Vibration and Stability of an Axially Moving and Spinning Rayleigh Beam
Jer-Rong Changa, Wei-Jr Linb, Ying-Chung Chenc, Siu-Tong Choid and Chun-Jung Huange
aDepartment of Aircraft Engineering, Air Force Institute of Technology, Kaoshiung, Taiwan 802, ROC.
bDepartment of Steel Research and Development, China Steel Corporation, Kaoshiung, Taiwan 812, ROC.
cDepartment of Aeronautical and Mechanical Engineering, Air Force Academy, Kaoshiung, Taiwan 802, ROC.
dDepartment of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan 701, ROC.
eInstitute of Aircraft and Maintenance, Far East University, Tainan, Taiwan 744, ROC.
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Abstract:
In this paper, Rayleigh beam theory and thefinite element method with variable-domain elementare used to derive the equations of motion of anaxially moving and spinning beam with circular crosssection. The rotary inertia and gyroscopic effect aretaken into account. The dynamical behavior of thesystem is observed for cases of different types ofaxial motion. For stability analysis of a spinningbeam with constant-speed axial extensiondeployment, eigenvalues of equations of motion areobtained to determine its stability, while Floquettheory is employed to investigate the stability of aspinning beam with periodical axial motion. Effect ofthe spinning speed of the beam on its vibration andstability is studied. Direct time numerical integration,based on a Runge-Kutta algorithm, is used to confirmthe results from Floquet theory.
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