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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/88065

    Title: 非線性懸吊彈性樑及端點減振器之研究
    Other Titles: The study of a nonlinear suspension elastic beam with an end point dynamic vibration absorber
    Authors: 張家嫚;Chang, Chia-Man
    Contributors: 淡江大學航空太空工程學系碩士班
    Keywords: 非線性;內共振;振動模態;動態減振器;Internal Resonance;Mode Shape;Dynamic Vibration Absorber;Elastic Foundation;Frequency response
    Date: 2013
    Issue Date: 2013-04-13 11:59:10 (UTC+8)
    Abstract: 本研究考慮一Bernoulli-Euler Beam之彈性樑,此彈性樑以鋼纜懸掛之,而鋼纜則以非線性彈簧與線性阻尼的組成來模擬其運動。在本研究中,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 (Time-Dependent Boundary Dynamic Vibration Absorber (DVA) ) 以分析該DVA對於樑之減振效果。有別於一般的振動問題之邊界設定,本研究之自由端點 (Free End) 因掛載一DVA,而為具有時間變化之邊界條件,因此吾人採用 Mindlin-Goodman 法分析此問題,並藉由多項式移位函數 (Shifting Polynomial Function) 將非齊次性邊界條件轉換為齊次性邊界條件。 此外,本文使用多尺度法 (Method of Multiple Scales (MOMS) ) 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 (1:3) 的內共振情形,吾人並繪製系統於穩態固定點 (Fixed Points) 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,並以數值模擬其時間域之振動情形,相互驗證之。此外,本研究將分析DVA的質量及彈簧係數對於整個系統之減振的影響,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,藉由改變風速的大小,利用Floquet Theory搭配Floquet Multipliers (F.M.) 判定法則來分析此系統之穩定性,吾人並以各種起始擾動及各種風速影響之下的Basin of Attraction圖形,觀察此系統之端點減振器在不同質量及彈性係數組合時,對於本系統穩定性的成效,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. The combination of mass and spring constant of the tip-attached dynamic vibration absorber (DVA) were investigated. This time-dependent non-homogeneous boundary condition problem was solved by Mindlin-Goodman method. By using the shifting polynomial function, one can transform this system to a homogeneous boundary problem. The method of multiple scales (MOMS) 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 Poincare Map was also utilized to identify the system instability frequency region of the jump phenomenon. The parameters of the tip attached DVA were studied. The internal resonance can be avoid for the existence of the DVA. 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.
    Appears in Collections:[航空太空工程學系暨研究所] 學位論文

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