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TECHNICAL PAPERS

Differential Transformation Approach for Free Vibration Analysis of a Centrifugally Stiffened Timoshenko Beam

[+] Author and Article Information
C. Mei

Department of Mechanical Engineering, The University of Michigan—Dearborn, 4901 Evergreen Road, Dearborn, MI 48128cmei@umich.edu

J. Vib. Acoust 128(2), 170-175 (Dec 02, 2005) (6 pages) doi:10.1115/1.2172260 History: Received January 19, 2005; Revised December 02, 2005

In this paper, the differential transformation approach is applied to analyze the free vibration of centrifugally stiffened Timoshenko beam structures. Such structures involve variable coefficients in the governing equations, which in general cannot be solved analytically in closed form. Both the natural frequencies and the mode shapes are obtained using the differential transformation technique. Numerical examples are presented and results are compared with available results in the literature.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

A cantilevered rotating beam

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Figure 2

Convergence of the first three modes listed in Table 1 at various dimensionless rotation speed, (a) p=0; (b) p=4; (c) p=8

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Figure 3

Mode shapes of the first three modes corresponding to varying dimensionless rotation speed p: p=0 (—), p=4(-∙-∙-∙), and p=8(⋯)

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Figure 4

Mode shapes of the first three modes corresponding to varying dimensionless hub offset α:α=0 (—), α=1(-∙-∙-∙), and α=2(⋯)

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