利用晶格波茲曼法結合壓電平板理論研究流固耦合下的壓電振動能量擷取系統

Development of Piezoelectric Energy Harvesting System in Fluid-Structure Interaction Based on Lattice Boltzmann Method and Piezoelectric Plate Theory

孔忠煦(Jung-Shiu Kung)

指導教授 ： 黃育熙

國立臺灣大學/工學院/機械工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202002374

摘要

本論文利用平板疊加法理論解析搭配晶格波茲曼法、有限元素模擬與實驗量測，探討陶瓷壓電雙晶片於單邊固定之邊界下的面外振動特性。理論解析首先利用線性壓電理論與力與力矩平衡條件式，將壓電三層結構等效為單層矩形平板參數，由於平板邊界條件共有八個，因此採用疊加法將平板拆成四個結構進行疊加，其特性為四個邊界條件會自動滿足，而剩下的四個邊界條件則可利用正交函數展開得到壓電平板在單邊固定邊界下的共振頻率與模態振形，接著再利用模態正交特性求出面外位移的暫態、穩態響應，以及壓電材料於正壓電效應的暫態電壓與穩態響應。接著利用晶格波茲曼法，模擬將圓柱複合平板置於流場後的渦街現象，計算流場造成的壓力代回理論解析獲得面外位移與電壓響應。
共振頻率、模態振形結果皆與有限元素分析數值計算結果進行比較，驗證理論分析之準確性與適用範圍，有限元素法進行單向耦合及雙向耦合模擬流場流經圓柱複合壓電平板結果皆可觀察出尾流的擾動，觀察壓電平板振動特性可發現單向耦合僅能觀察出平板的第一共振頻率，雙向耦合則能同時觀察到平板第一共振頻率以及流場激發的耦合頻率，而理論解析之晶格波茲曼法僅能觀察到流體頻率。
實驗量測方面使用電子斑點干涉術(AF-ESPI)針對壓電材料進行即時動態量測，紀錄模態振形與共振頻率，結合穩態掃頻之雷射都卜勒振動儀(LDV)量測結果進行比較，共振頻率與模態振形皆與理論、有限元素法符合。針對壓電材料在正壓電效應的發電效率，利用LDV及示波器同時量測壓電平板置於風洞的面外振動特性與電壓，由有限元素法與實驗量測的結果得知，雙向耦合較符合實驗結果，本論文開發的壓電平板結合流場以晶格波茲曼法最有效率且有一定的準確度。

關鍵字

壓電平板 ； 逆壓電效應 ； 疊加法 ； 晶格波茲曼法 ； 流固耦合 ； 單向耦合 ； 雙向耦合 ； 正壓電效應 ； 能量擷取系統 ； 風洞量測

並列摘要

This research analyzed the out-of-plate vibration and energy harvesting in clamped-free-free-free (CFFF) boundary condition which based on theoretical analysis with Lattice Boltzmann Method (LBM), finite element method (FEM) and experimental measurements. Theoretical analysis was used to derive the vibration characteristics of the piezoelectric plate under CFFF boundary condition and equivalent the material constants from three layers structure to a single layer structure. Then, applied superposition method to obtain the resonant frequencies and mode shapes of piezoelectric plate. Moreover, the orthogonality was used to estimate the out-of-plate mode shape and voltage generated by piezoelectric plate. Theoretical analysis also applied LBM to simulate flow around a cylinder and plate. This method was used to observe the vortex, and the pressure generated by flow was applied to plate. Therefore, the magnitude of pressure can be substituted to the of piezoelectric plate which mentioned before and calculate the out-of-plate vibration and voltage output.
In analysis of fluid-structure interaction, one-way coupled observe the first resonant frequency of piezoelectric plate and two-way coupled observe the first resonant frequency of piezoelectric plate and vortex frequency. The experimental measurements are used to obtain the dynamic characteristics of piezoelectric materials. The full-filed optically technique, called as amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), and the Laser Doppler Vibrometer (LDV) are used to obtain the vibration characteristics of piezoelectric plate. The results of resonant frequencies and mode shapes with theoretical analysis, and FEM are consistent which experimental measurements. The experimental measurements of energy harvesting system are that utilize LDV and oscilloscope to measure the vibration characteristics and voltage output simultaneously. As piezoelectric plate into wild tunnel, the results are corresponding to the simulation by two-way coupled system. In this study, high accuracy and the efficient analyzed method are developed by combination with LBM and piezoelectric plate theory.

並列關鍵字

piezoelectric plate ； converse piezoelectric effect ； superposition method ； LBM ； fluid-structure interaction ； one-way coupled system ； two-way-coupled system ； direct piezoelectric effect ； energy harvesting system ； wild tunnel

參考文獻

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