電子斑點干涉術的開發與板結構於固液耦合振動特性的分析與量測

Development of Electronic Speckle Interferometry Analysis and Measurement on Vibration Characteristics of Plate Structure Coupled with Fluid

林揚中(Yang-Zhong Lin)

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(2018年)

https://doi.org/10.6342/NTU201802628

摘要

摘要
本文主軸以電子斑點干涉術(ESPI)的全場量測技術貫穿全文，並開發ESPI量測技術應用於量測穩態、靜態、動態振動特性和平板承受動態外力所產生之波傳行為，文中亦搭配其他實驗方法、有限元素法模擬和理論計算同時作分析量測，本文主要應用ESPI實驗量測固液耦合之共振頻率與共振模態之振動問題，分析水深造成平板共振模態變化與共振頻率降低之現象。
本文首先說明ESPI光學理論，並從理論計算中得知干涉條紋之實際位移量，面外量測鋁合金懸臂板以及面內量測碳酸鋇壓電材料，並將量測所得結果與有限元素法模擬比較。ESPI和光纖位移計(FS)量測矩形鋁合金與壓電雙晶片懸臂板之結果互相比較，將實驗結果與ESPI實驗計算之位移量作比較，結果顯示ESPI量測所得之實際位移具有微米級定量的量測精度。
懸臂板的暫態波傳分析則運用模態展開法的理論解析，以模態形狀和時間函數建構平板的暫態位移，此解析解可用於分析平板承受任何形式動態外力所產生的暫態行為，例如應變、位移、速度和加速度等。實驗設計一對PVDF壓電薄膜感測器量測真實鋼珠撞擊的波源歷時，輸入至理論解析與有限元模擬中，並且與實驗量測結果比較，探討動態外力與觀察點位置對於平板暫態行為之影響，並應用理論從實驗暫態訊號中反求平板上外力作用的撞擊點，結果顯示透過模態分析後挑選較好的觀察點與撞擊點即可反算較準確的撞擊點位置。
本文最後討論結構板耦合流體之振動特性，流固耦合振動分析以空氣中之模態形狀為基底，將流場中平板面外變形視為空氣中模態形狀的線性疊加，此概念可運用於分析懸臂板和三邊固定板與流體耦合之振動特性，實驗量測使用ESPI量測水下平板的共振頻率以及拍攝水下平板的全場模態形狀。ESPI實驗量測隨著水深深度改變而影響結構板的共振頻率與共振模態，並與有限元素法模擬結果比較，結果顯示平板耦合流體後共振頻率和模態形狀皆會出現變化，而且流體的水深和邊界都會對於平板振動特性產生影響，結果顯示實驗量測和有限元素法模擬相當吻合，模態形狀扭曲及變形現象兩者結果也皆能呈現。

關鍵字

流固耦合 ； 電子斑點干涉術 ； 暫態波傳 ； 振動 ； 共振頻率 ； 模態 ； 等向性平板

並列摘要

Abstract
The main content for this thesis involves in developing Electronic Speckle Pattern Interferometry (ESPI) techniques in measuring steady state, static and dynamic characteristics as well as exploring the wave propagation behavior of a plate subjected to dynamic external forces. Together with the use of different experimental equipments. The ESPI is used to measure the resonance frequency of the solid-liquid coupling structures and the vibration problems of resonance mode in order to analyze the effect of water depth variation on the model shape and frequency of plates. The experimental results are used to compare with results obtained by Finite Element Method (FEM) and theoretical calculations.
The ESPI optical system is first explained in which the actual displacement of the interference fringes is calculated. The steady-state out-of-plane measurements of the aluminum alloy cantilever plate and the steady-state in-plane measurements of barium carbonate piezoelectric material are used in comparison to the finite element method. Both static and dynamic measurements of the piezoelectric bimorph cantilever plate can be done using ESPI and Fotonic Sensor (FS). By comparing both results, it is shown that ESPI can be used to measure the actual displacement up to sub-micron sensitivity.
Superposition method is used to determine the resonant frequencies and the mode shapes of the rectangular plate by constructing the transient displacement of the plate based on mode shape and time function. This analytical solution of displacement can then be used to analyze the transient behavior of the plate subjected to any form of dynamic external force for strain, velocity and acceleration. The experiment is carried out using a pair of PVDF (polyvinylidene fluoride) to measure the impact source duration of the steel ball’s impact. The measurements are used to compare with theoretical analysis and finite element simulations. This explores the influence of dynamic external force and observation positions of the plate transient behavior and are used to inverse determination of the impact position of dynamic force on the plate from the experimental transient signal. The results of this experiment are shown that better observation and impact locations can be selected from the modal analysis.
The thesis also discuss the vibration characteristics of the coupled fluid-structure vibration analysis base on the mode shape in the air. The out-of-plane deformation of the flow field is considered as a linear superposition of the mode shape in the air which is then used to analyze the vibrational characteristics of fluid coupling between a cantilever plate and a fixed plate on three boundaries. This experiment can be carried out using ESPI to measure the resonant frequency and the full field mode shape of the plate invermged in water. The experiment measures the effect of the resonance frequency and the resonant modes for different water depth. Furthermore, the water depth and the boundary of the fluid will have an effect on the vibration characteristic of the plate. It can be concluded that the experimental measurements are quite consistent with the finite element method simulation where both the mode shape distortion and the deformation phenomenon can be presented.

並列關鍵字

fluid-structure interaction ； ESPI ； wave propagation ； vibration ； resonant frequency ； resonant mode shape ； isotropic material

參考文獻

劉泓嶔, 馬劍清, “PVDF感測器應用於結構系統之動態量測能力探討”, 國立台灣大學機械工程研究所碩士論文, 2011.

張鈞凱, 馬劍清, “位移與應變暫態波傳之實驗量測、理論分析以及數值計算”, 國立台灣大學機械工程研究所碩士論文, 2011.

參考文獻

Abrate, S. (2007). Transient response of beams, plates, and shells to impulsive loads. ASME 2007 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers.

Bacon, D. R. (1982). "Characteristics of a PVDF membrane hydrophone for use in the range 1-100 MHz." IEEE Transactions on Sonics and Ultrasonics 29(1): 18-25.