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標題: 含壓電片複合材料旋轉樑動態特性之探討
Studies of Dynamic Behaviors of Rotating Composite Beams Containing Piezoelectric Strips
作者: 林高旭
關鍵字: 複合材料
出版社: 機械工程學系
摘要: 本文主旨建立一維三節點的有限元素來模擬複材旋轉樑的振動。此模式因含有橫向剪力變形、扭轉、翹曲、弦向曲率、側向位移與耦合效應等,又配合使用三節點的拉格朗治與拉格朗治-赫米特混合型內插函數,因此能更準確描述旋轉樑的振動。並利用壓電致動器與感測器來探討含脫層與無脫層旋轉樑的動態特性之差異性。 首先是改進張榮明[17]所採用的位移場,再根據位移場配合本構方程求出系統的應變能、動能與其它的能量項,藉由漢米爾頓原理結合有限元素法,並考慮位移的連續性,推導出含脫層複合材料旋轉樑的運動方程式與感測方程式。利用上述有限元模式分析含脫層與無脫層旋轉樑在自然頻率之差異性,並探討不同攻角、傾角與轉速對旋轉樑自然頻率的影響。其次利用壓電感測器與致動器,經由模態分析法,來建立系統模態空間的狀態方程,分析脫層對結構系統的動態特性的影響。
The objective of this thesis is to develop a one-dimensional three-node finite element model to simulate the vibration of rotating beams made of composite materials. This model has included structural effects such as transverse shear deformation, twisting, warping, chordwise curvature, sidewise bending, and deformation coupling. In addition, the mixed Lagrangian-Hermite type of interpolation functions are used to represent the twisting deformation, while Lagrangian interpolation functions are used for other displacement variables. As a result, the finite element model developed here is able to predict the vibration of rotating composite beams quite accurately. Furthermore, piezoelectric materials are added to the structure. They are used as actuators and sensors to monitor the dynamic responses of the rotating composite beam. The displacement field assumed for a beam adopted by R. M. Chang is also considered here but with a slight modification. The expressions of strain energy, kinetic energy as well as other energy terms of the rotating composite beam are obtained using this displacement field and the constitutive equations of materials. By employing the Hamilton''s principle together with the finite element method, the equations of motion as well as the sensor equations of rotating delaminated composite beams containing piezoelectric materials are derived. The effects of the stagger angle, precone angle and the rotating speed on the frequencies of the rotating delaminated composite beam and the intact one are investigated. Finally, the frequency domain responses of the above two types of composite beams are evaluated through the use of the piezoelectric actuators and sensors.
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