open crack beam is considered as an Euler-Bernoulli beam. The modified factor, , derived in this research is in good agreement with previous researcher's results for crack depth ratio less than 0.5. The natural frequencies and corresponding mode shapes for lateral vibration with different types of single-edge open crack beams can then be evaluated by applying this modified factor . The database of natural frequencies ratios between cracked and uncracked beams with varied cracked locations and depths are built. The two-dimensional contour maps of frequencies ratios are constructed from the database for the first three modes of a cracked beam with various crack locations and depths. The location and crack depth can be identified from the frequencies ratio contours database. The numerical model of the cracked beam can be applied as an inverse method to identify cracks in structures.
Keywords: cracked beam; Sectional flexibility factor; Identification
其他識別: U0005-0311201114493300
Appears in Collections:應用數學系所

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