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    Title: 非線性懸吊彈性樑及端點減振器之研究
    Authors: 王怡仁;張家嫚
    Contributors: 淡江大學航空太空工程學系
    Keywords: 非線性;內共振;振動模態;動態減振器;Nonlinear;Internal Resonance;Mode Shape;Dynamic Vibration Absorber
    Date: 2013-11-30
    Issue Date: 2014-07-31 12:51:46 (UTC+8)
    Publisher: 新竹市:中華民國航空太空學會
    Abstract: 本研究考慮一Bernoulli-Euler Beam 之彈性樑以鋼纜懸掛,而鋼纜以非線性彈簧與線性阻尼組成,彈性樑的一端為鉸接邊界支撐,另一端則掛載時變之動態減振器 (DVA) 。本研究因具有時間變化之邊界條件,所以採用 Mindlin-Goodman 法分析此問題。此外本文使用多尺度法解析此非線性系統,發現系統中第一模態及第二模態存在一對三的內共振情形,並繪製系統於穩態固定點的情況下,各模態的頻率響應圖,以觀察其非線性內共振現象,且以數值模擬其時間域之振動情形,相互驗證之。另外本研究將分析DVA 的質量及彈簧係數對於整個系統之減振影響,並提出最佳的質量與彈簧係數組
    合,可使系統達到最佳減振效果。最後,吾人以一簡單的空氣動力函數模擬氣流對於本彈性樑系統之阻尼的影響,利用Floquet Theory 搭配Floquet Multipliers (F.M.) 判定法則,繪製出Basin of Attraction圖形,觀察此系統之穩定性,以獲得最後結論。
    This study investigated the performance of a mass-spring dynamic vibration absorber (DVA) at the free end of a hinged-free elastic beam under simple harmonic excitation. This beam system was suspended by suspension cables. These cables were simulated by cubic nonlinear springs to examine the nonlinear characteristics of this system. This time-dependent non-homogeneous boundary condition problem was solved by Mindlin-Goodman method. The method of multiple scales was performed to solve the nonlinear equations. The 1:3 internal resonance was found at the 1st and 2nd modes of this beam system. The fixed point plots were obtained and compared with the numerical results to verify the system internal resonance. The Poincaré Map was also utilized to identify the system instability frequency region of the jump phenomenon. The optimal DVA mass and the spring constant were provided for best beam vibration reduction. Finally, the wind speeds and aerodynamic loads were included to investigate the stability of this system. The system stability was analyzed by Floquet theory and Floquet multipliers. The basin of attraction charts were made to verify the effects of the combinations of DVA’s mass and the spring constant at diverge speed.
    Relation: 2013中華民國航太學會學術研討會暨國科會航太學門專題研究計畫成果發表會=2013 AASRC Conference,8頁
    Appears in Collections:[航空太空工程學系暨研究所] 會議論文

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