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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/74678

    Title: 非線性懸吊之彈性樑的內共振分析
    Other Titles: The internal resonance analysis of a nonlinear suspension elastic beam
    Authors: 謝易哲;Hsieh, I-Che
    Contributors: 淡江大學航空太空工程學系碩士班
    王怡仁;Wang, Yi-Ren
    Keywords: 非線性;振動;內共振;Nonlinear;vibration;Internal Resonances
    Date: 2011
    Issue Date: 2011-12-28 19:17:34 (UTC+8)
    Abstract: 本研究係以一彈性樑為主架構,並以三次方非線性彈簧與線性阻尼模擬其懸吊鋼纜,以分析系統之非線性振動行為。其中,吾人採用多尺度法(Method of Multiple Scales)與正交化法(Orthogonality)來解析此系統之運動方程。由本研究的分析,發現此系統存在著3:1內共振特性,吾人也進一步探討其生成的條件及非線性懸吊之彈性樑的相關振動現象。
    本研究分別探討常見的四種邊界狀況之系統內共振(Internal Resonance,簡稱I.R.)分析,並分別激擾低模態(Lower Mode)跟高模態(Higher Mode),且由Fix Points解(穩態頻率響應)及相位圖(Phase Plot),來判斷系統之穩定性並觀察其非線性內共振現象。
    The internal resonance (I.R.) of a Bernoulli-Euler Beam with nonlinear suspensions (cubic nonlinear springs) and with different end supports was studied in this thesis. The Bernoulli-Euler Beam is suspended by nonlinear springs (similar to Winkler Type Foundation) to the top ceiling. Four different types of boundary conditions are considered in the study, which are hinged-hinged, hinged-roller support, fixed-fixed, and spring-spring support, respectively. A simple Aerodynamic loading is included to simulate this suspension bridge vibration system. This research is to find the I.R. conditions for the boundary conditions aforementioned and subjected to Aerodynamic and simple harmonic loadings. The method of Multiple Scales (MOMS) is applied to get the conditions for I.R. The classical structural Dynamic analysis is also employed for finding mode shapes of the beam for different boundary conditions. By using the orthogonal properties, this problem can be deduced to a to a time domain ordinary differential equation. The I.R. condition for the cases studied can be determined analytically. The analytical predictions are confirmed by the Fixed Point plots and phase plots.
    This research found that the 3:1 I.R. occurred in the case of hinged-hinged boundary conditions in the 1 and 3 modes. The 3:1 I.R. also occurred in the case of hinged-roller boundary conditions in the 1 and 3 modes. The 3:1 I.R. occurred in the case of fixed-fixed boundary conditions in the 2 and 4 modes. The 3:1 I.R. occurred in the case of spring-spring boundary conditions in the 2 and 4 modes.
    Appears in Collections:[Graduate Institute & Department of Aerospace Engineering] Thesis

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