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研究生:張建隆
研究生(外文):Chang, Chien Lung
論文名稱:利用Timoshenko梁理論分析脫層複合梁挫曲後振動分析
論文名稱(外文):Vibration of a composite beam of the through-width delamination relative to buckled states with Timoshenko-beam theory
指導教授:張明添簡國璋
學位類別:碩士
校院名稱:國立中興大學
系所名稱:土木工程學系
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:75
中文關鍵詞:複合材料振動挫曲頻率脫層
外文關鍵詞:compositevibrationpostbucklebuckledelaminationfrequency
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本文考慮一複合脫層梁挫曲後之變形及振動分析,並將剪力變形及轉動慣量考慮進控制方程式,梁之脫層為任意長度及任意厚度,梁兩端為固定邊界並承受軸向壓力.數值結果顯示複合材料對於挫曲後變形及其振動頻率影響甚鋸.
In this study, a composite laminated beam with through-width delamination subjected to axial load along two clamped edges is considered. The fiber of the layers with a composite laminated beam has different angles, and an across-the-width delamination is located between layers. Shear effect and rotary inertia terms, are taken into account in the governing equations of postbuckling deformation and vibration. Based on this model, postbuckling deformations of intact and delaminated beams are found analytically. By using the perturbation method, the frequencies of vibration of postbuckling state are found.
The numerical results show that the lengthwise delamination locations, delaminated length and thickness affect the postbuckling deformation and vibration frequency significantly. We found the out-of-phase modes also present in composite beam. It is almost a constant for interface 1 cases, but it decreases to small value or zero as the axial load increase for the others cases. The results of out-of-phase frequencies are different with Jane and Chen (1998) because material properties of composite make it.
Contents
Abstract 1
1. Introduction 2
2. Analysis Modeling 6
2-1 Basic Assumptions 6
2-2 Postbuckling Deformation 8
2-2-1 Governing Equation of Postbuckling Deformation 8
2-2-2 Formulation of Postbuckling Deformation 9
2-3 Vibration of a Delaminated Beam 12
2-3-1 Governing Equation of Vibration of a Delaminated Beam 12
2-3-2 Formulation of Vibration of a Delaminated Beam 13
3. Examples 18
3-1 Specimen Configuration 18
3-2 Result and Disscussion 20
3-2-1 Postbuckling Deformation 20
3-2-2 Frequencies of Vibration of Postbuckled states 55
Conclusions 62
References 63
Appendix: The coefficient of the deflection functions and B matrix 66
1. The coefficient of the deflection functions 66
2. B matrix 68
List of FiguresFigure 1. Modeling of Delamination 7
Figure 2. Sign Convention in Bending and Compressing 8
Figure 3. Sign Convention in Bending, Compressing and inertial forces 12
Figure 4 interface 1, L1 = 1 ft, 3 ft delamination : P= 0.1 Pcr, P = 0.2 Pcr and P =0.3 Pcr 23
Figure 5 interface 1, L1 = 1 ft, 3 ft delamination : P= 0.4 Pcr, P = 0.5 Pcr and P =0.6 Pcr 24
Figure 6 interface 1, L1 = 1 ft, 3 ft delamination : P= 0.7 Pcr, P = 0.8 Pcr and P =0.9 Pcr 25
Figure 7 interface 1, L1 = 2 ft, 3 ft delamination : P= 0.1 Pcr, P = 0.2 Pcr and P =0.3 Pcr 26
Figure 8 interface 1, L1 = 2 ft, 3 ft delamination : P= 0.4 Pcr, P = 0.5 Pcr and P =0.6 Pcr 27
Figure 9 interface 1, L1 = 2 ft, 3 ft delamination : P= 0.7 Pcr, P = 0.8 Pcr and P =0.9 Pcr 28
Figure 10 interface 1, L1 = 1 ft, 5 ft delamination : P= 0.1 Pcr, P = 0.2 Pcr and P =0.3 Pcr 29
Figure 11 interface 1, L1 = 1 ft, 5 ft delamination : P= 0.4 Pcr, P = 0.5 Pcr and P =0.6 Pcr 30
