纖維繞線複材圓管的導波波傳與材料彈性常數之反算研究

Abstract

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.