NDLI: Dynamics of a Spinning Hollow Rayleigh Beam in General Boundary Conditions

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Sheu, Geeng Jen
Copyright Year	2004
Abstract	The analytical solutions of the whirl speed, the critical speed and the mode shape of a spinning hollow beam in six general boundary conditions are presented in this paper. The beam is represented by a Rayleigh model with the rotatory moment inertia and the gyroscopic effects. It is shown that the critical speed be written in a function of the whirl ratio (λ) defined by the spinning speed over the whirl speed, the hollowness ratio (α) defined by the hollow area over the total area of the cross section, and the slenderness ratio (l) defined by the beam’s length over its outer radius. Only a finite number of critical speeds exist, and hence finite precessional modes can be found during overall operation ranges when λ > 1/2, and the number is independent of the boundary conditions. The steady state unbalanced response can be therefore expressed analytically in terms of the finite precessional modes in resonance.
Sponsorship	International Gas Turbine Institute
Starting Page	631
Ending Page	637
Page Count	7
File Format	PDF
ISBN	0791841715
DOI	10.1115/GT2004-53402
e-ISBN	0791837394
Volume Number	Volume 6: Turbo Expo 2004
Conference Proceedings	ASME Turbo Expo 2004: Power for Land, Sea, and Air
Language	English
Publisher Date	2004-06-14
Publisher Place	Vienna, Austria
Access Restriction	Subscribed
Subject Keyword	Mode shapes Spinning (textile) Whirls Spin (aerodynamics) Inertia (mechanics) Dynamics (mechanics) Boundary-value problems Resonance Steady state
Content Type	Text
Resource Type	Article

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