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Technical Briefs

Stiff-String Basis Functions for Vibration Analysis of High Speed Rotating Beams

[+] Author and Article Information
Jagadish Babu Gunda

Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India

Ranjan Ganguli1

Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, Indiaganguli@aero.iisc.ernet.in

1

Corresponding author.

J. Appl. Mech 75(2), 024502 (Feb 25, 2008) (5 pages) doi:10.1115/1.2775497 History: Received July 12, 2006; Revised June 18, 2007; Published February 25, 2008

A new rotating beam finite element is developed in which the basis functions are obtained by the exact solution of the governing static homogenous differential equation of a stiff string, which results from an approximation in the rotating beam equation. These shape functions depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. Using this new element and the Hermite cubic finite element, a convergence study of natural frequencies is performed, and it is found that the new element converges much more rapidly than the conventional Hermite cubic element for the first two modes at higher rotation speeds. The new element is also applied for uniform and tapered rotating beams to determine the natural frequencies, and the results compare very well with the published results given in the literature.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Rotating tapered beam element geometry

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Figure 3

Variation of shape functions along the elements (N=1, λ=12) with the new and conventional finite elements at high rotation speed

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Figure 4

Variation of shape functions along the elements (N=1, λ=200) with the new and conventional finite elements at very high rotation speed

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Figure 5

Convergence of the natural frequencies with λ=12

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Figure 6

Convergence of the natural frequencies with λ=200

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