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標題: 纖維加強複材旋轉軸-圓盤-葉片系統動態特性之探討
Free Vibration of Spinning Fiber Reinforced Composite Shaft-Disk-Blade Systems
作者: 張智勇
Yung, Chang Chih
關鍵字: Rotating shaft-disk-blade system;旋轉軸-圓盤-葉片系統;Composite material;Finite Element Method;Coupled vibration;複合材料;有限元素法;耦合振動
出版社: 機械工程學系
另外,延伸長纖維複合材料軸之研究,本文提出一含短纖維複合材料旋轉軸之動態特性分析。藉由 Mori-Tanaka 理論與等價同質體方法,可求出短纖維複合材料軸之等效彈性模數,其表示式為包含有纖維特性、纖維體積分率、纖維旋轉角度以及纖維形狀之函數。應用此等效之彈性模數與先前所推導旋轉軸之有限元素模型,可分析得到此短纖維複合材料旋轉軸之自然頻率、迴旋速度與臨界轉速等動態特性。

A finite element model for analyzing the vibration characteristics of composite shaft-disk-blade systems is presented here. The system consists of a composite blade attached to the rim of a rigid disk and a composite shaft to which the disk is fixed. This model is an extension of the composite blade and composite shaft models developed earlier by Chang et. al. by further taking also the coupling kinetic energy of the shaft and the blade into account. The extended Hamilton's principle in conjunction with the finite element method is employed in deriving the equations of motion of system. The dynamic characteristics such as natural frequencies, whirling speeds and mode shapes of the composite shaft-disk-blade system are studied for various material and geometry properties of the blade and shaft, as well as for various rotating speeds. The numerical results indicate that the existence of the coupling flexible motion between blade and shaft could have significant influences on the dynamic characteristics of the system. For the purpose of verification, the results obtained using the current finite element model are compared with those obtained using the available commercial software for the case of a free non-rotating shaft-disk-blade system made of an isotropic material.
The dynamic behaviors of the rotating composite shafts containing randomly oriented reinforcements are furthering investigated in this study. Incorporating the Mori-Tanaka mean-field theory to account for interaction at finite concentrations of reinforcements with the equivalent inclusion method, the effective elastic moduli are expressed as a function of phase properties, volume fraction, orientation angles, and reinforcements' shape. Based on shaft's model and taking these effective elastic moduli into account, the natural frequencies of the stationary shafts, and the whirling speeds as well as the critical speeds of the rotating shafts are presented.
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