臺灣博碩士論文加值系統

本論文應用一階剪變形理論推導纖維繞線複材圓管導波的頻散方程式，並數值計算圓管之環向波、扭轉波、縱波及撓性波全模態導波的頻散曲線，探討圓管導波的波傳特性。一階剪變形近似解與等向性圓管導波頻散曲線之正解有良好一致性，卻節省大量的計算時間。根據等向性圓管導波的相速度頻散曲線，以簡單體法反算圓管的一階剪變形修正係數，結果顯示周向剪變形修正係數 與Mindlin的結果一致，軸向剪變形修正係數 則稍微大。纖維纏繞角度為 的複材圓管之各積層假設為橫向等向性材料，圓管的六個有效勁度係數係對應各積層的五個獨立彈性常數及繞線角。當複材圓管的纖維繞線角度加大時，扭轉波的相速度會增快，縱波波速則逐漸減緩，撓性波波速的改變將視其模態而定。將相速度頻散曲線 及 之解析解模擬成量測值，以簡單體法搜尋複材圓管頻散曲線量測值及理論值之平方差的極小值，反算結果顯示在較廣的初始值範圍，複材圓管的勁度係數 、 、 及 仍具有良好的收斂性，但是 及 的收斂性較差。

The first order shear deformation theory for analysis of guided wave propagation in anisotropic circular cylindrical shells is developed in this thesis to determine the elastic stiffness constants of a filament wound composite tube. The phase velocity and group velocity dispersion curves of circumferential waves, torsional waves, longitudinal waves and flexural waves are numerically calculated. The approximate theory with the best fit of shear deformation correction factors has a very good agreement with the exact solution for isotropic tubes within the framework of elasticity and save a large number of computation time. The best determination of the shear deformation correction factor in circumferential direction approaches to Mindlin’s estimation, but the axial one converges to a slightly larger value. The material in each filament of a composite tube is assumed to be transversely isotropic with its symmetry at the winding angle to the axis. As the winding angle increases, phase velocities of the torsional waves become greater and those of the longitudinal waves are decreasingly less. But changes in wave speeds of the flexural waves depend on each individual mode. Six effective stiffness constants, corresponding to five independent elastic constants and winding angle of the composite tube, are determined using simplex algorithm to search the best fit of the least squares of errors among those predicated and measured phase velocities of and modes. The results indicate that the stiffness components , , and achieve proper convergence in a broad range of initial guess values, but and converge under limited conditions.

中文摘要…………………………………………………………………… i
英文摘要…………………………………………………………………… ii
誌謝………………………………………………………………………… iv
目錄……………………………………………………………………….. v
圖表目錄…………………………………………………….………….. vii
第一章 緒論………………………………………………………………. 1
1.1 研究背景…………………………………………………………. 1
1.2 文獻回顧…………………………………………………………. 1
1.3 內容簡介…………………………………………………………. 4
第二章理論基礎…………………………………………………………. 5
2.1 圓管導波之波傳方式…………………………………………… 5
2.2 非等向性材料之本構方程式……………………………………. 5
2.2.1 正交性性材料……..………………………………………. 6
2.2.2 橫向等向性材料……………………………………………. 6
2.2.3 座標轉換之材料彈性係數………………………………….. 7
2.2.4 積層複材圓管的勁度係數………………………………….. 9
2.3 一階剪變形理論………………………………………………….. 10
2.4 圓管波傳之運動方程式………………………………………….. 11
2.5 時諧導波之頻散方程式………………………………………….. 14
2.5.1 扭轉波……………………………………………….……….. 14
2.5.2 縱波…………………………………………………………... 15
2.5.3 撓性波………………………………………………………... 17
2.5.4 環向波………………………………………………………... 19
2.6 剪變形修正係數的反算………………………………………….. 21
2.6.1 計算例………………………………………………………... 21
2.7 材料性質的反算………………………………………………….. 21
2.7.1 反算原理……………………………………………………... 22
2.7.2 計算例………………………………………………………... 22
第三章 結果與討論…………………………………………………….… 23
3.1 數值方法…………………………………………………………. 23
3.2 鋼管的頻散曲線…………………………………………………. 24
3.2.1 相速度……………………………………………….…….... 24
3.2.2 群速度……………………………………………….…….... 25
3.3 複合材料圓管的頻散曲線………………………………………. 26
3.4 剪變形修正係數…………………………………………………. 28
3.5 材料性質的反算…………………………………………………. 28
第四章 結論……………………………………………………………... 30
參考文獻…………………………………………………………………. 32
附錄A……………………………………………………………………. 35
附錄B……………………………………………………………………. 39
附表………………………………………………………………………. 46
附圖………………………………………………………………………. 48

