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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 蘇偉? | |
dc.contributor.author | I-Chie Huang | en |
dc.contributor.author | 黃奕傑 | zh_TW |
dc.date.accessioned | 2021-06-17T09:09:24Z | - |
dc.date.available | 2019-11-04 | |
dc.date.copyright | 2019-11-04 | |
dc.date.issued | 2019 | |
dc.date.submitted | 2019-10-16 | |
dc.identifier.citation | [1] R. Bhat, 'Transverse vibrations of a rotating uniform cantilever beam with tip mass as predicted by using beam characteristic orthogonal polynomials in the Rayleigh-Ritz method,' Journal of Sound and Vibration, vol. 105, no. 2, pp. 199-210, 1986.
[2] H. Yoo and S. Shin, 'Vibration analysis of rotating cantilever beams,' Journal of Sound and vibration, vol. 212, no. 5, pp. 807-828, 1998. [3] M. A. C. F. Lima, 'Rotating cantilever beams: Finite element modeling and vibration analysis,' Ph.D. thesis, Faculdade de Engenharia da Universidade do Porto, 2012. [4] S. Hoa, 'Vibration of a rotating beam with tip mass,' Journal of sound and vibration, vol. 67, no. 3, pp. 369-381, 1979. [5] H. Kim, H. H. Yoo, and J. Chung, 'Dynamic model for free vibration and response analysis of rotating beams,' Journal of Sound and Vibration, vol. 332, no. 22, pp. 5917-5928, 2013. [6] F. J. Shaker, 'Effect of axial load on mode shapes and frequencies of beams,' Technical Report, NASA, TN D-8109,1975. [7] Ö. Turhan and G. Bulut, 'On nonlinear vibrations of a rotating beam,' Journal of sound and vibration, vol. 322, no. 1-2, pp. 314-335, 2009. [8] O. Thomas, A. Sénéchal, and J.-F. Deü, 'Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams,' Nonlinear Dynamics, vol. 86, no. 2, pp. 1293-1318, 2016. [9] P. Apiwattanalunggarn, S. W. Shaw, C. Pierre, and D. Jiang, 'Finite-element-based nonlinear modal reduction of a rotating beam with large-amplitude motion,' Journal of Vibration and Control, vol. 9, no. 3-4, pp. 235-263, 2003. [10] Nayfeh and Ali Hasan, Nonlinear interactions: analytical, computational, and experimental methods. Wiley New York, 2000. [11] A. H. Nayfeh and B. Balachandran, Applied nonlinear dynamics: analytical, computational, and experimental methods. John Wiley & Sons, 2008. [12] A. H. Nayfeh and P. F. Pai, Linear and nonlinear structural mechanics. John Wiley & Sons, 2008. [13] M. Brennan, I. Kovacic, A. Carrella, and T. Waters, 'On the jump-up and jump-down frequencies of the Duffing oscillator,' Journal of Sound and Vibration, vol. 318, no. 4-5, pp. 1250-1261, 2008. [14] D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers. Oxford University Press 2007. [15] W. J. Su and J. W. Zu, 'Modeling of V-shaped beam-mass piezoelectric energy harvester: impact of the angle between the beams,' in ASME 2012 International Mechanical Engineering Congress and Exposition, 2013, pp. 573-579: American Society of Mechanical Engineers Digital Collection. [16] H. Wu, L. Tang, Y. Yang, and C. K. Soh, 'A novel two-degrees-of-freedom piezoelectric energy harvester,' Journal of Intelligent Material Systems and Structures, vol. 24, no. 3, pp. 357-368, 2013. [17] F. Khameneifar, S. Arzanpour, and M. Moallem, 'A Piezoelectric Energy Harvester for Rotary Motion Applications: Design and Experiments,' IEEE/ASME Transactions on Mechatronics, vol. 18, no. 5, pp. 1527-1534, 2013. [18] M. Guan and W.-H. Liao, 'Design and analysis of a piezoelectric energy harvester for rotational motion system,' Energy Conversion and Management, vol. 111, pp. 239-244, 2016. [19] H.-X. Zou et al., 'Design and experimental investigation of a magnetically coupled vibration energy harvester using two inverted piezoelectric cantilever beams for rotational motion,' Energy Conversion and Management, vol. 148, pp. 1391-1398, 2017. [20] A. Erturk and D. J. Inman, Piezoelectric energy harvesting. John Wiley & Sons, 2011. [21] A. Erturk and D. J. Inman, 'A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters,' Journal of vibration and acoustics, vol. 130, no. 4, p. 041002, 2008. [22] H. Lee, 'Effect of gravity on the stability of a rotating cantilever beam in a vertical plane,' Computers & structures, vol. 53, no. 2, pp. 351-355, 1994. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/74878 | - |
