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TECHNICAL PAPERS

Free Vibrations of a Rotating Inclined Beam

[+] Author and Article Information
Sen Yung Lee1

Professor of Mechanical Engineering Department, National Cheng Kung University, Department of Mechanical Engineering, Tainan, 701 Taiwansylee@mail.ncku.edu.tw

Jer Jia Sheu

 National Cheng Kung University, Tainan, Taiwan, Republic of China

1

Author to whom correspondence should be addressed.

J. Appl. Mech 74(3), 406-414 (Mar 24, 2006) (9 pages) doi:10.1115/1.2200657 History: Received February 25, 2005; Revised March 24, 2006

By utilizing the Hamilton principle and the consistent linearization of the fully nonlinear beam theory, two coupled governing differential equations for a rotating inclined beam are derived. Both the extensional deformation and the Coriolis force effect are considered. It is shown that the vibration system can be considered as the superposition of a static subsystem and a dynamic subsystem. The method of Frobenius is used to establish the exact series solutions of the system. Several frequency relations that provide general qualitative relations between the natural frequencies and the physical parameters are revealed without numerical analysis. Finally, numerical results are given to illustrate the general qualitative relations and the influence of the physical parameters on the natural frequencies of the dynamic system.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometry and coordinate system of a rotating inclined beam

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Figure 2

Influence of the setting angle ψ and the inclination angle θ on the fundamental natural frequencies of a rotating cantilever beam with hub radius (μ=1,α=5,Lz=70)

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Figure 3

Influence of setting angle ψ and inclination angle θ on the fundamental natural frequencies of a rotating cantilever beam without hub radius (μ=0,α=5,Lz=70)

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Figure 4

Influence of setting angle ψ and inclination angle θ on the second natural frequencies of a rotating cantilever beam with hub radius (μ=1,α=5,Lz=70)

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Figure 5

Influence of setting angle ψ and inclination angle θ on the second natural frequencies of a rotating cantilever beam without hub radius (μ=0,α=7,Lz=70)

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Figure 6

Influence of the rotating speed and the inclination angle θ on the fundamental natural frequencies of a rotating cantilever beam with a hub radius (μ=2,ψ=90°,Lz=35; dashed lines: the Coriolis force effect ignored; real line: the Coriolis force effect considered)

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Figure 7

Influence of the rotating speed and the inclination angle θ on the fundamental natural frequencies of a rotating cantilever beam with hub radius (μ=2,ψ=90°,Lz=70; dashed lines: the Coriolis force effect ignored; real line: the Coriolis force effect considered)

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