Vibration and Stability of an Axially Moving and Spinning Rayleigh Beam

軸向移動與旋轉雷立夫樑之振動與穩定性分析

Jer-Rong Chang(張哲榮) ； Wei-Jr Lin(林暐智) ； Ying-Chung Chen(陳膺中) ； Siu-Tong Choi(崔兆棠) ； Chun-Jung Huang(黃俊榮)

《中國機械工程學刊》 44卷1期 (2023/02) Pp. 1-10

摘要

In this paper, Rayleigh beam theory and the finite element method with variable-domain element are used to derive the equations of motion of an axially moving and spinning beam with circular cross section. The rotary inertia and gyroscopic effect are taken into account. The dynamical behavior of the system is observed for cases of different types of axial motion. For stability analysis of a spinning beam with constant-speed axial extension deployment, eigenvalues of equations of motion are obtained to determine its stability, while Floquet theory is employed to investigate the stability of a spinning beam with periodical axial motion. Effect of the spinning speed of the beam on its vibration and stability is studied. Direct time numerical integration, based on a Runge-Kutta algorithm, is used to confirm the results from Floquet theory.

關鍵字

axially moving ； spinning ； vibration ； stability ； Rayleigh beam

並列摘要

本文採用雷立夫樑理論與可變域元素之有限元素法推導出具圓形截面的軸向移動和旋轉樑之運動方程式，其中考慮樑之旋轉慣性與陀螺效應，並藉由不同類型的軸向運動來觀察系統的動態行為。對具有定速軸向延伸的旋轉樑，求其運動方程式的特徵值來確認其穩定性，並用Floquet理論來分析具有週期性軸向移動旋轉樑的穩定性。本文探討了樑的旋轉速度對其振動與穩定性的影響，並使用直接時間數值積分方法（Runge-Kutta）來確認Floquet理論的結果。