[1]G. Herrmann and I. Mirsky (1956), “Three-dimensional and shell theory analysis of axially symmetric motions of cylinders,” ASME Journal of Applied Mechanics, 23, 563-568.
[2]D. C. Gazis (1959), “The three-dimension investigation of the propagation of waves in hollow circular cylinders-I. Analytical foundation; II. Numerial results,” J. Acout. Soc. Am., 31, 568-578.
[3]I. Mirsky (1964), “Vibrations of orthotropic, thick, cylindrical shells,” J. Acout. Soc. Am., 36, 41-51.
[4]I. Mirsky (1965), “Wave propagation in transversely isotropic circular cylinders, Part I: Theory; Part II: Numerical results,” J. Acout. Soc. Am., 37, 1016-1021.
[5]A. E. Armenakas (1965), “Torsional waves in composite rods,” J. Acout. Soc. Am., 38 , 439-446.
[6]J. H. Heimann and H. Kolsky (1966), “The propagation of elastic waves in thin cylindrical shells,” J. Mech. Phys. Solids, 14, 121-130.
[7]K. H. Huang and S. B. Dong (1984), “Propagating waves and edge vibrations in anisotropic composite cylinders,” Journal of Sound and Vibration, 96, 363-379.
[8]T. Kohl, S. K. Datta and A. H. Shah (1992), “Axially symmetric pulse propagation in semi-infinite hollow cylinders,” AIAA Journal, 30, 1617-1624.
[9]T. Kohl, S. K. Datta, A. H. Shah and N. Rattanawangcharoen (1992), “Mode-coupling of waves in laminated tubes,” Journal of Composite Materials, 26, 661-682.
[10]N. Rattanawangcharoen, A. H. Shah (1992), “Wave propagation in laminated composite circular cylinders,” International Journal of Solids and Structures, 29, 767-781.
[11]C. Y. Glandier, Y. H. Berthelot and J. Jarzynski (1992), “Wave-vector analysis of the forced vibrations of cylindrical shells of finite length,” J. Acout. Soc. Am., 92, 1985-1993.
[12]M. S. Caceci and W. P. Cacheris (1984), “Fitting curves to data: the simplex algorithm is the answer,” Byte, 340-362.
[13]M. R. Karim and A. K. Mal (1990), “Inversion of leaky Lamb wave data by simplex algorithm,” J. Acout. Soc. Am., 88, 482-491.
[14] A. G. Every and W. Sachse (1990), “Determination of the elastic constants of anisotropic solids from acoustic-wave group-velocity measurements,” Physical Review B, 42, 8196-8205.
[15] T. T. Wu and Y. H. Liu (1999), “Inverse determinations of thickness and elastic properties of a bonding layer using laser-generated surface waves,” Ultrasonics, 37, 23-30.
[16]R. D. Mindlin (1951), “Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates,” ASME Journal of Applied Mechanics, 31-38.
[17]林克劼，“複材層板微破壞的音洩波傳研究”， 國立交通大學機械工程研究所碩士論文,民國八十八年七月.
[18]駱東春，“圓管的導波波傳研究”， 國立交通大學機械工程研究所碩士論文,民國八十三年六月.
[19]K. F. Graff (1951), Wave Motion in Elastic Solids, Chap. 4, Dover Publications.
[20]I. Mirsky and G. Herrmann (1957), “Nonaxially symmetric motion of cylindrical shells,” J. Acout. Soc. Am., 29, 1116-1123.
[21]J. D. N. Cheeke, X. Li and Z. Wang (1995), “Characteristics of circumferential waves in thin walled tube acoustic devices,” IEEE Ultrasonic Symposium, 441-444.
[22]D. N. Alleyne, M. J. S. Lowe and P. Cawley (1998), “The reflection of guided waves from circumferential notches in pipes,” ASME Journal of Applied Mechanics, 65, 635-641.