Frequencies of Longitudinal Vibration for a Slender Rod of Variable Section

The natural frequencies of a slender, homogeneous, fixed-free rod of variable section are studied in a one-dimensional theory. The rod is uniform at the fixed end for a certain distance L1, and then tapers for a distance L2 so that the cross-sectional area varies linearly. The frequency equation is...

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Bibliographic Details
Published in:Journal of applied mechanics 1953-06, Vol.20 (2), p.173-177
Main Authors: Lubkin, James L, Luke, Yudell L
Format: Article
Language:English
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Summary:The natural frequencies of a slender, homogeneous, fixed-free rod of variable section are studied in a one-dimensional theory. The rod is uniform at the fixed end for a certain distance L1, and then tapers for a distance L2 so that the cross-sectional area varies linearly. The frequency equation is derived and its first five zeros are tabulated for several ratios of L1 to L2, and various tapers. The first few terms of asymptotic expansions for the roots of the frequency equation are presented and discussed.
ISSN:0021-8936
1528-9036
DOI:10.1115/1.4010645