Figure 12 interface 1, L1 = 1 ft, 5 ft delamination : P= 0.7 Pcr, P = 0.8 Pcr and P =0.9 Pcr 31
Figure 13 interface 1, L1 = 2 ft, 5 ft delamination : P= 0.1 Pcr, P = 0.2 Pcr and P =0.3 Pcr 32
Figure 14 interface 1, L1 = 2 ft, 5 ft delamination : P= 0.4 Pcr, P = 0.5 Pcr and P =0.6 Pcr 33
Figure 15 interface 1, L1 = 2 ft, 5 ft delamination : P= 0.7 Pcr, P = 0.8 Pcr and P =0.9 Pcr 34
Figure 16 interface 2, L1 = 1 ft, 3 ft delamination : P= 0.1 Pcr, P = 0.2 Pcr and P =0.3 Pcr 35
Figure 17 interface 2, L1 = 1 ft, 3 ft delamination : P= 0.4 Pcr, P = 0.5 Pcr and P =0.6 Pcr 36
Figure 18 interface 2, L1 = 1 ft, 3 ft delamination : P= 0.7 Pcr, P = 0.8 Pcr and P =0.9 Pcr 37
Figure 19 interface 2, L1 = 2 ft, 3 ft delamination : P= 0.1 Pcr, P = 0.2 Pcr and P =0.3 Pcr 38
Figure 20 interface 2, L1 = 2 ft, 3 ft delamination : P= 0.4 Pcr, P = 0.5 Pcr and P =0.6 Pcr 39
Figure 21 interface 2, L1 = 2 ft, 3 ft delamination : P= 0.7 Pcr, P = 0.8 Pcr and P =0.9 Pcr 40
Figure 22 interface 2, L1 = 1 ft, 5 ft delamination : P= 0.1 Pcr, P = 0.2 Pcr and P =0.3 Pcr 41
Figure 23 interface 2, L1 = 1 ft, 5 ft delamination : P= 0.4 Pcr, P = 0.5 Pcr and P =0.6 Pcr 42
Figure 24 interface 2, L1 = 1 ft, 5 ft delamination : P= 0.7 Pcr, P = 0.8 Pcr and P =0.9 Pcr 43
Figure 25 interface 2, L1 = 2 ft, 5 ft delamination : P= 0.1 Pcr, P = 0.2 Pcr and P =0.3 Pcr 44
Figure 26 interface 2, L1 = 2 ft, 5 ft delamination : P= 0.4 Pcr, P = 0.5 Pcr and P =0.6 Pcr 45
Figure 27 interface 2, L1 = 2 ft, 5 ft delamination : P= 0.7 Pcr, P = 0.8 Pcr and P =0.9 Pcr 46
Figure 28 interface 3, L1 = 1 ft, 3 ft delamination : P= 0.7 Pcr, P = 0.8 Pcr and P =0.9 Pcr 47
Figure 29 interface 3, L1 = 2 ft, 3 ft delamination : P = 0.8 Pcr and P =0.9 Pcr 48
Figure 30 interface 3, L1 = 1 ft, 5 ft delamination : P= 0.2 Pcr, P = 0.3 Pcr and P =0.4 Pcr 49
Figure 31 interface 3, L1 = 1 ft, 5 ft delamination : P= 0.5 Pcr, P = 0.6 Pcr and P =0.7 Pcr 50
Figure 32 interface 3, L1 = 1 ft, 5 ft delamination : P = 0.8 Pcr and P =0.9 Pcr 51
Figure 33 interface 3, L1 = 2 ft, 5 ft delamination : P= 0.1 Pcr, P = 0.2 Pcr and P =0.3 Pcr 52
Figure 34 interface 3, L1 = 2 ft, 5 ft delamination : P= 0.4 Pcr, P = 0.5 Pcr and P =0.6 Pcr 53
Figure 35 interface 3, L1 = 2 ft, 5 ft delamination : P= 0.7 Pcr, P = 0.8 Pcr and P =0.9 Pcr 54
Figure 36 Frequencies versus the axial load (interface 1, L1 = 1 ft, 3 ft delamination) 58
Figure 37 Frequencies versus the axial load (interface 1, L1 = 2 ft, 3 ft delamination) 58
Figure 38 Frequencies versus the axial load (interface 1, L1 = 1 ft, 5 ft delamination) 58
Figure 39 Frequencies versus the axial load (interface 1, L1 = 2 ft, 5 ft delamination) 59
Figure 40 Frequencies versus the axial load (interface 2, L1 = 1 ft, 3 ft delamination) 59
Figure 41 Frequencies versus the axial load (interface 2, L1 = 2 ft, 3 ft delamination) 59
Figure 42 Frequencies versus the axial load (interface 2, L1 = 1 ft, 5 ft delamination) 60
Figure 43 Frequencies versus the axial load (interface 2, L1 = 2 ft, 5 ft delamination) 60
Figure 44 Frequencies versus the axial load (interface 3, L1 = 1 ft, 3 ft delamination) 60
Figure 45 Frequencies versus the axial load (interface 3, L1 = 2 ft, 3 ft delamination) 61
Figure 46 Frequencies versus the axial load (interface 3, L1 = 1 ft, 5 ft delamination) 61
Figure 47 Frequencies versus the axial load (interface 3, L1 = 2 ft, 5 ft delamination) 61
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