含裂紋長方形平板之自然頻率研究

Study of Natural Frequency of Rectangular Plate with Crack

方建嵐(Chien-Lan Fang)

指導教授 ： 施延欣

中原大學/工學院/機械工程研究所/碩士(2001年)

https://doi.org/10.6840/cycu200100283

摘要

中文摘要
本研究對含直裂式裂紋長方形平板之自然頻率分析，利用ANSYS5.5版分析軟體建立二維之有限元素網格化平板。首先決定在裂紋近端之網格化模型，再加以計算含直裂式裂紋平板之自然頻率。在裂紋的幾何範圍上，取裂紋長度比為0.0到0.5，而平板之長寬比為0.5到2.5，考慮平板在不同之拘束條件(C-F-F-F和S-S-S-S)及在不同裂紋位置下，五個特徵值之自然頻率。得到之結果再跟現有之文獻做一比較，看其變化趨勢及誤差是否合理。最後根據ANSYS5.5所得到之含裂紋平板之自然頻率數據，利用曲線貼合的數值方法求取一組可計算無因次化自然頻率之雙參數多項式。結果可得到當裂紋長度增加時，長方形平板的自然頻率會減少。以及當平板受簡支撐時，長方形平板的長寬比增加，自然頻率也同時會增加。

關鍵字

裂紋 ； 平板 ； 自然頻率

並列摘要

ABSTRACT
The natural frequency of the rectangular plate with a straight crack analysis is investigated in this study. Using ANSYS5.5 software to build two dimensional finite element mesh of the rectangular plate, and selection the geometry of element mesh around crack tip, the natural frequency of the rectangular plate with the straight crack is determined. In the crack of geometry range, the ratio of crack length to the plate length is considered between 0.0 and 0.5. And the aspect ratio of the plate is considered between 0.5 and 2.5. The natural frequencies under the different boundary conditions (C-F-F-F and S-S-S-S) and the different positions of the crack length in the plate are considered. By comparing the natural frequency for different crack length with appropriated published results, the variations of natural frequency on center and edge location have been discussed. Based on ANSYS results of natural frequency of rectangular plate with straight crack, the dimensionless frequency parameters are determined by curve fitting technique. The dimensionless frequency parameter of the rectangular plate decreases with increasing of the crack length. The dimensionless frequency parameter of simply supported plate increases with the increasing the aspect ratio in this study.

並列關鍵字

natural frequency ； plate ； crack

參考文獻

1. A. W. Leissa, 1969 NASA SP-160. Vibration of plates

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5. K. M. Liew, K. C. Hung and M. K. Lim, 1994 Engineering Fracture Mechanics 48, 393-404. “A Solution Method For Analysis of Cracked Plates Under Vibration.”

6. B. Stahl and L. M. Keer, 1972 Int. J. Solids Structures 8, 69-91. “Vibration and Stability of Cracked Rectangular Plates.”