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TECHNICAL PAPERS

Rotation Effects on Vibration of Structures Seen From a Rotating Beam Simply Supported off the Rotation Axis

[+] Author and Article Information
J. Kim

Structural Dynamics Research Laboratory, Mechanical Engineering, University of Cincinnati, Cincinnati, OH 45221-0072jay.kim@uc.edu

J. Vib. Acoust 128(3), 328-337 (Nov 30, 2005) (10 pages) doi:10.1115/1.2172261 History: Received February 07, 2005; Revised November 30, 2005

In rotating beams, the Coriolis force acts through the mass and rotary inertias of the beam. A rotating beam simply supported off the axis of rotation is used as an example to study effects of this Coriolis force on vibration of structures. By adopting such a simple model, mass- and rotary inertia-induced terms in the free vibration responses can be obtained in separate, closed forms. The effect of each of these terms on vibration characteristics of the rotating beam is discussed in relation to parameters such as nonrotating natural frequencies, the rotation speed, and the slenderness ratio. Practical implications of these results in analyses of rotating structures of other types are discussed, for example estimating the significance of rotary inertias in relation to the slenderness ratio and the rotation speed.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 2

Infinitesimal element of beam in vibration subjected to a constant rotation

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Figure 3

Effective shear force caused by the gyroscopic moment

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Figure 4

(a) Natural frequencies of the rotating beam of circular section represented in rotating coordinates. (b) Natural frequencies of the circular rotating beam in rotating coordinates with directional information: positive frequency represents the forward mode and negative frequency represents the backward mode. (c) Natural frequencies of the circular rotating beam in nonrotating coordinates with directional information: positive frequency represents the forward mode and negative frequency represents the backward mode

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Figure 5

Motion of the rotating beam described in nonrotating coordinates: (a) circular beam and (b) rectangular beam

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Figure 9

The effect of rotary inertias on natural frequencies of the rectangular beam of slenderness ratio 10 and ε=2, described in nonrotating coordinates.---: when rotary inertias are considered,———: when rotary inertias are ignored.

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Figure 10

Motion of a rotor shaft in whirling

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Figure 11

Natural frequencies of the rotor shaft and rotating beam of the same circular section of slenderness ratio 10.———: rotor shaft, ---: rotating beam.

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Figure 1

(a) Rotating beam subjected to a constant rotation described in rotating coordinates. (b) Rotating beam subjected to a constant rotation described in nonrotating coordinates.

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Figure 6

(a) Natural frequencies of a rectangular beam of ε=Iyy∕Izz=3 when rotary inertias ignored and described in rotating coordinates. ω̂1:———, ω̂2:-∙-∙-∙, ω̂3:–––, ω̂4:∙⋯(b) Mode shape parameter Im(U3∕U2) of the rectangular beam in (a). ω̂1:———, ω̂2:-∙-∙-∙, ω̂3:–––, ω̂4:∙⋯(c) Natural frequencies of the rectangular beam in (a) described considering the direction of the motion. (d) Natural frequencies of the rectangular beam in (c) described in nonrotating coordinates.

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Figure 7

The effect of rotary inertias on natural frequencies of the circular beam of slenderness ratio 10, described in nonrotating coordinates.---: when rotary inertias are considered,———: when rotary inertias are ignored.

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Figure 8

The effect of rotary inertias on natural frequencies of the rectangular beam of slenderness ratio 20 and ε=2, described in nonrotating coordinates.---: when rotary inertias are considered,———: when rotary inertias are ignored.

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