一種應用於基座激振之二自由度結構系統參數的鑑別方法

A New Parameter Identification Method for Two-degree-of-freedom Base-excited Structural Systems

10.6841/NTUT.2011.00407

蘇敬鈞

系統鑑別 ； 能量消耗 ； 雙自由度震盪器 ； Parameter identification ； Dissipative energy ； Two-dof oscillator

臺北科技大學機電整合研究所學位論文

2011年

碩士

黎文龍

繁體中文

近年來在多自由度系統之相關研究中，系統參數鑑別已成為重要之研究趨勢。本研究目的為雙自由度結構系統在基座激振下進行參數鑑別，首先建構一比例性阻尼雙自由度線性運動方程式，並對系統輸入掃頻訊號以獲取系統之兩阻尼頻率，且分別將阻尼頻率作外激頻率，同時量測基座輸入訊號及兩質塊動態響應訊號，再藉由座標轉換式將其運動方程式轉變為非耦合狀態。最後，將模態座標與模態力作乘積調變，觀察調變後之傅立葉係數，方可鑑別出系統之參數值。 在數值模擬中，觀察系統分別在三種不同參數設定及各種模態阻尼比之情況下，以MATLAB SIMULINK 模擬系統之動態響應。由結果顯示，雖系統在微小阻尼比或大於5%的情況下，利用半能量法所鑑別出系統之品質因子會有較大誤差，但利用本研究方法亦可精準鑑別系統之參數值。 在實驗驗證方面，本研究製作一近似質量–阻尼–彈簧之雙自由度之結構模型，且分別在結構阻尼、水及潤滑油之黏滯阻尼情況下鑑別系統之模態質量及模態勁度參數值。由實驗結果顯示，雖利用本研究方法能有效鑑別系統之參數值，但當系統在小阻尼之情況下進行鑑別，可能伴隨著較大的誤差結果。

In recent years, the research of identifying parameter of multi-degree-of-freedom system is significant trend. The main objective of the present report is to derive a method for identifying two-degree-of-freedom system parameter under the harmonic motion of base. First, we obtain the linear equations of motion of a proportional damped system in matrix form that starts with giving a chirp excitation to the target system, and to locate the damped frequency of the oscillator which the external excitation frequency is purposely changed to that frequency. In the meantime, the displacement of the base and the displacement of the mass need to be recorded that is substitute the modal transformation into that equation, and invoke the orthogonality properties of the mode matrix. Finally, we observe Fourier coefficients of the product modulation of inputs and its output that is valid to recognize the system parameter. In the numerical simulations, Simulink toolbox of MATLAB is chosen for simulating dynamic response in three parameter settings and different modal damping ratio. Even though the damping ratio is under extremely small or higher than 5%, there are larger errors when identified the quality factor by half power point .However, the numerical simulations results showed the substantiated validity of the method. Following the numerical simulations, the experimental validation was also carried out. A two-degree-of-freedom system is designed and manufactured to mimic real mass-damping-stiffness system. The report applying the formulations provided to recognize the structural damping, water and lubricant viscously damped systems modal mass and modal stiffness. Although the experimental results could verified the correction of the method, there are more errors of the identified modal mass and modal stiffness when the system damping is small.

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