位移與應變暫態波傳之實驗量測、理論分析以及數值計算

Experimental Measurement, Theoretical Analysis and Numerical Calculation of Transient Wave Propagation of Displacement and Strain

張鈞凱(Chun-Kai Chang)

指導教授 ： 馬劍清

國立臺灣大學/工學院/機械工程學研究所/碩士(2011年)

https://doi.org/10.6342/NTU.2011.00919

摘要

壓電薄膜感測器(PVDF)與布拉格光纖光柵(FBG)，是近年來常被學者研究的兩種感測器。本文主要利用PVDF感測器可量測壓力的特性，將其黏貼於待測物表面以獲得動態外力作用的波源歷時，利用此方法獲得外力的優點在於PVDF本身輕薄不影響待測物系統、易黏貼於各待測物表面且具有優異的動態量測能力，本文也建立PVDF量測動態外力作用於薄板結構的方法。另一方面，研究中將利用FBG能量調變法來量測結構物的應變與位移並與其他感測器比較，針對FBG三維量測系統的動態量測能力做相關的探討。
本文利用量測到的波源歷時配合理論分析與有限元素法數值計算(ABAQUS)來獲得結構物的暫態波傳行為。其中理論計算本文利用兩種方法分析分別為模態疊加法與拉普拉斯轉換法，對於拉普拉斯轉換域下的逆轉換計算通常是很複雜的，為了使計算更簡單與有效率，我們利用Durbin拉普拉斯數值逆轉換的方式來獲得半解析半數值的理論解，並利用模態疊加法的理論正解來驗證拉普拉斯轉換法配合Durbin拉普拉斯數值逆轉換的正確性。在大多數工程結構問題上要獲得理論解是不容易的工作，因此本文也利用有限元素法模擬結構物的暫態波傳行為。最後將理論分析與有限元素法數值計算的結果與實驗量測比較，驗證實驗量測的正確性。

關鍵字

布拉格光纖光柵 ； 壓電薄膜 ； PVDF ； 有限元素法 ； 能量調變法 ； 暫態波傳 ； 波源歷時 ； 模態疊加法 ； 拉普拉斯轉換法 ； 數值拉普拉斯逆轉換

並列摘要

Recently, piezoelectric film(PVDF) and fiber Bragg grating(FBG) are usually investigated by researcher. We use the FBG with power modulated sensing method to measure strain and displacement of the structure, and compared the sensing results with other sensors. Also, we investigate and discuss the dynamic measurement ability of the three-dimensional FBG measurement system. Then, PVDF can be used to measure pressure and dynamic external force history and has many advantages such as light, thin, excellent dynamic measurement ability and easy to adhesive on the object surface. In this thesis, we establish a measurement method to measure the dynamic force history on thin plate structures.
We can use the force history to conduct theoretical analysis and numerical calculation of finite element method(ABAQUS) then obtain the results of transient wave propagation within the structure. In theoretical analysis, we use the normal mode method and the Laplace transform method to calculate the results of transient wave propagation within the structure. For the Laplace transform method, it’s difficult to derive the inversion in transform domain. Therefore, we use the Durbin numerical inversion method to inverse the solution in transform domain and the inversion can be easier and more efficient. Besides, we use the exact solution determined by normal mode method to compare with the solution determined by Laplace method. It’s not easy to obtain the theoretical solution of transient wave propagation within the structure in most of engineering structure issue, thus, we can use the finite element method to estimate it. Finally, we compare the transient response of theoretical analysis, finite element method and experimental measurement to verify the accuracy of experimental measurement.

並列關鍵字

fiber Bragg grating ； piezoelectric film ； PVDF ； finite element method ； power modulated sensing method ； transient wave propagation ； force history ； normal mode method ； Laplace transform method ； numerical inversion of Laplace

參考文獻

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