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研究生: 洪育凱
Hung, Yu-Kai
論文名稱: 貼附有壓電片之多跨距Mindlin板承受移動負載之動態分析
Dynamic Analysis of Moving Load on Multi-span Mindlin Plate Surface-Mounted with Piezoelectric Layer
指導教授: 王榮泰
Wang, Rong-Tyai
學位類別: 碩士
Master
系所名稱: 工學院 - 工程科學系
Department of Engineering Science
論文出版年: 2018
畢業學年度: 106
語文別: 中文
論文頁數: 78
中文關鍵詞: 多跨距之簡支撐板壓電片模態法移動負載電荷
外文關鍵詞: Multi-span Mindlin plate, Piezoelectric, modal analysis, moving load, electric charge
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  •   本文探討一塊貼附有壓電片之多跨距Mindlin簡支撐板在承受移動負載時的振動分析,結構上層為鋁板,並在其下方貼附有壓電片。利用模態法來計算整體結構之自然振動頻率,並探討此多跨距結構板在承受移動負載下之動態響應。
      模態法方面,為了解壓電簡支撐板之力學行為,需利用應力場、應變場及結構位移關係於求出應變能、動能。再以Hamilton’s principle建立 結構之運動方程式,進而求得模態頻率與模態函數,並探討在不同結構參數的情況下對於模態頻率之影響。
      應用模態法分析結果為基礎,在結構上施加一移動負載,接著利用模態疊加法及Runge-Kutta數值方法求解結構承受移動負載之動態響應,進而探討結構之響應、電荷收集情形、壓電效應電壓,最後也探討移動負載之速度對於整體結構響應的變化,以及找出移動負載之臨界速度。

    The purpose of this thesis is to explore the dynamic analysis of the multi-span Mindlin plate with a piezoelectric segment surfaced-mounted on each span. The governing equations and boundary conditions of the entire plate are derived via the Hamilton’s principle. The natural frequencies and the corresponding sets of mode shape functions are obtained by analytical method. The method of modal analysis is adopted to investigate the dynamic responses of the host plate and the electric charge accumulated on the surfaces of the piezoelectric segment caused by a moving load. The effects of moving velocity of the load and the geometric parameters of the piezoelectric segment on both histories of the displacement of the host plate and the electric charge accumulation on the piezoelectric surfaces are investigated.
    There is a critical velocity of the moving load to cause the absolute maximum deflection of the host plate. Furthermore, there is another critical velocity of the moving load to induce make the absolute maximum electric charge on the surfaces of the piezoelectric segment. As the number of span is increased, the maximum displacement at the center of the first span of the simply-supported multi-span plate is reduced.

    摘要 I Extended Abstract II 誌謝 VI 目錄 VII 表目錄 X 圖目錄 XII 符號說明 XV 第一章 緒論 1 1-1 研究動機與目的 1 1-2 文獻探討 2 1-3 論文架構 4 1-4 論文架構流程 5 1-5 基本假設 6 第二章 研究方法及內容 7 2-1 研究模型設定 7 2-1-1 幾何結構 7 2-1-2 位移函數 9 2-1-3 鋁板之位移、轉角、應力、應變、應變能 11 2-1-4 壓電材料基本參數 13 2-1-5 壓電材料位移、轉角、應力、應變、應變能 15 2-1-6 結構方程式與邊界條件 18 2-2 模態法分析 21 2-2-1 改寫結構的運動方程式 21 2-2-2 以矩陣形式表示位移函數及合力場函數 23 2-2-3 自然振動頻率 28 2-3 承受負載分析 31 2-3-1 移動負載響應 31 2-3-2 Runge-Kutta 法解移動負載方程式 33 第三章 案例討論與數據分析 36 3-1 材料參數設定 36 3-2 自然頻率與模態 37 3-2-1 結構自然頻率 37 3-2-2 改變結構幾何條件之自然頻率 38 3-3 單一結構承受移動負載之分析 40 3-3-1 改變鋁板之厚度對於結構響應之比較 41 3-3-2 改變壓電片之厚度對於結構響應之比較 48 3-4 多跨距結構受移動負載之分析 55 3-4-1 多跨距結構之自然振動頻率 56 3-4-2 多跨距結構承受移動負載之比較 57 3-4-2 移動負載的速度對於結構響應之比較 64 第四章 結論與未來展望 71 4-1 結論 71 4-2 未來展望 73 參考文獻 74 附錄A 76 附錄B 78

    1. R. D. Mindlin, “Influence of rotary inertia and shear on flexural motions of isotropic elastic plates,” Journal of Applied Mechanics, Vol. 18, pp.31-38, 1951.
    2. R. D. Mindlin, A. Schacknow and H. Deresiewicz, “Flexural vibrations of rectangular plates,” Journal of Applied Mechanics, Vol. 23, pp. 431-436, 1955.
    3. E. Reissner and Y. Stavsky, “Bending and stretching of certain types of heterogeneous aeolotropic elastic plates,” Journal of Applied Mechanics, Vol. 28, pp. 402-408, 1961.
    4. A. W. Leissa, “The free vibration of rectangular plates,” Journal of Sound and Vibration, Vol. 31, pp. 257-293, 1973.
    5. N. S. Putcha and J. N. Reddy, “Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory,” Journal of Sound and Vibration, Vol. 21, pp. 2201-2219, 1985.
    6. J. N. Reddy, Mechanics of Laminated Composite Plates: Theory and Analysis, CRC Press, 1997.
    7. Y. Xing and B. Liu, “Closed form solutions for free vibrations of rectangular Mindlin plates,” Acta Mechanica Sinica, Vol. 25, pp. 689-698, 2009.
    8. J. A. Gbadeyan and S. T. Oni, “Dynamic behavior of beams and rectangular plates under moving loads,” Journal of Sound and Vibration, Vol. 182, pp. 677-695, 1995.
    9. J. S. Wu, M. L. Lee and T. S. Lai, “The dynamic analysis of a flat plate under a moving load by the finite element method,” International Journal for Numerical Methods in Engineering, Vol. 24, pp. 743-762, 1987.
    10. J. J. Wu, A. R. Whittaker and M. P. Cartmell, “The use of finite element techniques for calculating the dynamic response of structures to moving loads,” Computers & Structures, Vol.78, pp. 789-799, 2000.
    11. C. Johansson and C. Pacoste, “Closed-form solution for the mode superposition analysis of the vibration in multi-span beam bridges caused by concentrated moving loads,” Computers & Structures, Vol.119, pp. 85-94, 2013.
    12. R.D. Mindlin, “Forced thickness – shear and flexural vibrations of piezoelectric crystal plates,” Journal of Applied Physics, Vol. 22, pp.83-88, 1952.
    13. A. Fernandes and J. Pouget, “Accurate modelling of piezoelectric plates: single-layered plate,” Archive of Applied Mechanics, Vol.71, pp.509-524, 2001.
    14. A. Fernandes and J. Pouget, “Two-dimensional modelling of laminated piezoelectric composites: analysis and numerical results,” Thin-Walled Structures, Vol.39, pp. 3-22, 2001.

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