複材機翼結構模擬的相關研究已可由許多氣彈方面的文獻做參考，但更真實地模擬成考慮翼形函數的複材夾心樑則相當罕見，並且一般藉由有限元素所做的分析結果通常難以明確地觀察當中之物理意義。在本研究中，將推導出考慮翼形函數與加入剪應變及翹曲限制的機翼運動方式，並解出自由振動下各位移相對應之自然頻率及模態解析解。一般少見的夾心樑模態間正交關係，包含考慮縱向位移(deflection)、扭轉角度(torsion angle)與旋轉角度(rotation angle)將在本文中有詳細的推導，利用此關係可進一步由模態分析(modal analysis)處理機翼受力振動問題。在振動控制方面，在機翼上下表面黏附壓電感測器與致動器，並利用最佳理論與Kalman filter做觀測器的線性二次高斯控制演算法(LQG)來設計一輸出回授(output feedback)的控制系統。

在自然頻率方面的探討，包括(1)橫向剪應變(2)翼形函數(3)翹曲限制等影響。在振動控制方面，利用MATLAB下的simulink工具做數值模擬，前幾個模態振動將被有效地抑制。

Some investigations of composite wing structure such as divergence and flutter problems can be found, it is rarely seen the research about wing model which was simulated as composite sandwich plate with airfoil section. Besides, it is often hard to observe definite physical meanings by finite element analysis. In our study, equations of motion including airfoil function, transverse shear deformation, and warping restraint will be established, and analytical solutions of natural frequencies and mode shapes will also be solved. The orthogonality relations, which consist deflection, torsion angle, and rotation angle, will also be proved in this study. Through the establishment of the orthogonality relation, the forced vibration problems can then be solved by modal analysis. In vibration control, we use piezoelectric sensors and actuators to bond on upper and lower wing surface, and combine a controller that minimizes an objective function of quadratic form by using a Kalman filter as an observer (LQG control method) to design an output feedback control system.

Several interesting parameters about natural frequencies were discussed in numerical examples: (1) transverse shear deformation, (2) airfoil shape, (3)warping restraint effect. In vibration control analysis, the numerical simulations were done with the assist of the software MATLAB toolbox simulink, which show that first few vibration modes are successfully suppressed.

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