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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/118535


    Title: 線性減振器與非線性能量槽於非線性樑之減振及穩定性研究
    Other Titles: Vi Bration and Stability Analysis of the Nonlinear Vibration Aborber (Nonlinear Energy Sink) on a Nonlinear Beam
    Authors: 王怡仁
    Keywords: 減振器;時間多尺度法;非線性振動;非線性能量槽;歐拉-伯努力樑;可調質量減振器;多尺度法
    Date: 2018-10
    Issue Date: 2020-04-09 12:12:25 (UTC+8)
    Abstract: 本研究考慮一歐拉-伯努力樑( Euler-Bernoulli Beam)在兩端絞接(hinged - hinged)之邊界條件下,同時受到拉伸效應(Stretching Effect)及空氣動力(Aerodynamic)影響之振動情形。而文中也將提到樑因為拉伸效應所導致的非線性振動現象,即討論非線性簡支樑(nonlinear hinged-hinged beam)之振動行為,並在非線性簡支樑下方掛載一可調質量減振器(Tuned Mass Damper (TMD))或具非線性彈性係數之非線性可調質量減振器(nonlinear Tuned Mass Damper),以分析該TMD對樑之減振效果。本研究使用多尺度法(Method of multiple scales (MOMS))分析系統於穩態固定點(Fixed Points)時各模態之頻率響應(Frequency response),之後吾人將以數值方法求得一閉迴路(closed loop)耦合數值解,並全面分析非線性簡支樑附加線性TMD或非線性TMD時各項參數(如TMD之質量比、掛載位置、阻尼係數、彈性係數、非線性彈性係數)對樑之影響,同時吾人將繪製3D MAP(3D maximum amplitude plots)與3D MACP(3D maximum amplitude contour plots)以利相互對照及分析。而文中除了以時間響應(Time Response)圖驗證3D MACP之正確性外,也使用因次分析法解得非線性TMD運動方程之解析解, 並將該解所求得之開迴路(open loop)解析解與先前提的閉迴路數值解相互比較,以獲得進一步的驗證,同時吾人也將給出非線性TMD振動率之明確關係式。最後吾人將以RK4(Fourth-Order Runge-Kutta)求出系統之Floquet Transition Matrix並搭配F.M.(Floquet Multipliers)判定法繪製BOA(Basin of Attraction)圖以探討系統在空氣動力作用下之穩定性。此外,吾人也使用Poincaré Map驗證BOA圖之正確性。本研究將提供最佳TMD的質量比、掛載位置、彈性係數、非線性彈性係數,並分析在系統受到空氣動力作用時須注意之項,以做為產學界未來研究之參考。
    Relation: 線性減振器與非線性能量槽於非線性樑之減振及穩定性研究
    Appears in Collections:[航空太空工程學系暨研究所] 研究報告

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