dc.description.abstract | 本研究建立一幾何非線性的旋轉雙自由度折返懸臂樑於鉛直平面旋轉振動的系統,探究其非線性行為對頻率響應以及穩定度的影響,並建立理論模型,以驗證實驗結果。首先,利用牛頓第二定律搭配非線性的邊界條件,建立單旋轉樑於鉛直平面旋轉的統御方程式。而後使用Galerkin’s discretization 將空間及時間函數分離,找到其正規化條件以推導出其運動方程式,並將非線性取至三次項。可觀察出此方程式為一Mathieu’s 方程式搭配著幾何非線性項。接下來採用微擾法對其共振頻附近進行分析,得到一近似解析解,此解可用來研究各參數對整體系統振幅的影響;第二,延伸上述單自由度旋轉樑的研究步驟,建立雙自由度旋轉折返樑於鉛直平面下振動的模型,比較離心力對於不同擺放方向之樑的影響及其造成共振頻的改變,並觀察幾何非線性於旋轉環境下所造成的硬化或軟化非線性;第三,在貼附單壓電片於雙自由度折返樑後,分別對其進行鉛直激振以及旋轉環境的掃頻試驗,觀察其電壓頻率響應。最後,配合實驗以及前面推出的模型來擬合對照,對其定性討論現象,並觀察定量上與實驗的差距,探討其誤差的可能性。 | zh_TW |
dc.description.abstract | We model a geometrically nonlinear rotating two-degree-of-freedom cantilever cutout beam in a vertical plane and exploit the influence of nonlinear behavior on frequency responses and stability of the beam. A theoretical model is developed and verified with the experimental results. First, Newton's second law along with nonlinear boundary conditions is used to establish the governing equation for a single rotating beam in the vertical plane. The Galerkin’s discretization scheme is used to separate the spatial and temporal variables. The normalization conditions are determined and used to derive the equation of motion. The nonlinearity is taken up to the cubic term. It can be observed that the equation of motion is a Mathieu’s equation with the geometric nonlinear terms. Next, the perturbation method is used to obtain an approximate analytical solution near the resonance frequency. This solution can be used to study the influence of each parameter on the amplitude of the overall system. Second, continued with the above-mentioned single-degree-of-freedom rotating beam, we further established and the model of the vibration of the two-degree-of-freedom rotating cutout beam in a vertical plane. The centrifugal force is examined to see its influence on thenatural frequency of the beam installed in different orientations. The hardening or softening phenomenon due to geometric nonlinearity from rotating environment are then discussed. Third, a piezoelectric layer is attached on the two-degree-of-freedom cutout beam. The base-excitation and the sweeping tests of the rotating environment are carried out respectively to observe the voltage responses., The waveforms at specific driving frequencies are also investigated. Finally, we compare the model with the experiment results and discuss the possible causes of the errors. | en |
dc.description.provenance | Made available in DSpace on 2021-06-17T09:09:24Z (GMT). No. of bitstreams: 1 ntu-108-R06522633-1.pdf: 3568115 bytes, checksum: 7d5b23556dd99cbe17a6f1b6a63b6fbb (MD5) Previous issue date: 2019 | en |
dc.description.tableofcontents | 誌謝 i
中文摘要 ii ABSTRACT iii 目錄 iv 圖目錄 vi 表目錄 viii Chapter 1 緒論 1 1.1 前言 1 1.2 文獻回顧 2 1.3 研究動機與方法 6 Chapter 2 懸臂樑於鉛直平面旋轉之動態響應模型 7 2.1 數學模型 7 2.1.1 牛頓第二定律 8 2.2 Galerkin discretization 12 2.2.1 模態分析 12 2.2.2 正規化 13 2.2.3 Duffing三階非線性運動方程式 14 2.3 在一倍自然頻率附近振動之振幅 17 Chapter 3 折返樑於鉛直平面旋轉之動態響應模型 20 3.1 數學模型 21 3.2 模態分析 25 3.3 折返樑Duffing三階統御方程式 28 Chapter 4 折返樑定性討論 32 4.1 旋轉特性 32 4.1.1 大位移旋轉 32 4.1.2 應力硬化 33 4.1.3 自然頻率分析 33 4.2 模態轉向 35 4.3 參數處理 37 4.4 參數比較 39 4.4.1 影響自然頻率係數比較 39 4.4.2 影響非線性係數之比較 44 4.4.3 頻率響應 46 Chapter 5 實驗配置 48 5.1 原型設計 48 5.1.1 折返樑本體 48 5.1.2 旋轉平台 50 5.2 實驗設備 51 5.3 實驗流程 53 5.3.1 基底激振實驗 53 5.3.2 旋轉激振實驗 54 Chapter 6 驗證與討論 55 6.1 組別A驗證 56 6.2 組別B驗證 61 6.3 組別C驗證 65 Chapter 7 結論 69 7.1 結論 69 7.2 誤差分析 69 7.2.1 頻率誤差 69 7.2.2 振幅誤差 70 7.3 未來展望 70 Reference 71 | |
dc.language.iso | zh-TW | |
dc.title | 雙自由度折返樑於旋轉式壓電能量採集之分析 | zh_TW |
dc.title | Analysis of a Two-degree-of-freedom Cut-Out Beam for Rotational Piezoelectric Energy Harvesting | en |
dc.type | Thesis | |
dc.date.schoolyear | 108-1 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 陳蓉珊,陳任之 | |
dc.subject.keyword | 幾何非線性,旋轉運動,壓電能量採集,多模態, | zh_TW |
dc.subject.keyword | geometrical nonlinear,rotational motion,piezoelectric energy harvester,multimodal, | en |
dc.relation.page | 72 | |
dc.identifier.doi | 10.6342/NTU201904135 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2019-10-16 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 機械工程學研究所 | zh_TW |
顯示於系所單位: | 機械工程學系 |
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