顫振(Flutter)現象為橋梁受風載所產生之一種氣彈互制行為。傳統上，橋梁顫振導數(Flutter Derivative)之識別採自由振動方式，但其實驗結果常受週遭試驗環境影響，而且將自由振動頻率當成外力擾動頻率亦會造成結果上之誤差。為克服上述缺點，本研究使用間接式強制振動的實驗方式，研擬一套新的顫振導數識別方法。首先由伺服馬達給予振動平台強制振動，透過彈簧擾動橋面板斷面結構模型，然後量測其在平滑流場下之氣彈互制反應。
    實驗流程分為非耦合顫振導數識別與耦合顫振導數識別，均藉由氣彈互制反應之轉換函數實驗值與理論值比較，在頻率域以曲線擬合最佳化識別出理論式中最佳參數，最後得到橋梁之顫振導數。其中於理論部分引用狀態空間方程式之觀念進行推導，而最佳化過程則引用基因演算法(Genetic Algorithm) 求解，以確保得到全域最佳解。
    本論文以寬深比為27之削角流線型平板斷面模型為例，使用淡江大學土木系風洞實驗室進行上述識別實驗，結果顯示所識別得之顫振導數頗具一致性，而且其值相當接近Theodorsen函數所描述之理想平板理論值，顯示間接式強制振動新識別法能可靠識別顫振導數。

Flutter is one of the aero-elastic behaviors in the wind-induced motion of bridges.  The conventional approach for identifying flutter derivatives of bridges is to use the free vibration method which has disadvantages, such as lack of consistency due to high sensitivity of free vibration responses to the test condition/environment, and the error inherited by treating free vibration frequency as excitation frequency.  To overcome these shortcomings, this thesis presents a new identification approach by utilizing indirect forced actuation in cooperation with wind tunnel tests.  In the experiment setup, the bridge section model is connected to a two-axis actuating device through serial connection of springs.  Under the excitation of the actuation device and smooth wind flow, the aero-elastic response of the section model is thus measured.
  	The identification scheme proposed is composed of two parts, one is for uncoupled flutter derivatives and the other is for couple ones.  By comparing the frequency response function of aero-elastic responses with the theoretical values that are derived based on state space equation theory, the optimal parameters involved in the theoretical formula can be determined by using curve-fitting optimization which employs the Genetic Algorithm (GA) in the searching process to ensure achieving  global optimum.
    For demonstration of this approach, the bridge section model of a chamfered plate with a width/depth ratio of 27 was used for identification in the wind tunnel tests, and the results were successfully obtained.  The identified flutter derivatives were shown to be fairly consistent and close to the theoretical values in the perfect flat plate, which can be derived from the Theodorsen functions.  Therefore, it is concluded that the indirect forced vibration approach is a reliable method for identifying bridge flutter derivatives.

第一章 導論...............................................1
1.1前言...................................................1
1.2研究動機與目的.........................................2
1.3文獻回顧...............................................2
1.4橋樑之受風效應.........................................4
1.4.1抖振.................................................5
1.4.2顫振.................................................5
1.4.3扭轉不穩定現象.......................................7
1.4.4渦流顫振.............................................7
1.4.5風馳效應.............................................8
1.5風力係數及顫振導數.....................................9
1.5.1風力係數.............................................9
1.5.2顫振導數............................................10

第二章 理論與分析........................................12
2.1橋面板受間接強制振動與平滑流場風力作用之運動方程式....12
2.2強制振動系統識別之相關理論............................13
2.3曲線擬合..............................................14
2.4斷面模型結構物特性之識別..............................18
2.4.1結構垂直向自然頻率之識別............................19
2.4.2結構扭轉向自然頻率之識別............................19
2.4.3橋面板之質量率定....................................20
2.4.4橋面板之轉動慣量率定................................21
2.5強制振動下顫振導數識別之概念..........................22
2.5.1顫振自激力..........................................22
2.5.2非耦合項顫振導數之識別..............................29
2.5.3耦合項顫振導數之識別................................35
2.6參數最佳化-基因演算法.................................40

第三章 實驗設備與實驗流程................................46
3.1實驗設備介紹..........................................46
3.1.1大氣風洞實驗室......................................46
3.1.2斷面模型............................................46
3.1.3實驗儀器............................................47
3.1.4量測系統介紹........................................48
3.2實驗流程..............................................49
3.2.1結構系統識別實驗....................................50
3.2.2顫振導數系統識別實驗................................53
第四章 實驗結果討論與比較................................62
4.1結構物特性系統識別之結果..............................62
4.2非耦合顫振導數系統識別之結果..........................63
4.3耦合顫振導數系統識別之結果............................64

第五章 結論與展望........................................78

參考文獻.................................................80

附錄A....................................................81

1.	Bratt, J. B. and Scruton, C.“Measurement of Pitching Moment Derivatives for an Aerofoil Oscillating about the Halfchord Axis”,British Aerodynamical Research Council, R.＆M., No.1921,1938.
2.	G. Diana, F. Resta, A. Zasso, M. Belloli, D. Rocchi  “Forced motion and free motion aeroelastic tests on a new concept dynamometric section model of the Messina suspension bridge”  , Journal of Wind Engineering and Industrial Aerodynamics 92 (2004)441-462.
3.	Halfman, R. L.“Experimental Aerodynamic Derivatives of a Sinusoidally Oscillating Airfoil in Two-Dimensional Flow”,NACA Technical Report,1108,1952.
4.	Matsumoto and Y . Daito , ” Torsional flutter of bluff bodies”, Journal of Wind Engineering and Industrial Aerodynamics, v 69-71,Jul-Oct, 1997.
5.	Scanlan, R. H. and Sabzevari, A.“Suspension Bridge Flutter Revisited”,ASCE Structural Engineering Conference,1967.
6.	Scanlan , R. H. and Tomko , J. J. ,”Airfoil and Bridge deck Flutter Derivatives”, J. of Eng. Mech. Div. , v.97, pp.1717~1737 , 1971.