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題名 | 具端點質塊之軸向移動自旋樑之非線性動態建模=Non-Linear Dynamic Modeling of an Axially Moving and Spinning Beam with a Tip Mass |
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作者 | 張哲榮; 許耿禎; 周炳煌; | 書刊名 | 航空技術學院學報 |
卷期 | 5:1 民95.08 |
頁次 | 頁405-417 |
分類號 | 446.11 |
關鍵詞 | 軸向移動; 自旋; 樑; 動態建模; 漢彌頓原理; Axially moving; Spinning; Beam; Dynamic modeling; Hamilton's principle; |
語文 | 中文(Chinese) |
中文摘要 | 本研究針對具端點質塊之軸向移動自旋樑在剛體牆拘束下,建立其非線性動態耦合模型。使用提末辛科樑理論,考慮樑上任意點具三個平移及三個轉動自由度,模擬軸向移動自旋樑非線性的運動情形。軸向移動自旋樑在剛體牆支承進出移動,其動能與應變能的推導,分成剛體牆內部與外部兩部份:在剛體牆內部,樑受其拘束作用,兩個側向平移位移受限為零;在剛體牆外部,樑則作自由振動。一平行於軸向運動的外力,施加於自旋樑在剛體牆端。使用漢彌頓原理,推導出系統之統御方程式,計有一條描述軸向運動的積微分方程式與十條描述撓性振動的二階偏微分方程式及其相關的二十個邊界條件。由方程式中可看出,撓性樑的軸向剛體移動與撓性振動及各撓性振動間均有耦合現象,並有科氏加速度及陀螺效應。另外,由本論文可簡化為純軸向移動樑或純自旋樑的模式。 |
英文摘要 | In this paper, the nonlinear dynamic coupling model for an axially moving and spinning beam with a tip mass restrained by rigid wall support is established. Based on Timoshenko theory, three translational and three rotational degrees of freedom of arbitrary point of the beam are considered to model the motion for the axially moving and spinning beam. The formulation of the kinetic energy and strain energy of the beam are divided into two parts. Inside the rigid wall, the beam is restrained from vibrating laterally, while outside the rigid wall, the beam vibrates freely. An external force parallel to the axial motion of the beam is applied on the end of the beam inside the wall. The equations of motion of the beam are derived applying Hamilton’s principle. It is derived that one integral-differential equation describing the axial motion and ten second-order partial differential equations describing the flexible vibrations. And there are twenty associated boundary conditions. From these equations, it is seen that the axial rigid-body motion is coupled with the flexible vibrations and the flexible vibrations are also coupled each other. The Coriolis accelerations and the gyroscopic effects are also found. Besides, this paper can also be simplified to be the model of axially moving beam or spinning beam. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。