平板之雷射超音波的生成與量測

Abstract

本論文探討金屬平板上之雷射超音波的生成與偵測，應用於鋁板之非接觸超音波檢測。鋁板微熱輻射吸收率低之等方性平板，單點聚焦之雷射超音波生成技術較難在平板結構上產生高頻之板波，為了探討雷射超音波生成板波的機制，本研究以一階剪變形板理論為基礎，推導格林函數及其一階導函數，以力矩張量模擬等方性平板受脈衝雷射瞬間加熱所產生的熱膨脹應變，以替代理論模擬生成之超音波波傳。格林函數導函數的數值積分係將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式計算具有高度振盪性質的二維波數積分，雷射超音波之暫態波傳係以逆傅立葉快速轉換計算求得。 等方性平板表面受點聚焦雷射加熱產生均勻的熱應變，僅會產生撓性波與延性波，無法生成 板波。數值模擬結果顯示雷射生成之撓性波具有明顯的頻散現象，且振盪次數隨著試片厚度減薄而增加。因為一階剪變形板理論之 板波的相速度在相同頻率下均小於三維彈性力學解，所以一階剪變形板理論的數值結果應限制適用範圍低於 板波的截止頻率(約 )。本研究並建構一外差式雷射干涉儀的雛形，可供量測平板試片面外位移的暫態波傳訊號。

Surface responses of laser-induced ultrasound in metal plates are studied in this thesis to establish theoretical background for laser-based ultrasonic nondestructive evaluation technology. The representation theorem with seismic moment tensors is used to formulate dynamic responses of plate waves caused by the surfaces of specimens rapidly insonified by point-focus pulsed laser. Transient responses of the thermo-elastic waves are convolutions of those moment tensors and their corresponding spatial derivatives of Green's functions. The Green's functions are derived by the first order shear deformation plate theory and represented as a two-dimensional wave number integrals in frequency domain without loss of generality. Numerical evaluations were carried out by an iteration scheme based on integration by parts of the oscillatory exponential functions and power series, which approximated the integral kernels. The convolution was evaluated by the Fourier transform technique. The point-focus pulsed laser results in both extensional and flexural waves in isotropic plates. But the SH plate waves can not be generated because of uniform thermal expansion in all directions of the isotropic specimen. Numerical results showed that the laser-induced flexural wave features significant dispersion and the oscillating cycles increase with the decrease of plate thickness. The phase velocities of waves predicted by the first order shear deformation plate theory are less than those of exact solutions. A good approximation was achieved in the broad frequency range below the cut-off frequency of waves about 1.7 MHz’mm. A prototyped heterodyne laser interferometer was also developed for future measurement of out-of-plane motion of laser-induced plate waves.