複材層板微破壞的音洩波傳研究

Abstract

複材層板微破壞的音洩波傳研究 研究生 ： 林 克 劼 指導教授 ： 尹 慶 中 國立交通大學機械工程研究所 摘 要 本論文以替代理論分析複材層板內部微破壞所產生的音洩波傳， 應用地震學之力矩張量模擬複材層板內的纖維斷裂、母材裂縫及等破壞之音洩波源，複材層板微破壞所產生的板波暫態波傳為力矩張量與格林函數之一階導函數的褶積。層板內部時諧集中負荷所產生的動態格林函數係以一階剪變形板理論推導獲得，並以數值積分方法將格林函數一階導函數的核函數，以雙波數二階齊次多項式近似，應用部分積分的疊代關係計算具有高度振盪性質的二維波數積分，層板微破壞所產生的音洩暫態波傳係以逆傅立葉快速轉換計算求得。數值模擬除了考慮傳統音洩感測器偵測結構表面的面外擾動，並分析撓性波與延性波面內位移的暫態波傳，可供次世代音洩感測器偵測結構面內位移或應變的參考。 以一階剪變形板理論近似三維彈性力學解，可以簡化複材層板之板波波傳的計算程序。依據基本撓性波頻散曲線的三維彈性力學解，應用簡單體法可求得一階剪變形板理論之剪變形修正係數的最佳值，確保近似解在音洩頻率範圍內具有良好的準確性。 撓性波近似解的截止頻率較正解的頻率低，沿纖維方向波傳之偏差量又明顯較其他波傳方向大，故一階剪變形板理論的近似解應限制應用於頻率與板厚乘積小於 的範圍。

Acoustic Emission Wave Progagation due to Microfractures in Composite Laminates Student : K. Jack Lin Advisor : Dr. Ching-Chung Yin Department of Mechanical Engineering National Chiao Tung University ABSTRACT Surface responses of acoustic emission waves resulted from microfractures in composite laminates is theoretically studied in this thesis. The representation theorem with seismic moment tensors is used to formulate dynamic responses due to formation of the micro-defects, such as fiber-breakage, matrix cracking, in composites. Transient responses of the acoustic emission waves are the convolutions of those moment tensors and their corresponding spatial derivatives of Green's functions. The convolution is evaluated by the Fourier transform technique. The Green's functions are represented in terms of two-dimensional wave number integrals in frequency domain and derived by the first order shear deformation plate theory. The integral kernels are approximated by the second-order homogeneous polynomials of dual variables. Numerical evaluations were carried out by an iteration scheme based on integration by parts of power series and the oscillatory exponential functions. The present method establishes the theoretical background not only for analysis of the out-of-plane AE waves but also for further understanding the in-plane motions measured by AE sensors of next generation. Instead of formulation by three-dimensional elasticity, the first order shear deformation plate theory can simplify the calculation of wave propagation of AE in laminates without loss of accuracy. In this thesis the shear deformation correction factors were obtained from the exact solutions of dispersion curves of the waves by simplex-based inverse method. The cut-off frequency of waves calculated by the first order shear deformation plate theory are lower than the exact solutions. The deviation becomes the most in orientation along the fibers. A good approximation was limited in the broad range of the product of frequency and plate thickness below .