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TECHNICAL PAPERS

Vibrations of Tapered Timoshenko Beams in Terms of Static Timoshenko Beam Functions

[+] Author and Article Information
D. Zhou

School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210014, P. R. China

Y. K. Cheung

Department of Civil Engineering, The University of Hong Kong, Hong Kong

J. Appl. Mech 68(4), 596-602 (Aug 15, 2000) (7 pages) doi:10.1115/1.1357164 History: Received November 30, 1999; Revised August 15, 2000
Copyright © 2001 by ASME
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References

Figures

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The sketch of beams with continuously varying cross section; (a) the variation of cross-sectional area when r>0; (b) the variation of cross-sectional moment of inertia when s>0; (c) the variation of cross-sectional area when r<0; (d) the variation of cross-sectional moment inertia when s<0
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The first two eigenfrequencies of cantilevered sharp-ended Timoshenko beams with linearly varying thickness and/or width via the thickness-length ratio h1/l: –•– Ω1 and - -•- - Ω2 for the beams with linear varying thickness; –▴– Ω1 and - -▴- - Ω2 for the beams with linear varying width; –▪– Ω1 and - -▪- - Ω2 for the beams with linear varying both thickness and width
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The first three eigenfrequencies of cantilevered Timoshenko beams with linearly varying thickness via the thickness-length ratio h1/l for two values of truncation factors α=0.25 and α=0.5
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The first three eigenfrequencies of cantilevered Timoshenko beams with linearly varying width via the thickness-length ratio h1/l for two values of truncation factors α=0.25 and α=0.5
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The first three eigenfrequencies of cantilevered Timoshenko beams with linearly varying both thickness and width via the thickness-length ratio h1/l for two values of truncation factors α=0.25 and α=0.5
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The fundamental eigenfrequencies of cantilevered Timoshenko beams with the same thickness and width variation via the thickness-length ratio h1/l for the truncation factor α=0.5
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The first two eigenfrequencies of cantilevered sharp-ended Timoshenko beams via the thickness-length ratio h1/l: –•– Ω1 and - -•- - Ω2 for taper factors r=1,s=2; –▴– Ω1 and - -▴- - Ω2 for taper factors r=1/2,s=3/2; –▪– Ω1 and - -▪- - Ω2 for taper factors r=1/2,s=1/2

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