PVDF薄膜應用於矩形平板結構的動態響應與波源歷時之數值分析與實驗量測

Abstract

PVDF薄膜具有延展性佳、易裁切、低密度、質量小以及Q值小等優點，使PVDF薄膜非常適合作為感測器，在許多領域中都有相關應用，例如水下流速計、微型麥克風、生醫科技的心跳監測器等。透過本實驗室開發的PVDF薄膜量測技術，可量測結構的面內應變和波源歷時，本文主要使用上述的PVDF薄膜量測能力，針對矩形薄板、不同厚度的厚板以及固液耦合的動態波傳問題作深入探討。 近年來本實驗室開發的PVDF薄膜量測技術已有很好的成果，在薄板的動態應變量測和波源歷時的擷取皆非常成熟，但對於面內應變訊號尚未完成定量，本文首先探討PVDF薄膜於懸臂板和CCCF平板上的面內應變量測，以平板理論解析解進行分析比對實驗訊號的波形和振幅之正確性，再進行時頻分析獲得平板各模態的阻尼比，比較長時間時理論訊號考慮阻尼效應的結果，是否和實驗訊號的振幅衰減情況相符。基於PVDF薄膜在薄板結構上的應變訊號量測之正確性，將量測物件擴展至CCCF水箱和薄殼腔體，以相同實驗方式量測不同水深對CCCF平板的影響。探討PVDF薄膜和光纖位移計量測平板的共振頻率、暫態訊號及阻尼比對水深的變化，顯示PVDF薄膜於固液耦合的動態波傳問題之量測能力依然很好。 本文亦探討PVDF薄膜應用於全自由邊界的厚板之暫態面內應變和波源歷時量測，藉由不同寬厚比的厚板之鋼珠撞擊實驗，將實驗應變訊號與有限元素法的模擬結果進行比較，歸納PVDF薄膜於厚板的波源歷時擷取方式，並確認其量測結果的正確性。最後探討鋼珠直接撞擊厚板的接觸時間和赫茲接觸理論的差異，將赫茲理論計算的波源歷時帶入有限元素法中，得到量測點的暫態面內應變模擬結果，與實驗訊號比對波形和振幅量值，進而整理、歸納不同厚度的實驗比較結果，驗證赫茲理論中波源歷時之波形和接觸時間能夠應用於厚板實驗，並修正且建立其波源歷時的模型。

There are many advantages of the PVDF films, such as flexibility, no limitations of size or shape, low density and mass, small Q value, which makes PVDF film very suitable as a sensor. PVDF films has applications in many fields, such as flow meter, pressure gage, microphone, heartbeat rate monitor. The time history of in-plane strain and impact history of the structure could be measured by the PVDF films. In this thesis, the PVDF film sensor has been used to measure the dynamic behaviors of rectangular thin plates, thick plates with different thicknesses and fluid-plate interaction system. Recently, the above mentioned measurement methods of the PVDF film have a good technology maturity. However, the quantitative measurement of the in-plane strain of the plates has not been completed yet. Firstly, this thesis obtains the transient in-plane strain of the cantilever and CCCF plate using PVDF films. According the theoretical analysis of the rectangular plate, the experimental signals are consistent with the transient results. The damping ratio for each resonant frequency is determined from the short-time Fourier analysis. The damping effect is considered in theoretic transient analysis for the long-time responses, and compared with the experimental signals. Based on the excellent result of the strain from PVDF film, the investigation is extended to the CCCF and finite water tank. The influence of different water depth on the CCCF plate is discussed base on the same experimental arrangement. From the results of the resonant frequency, transient signal, and damping ratio of PVDF and fotonic sensor, it is noted that the performance of PVDF films in fluid-structure interaction problem is also quite well. This thesis also performs the transient in-plane strain and impact history measurement of the thick plates with free boundary condition. Through the impact experiments of thick plate with different thickness, the comparison between experiment and FEM results are provided. We analyze the impact history from the PVDF film, and provide useful results. Finally, the contact time of the steel ball directly impacting the thick plates with different thickness are compared with the Hertz contact theory. The impact histories from Hertz theory are used in FEM to determine the transient in-plane strain results. The comparisons between the theoretical results and experimental strain signals are used to establish an impact formulation for the thick plate.