An exact frequency equation in closed form for Timoshenko beam clampled at both ends

The author has discovered several errors which are not typographical in the frequency equations for a Timoshenko beam clamped at both ends by Huang who presented the frequency equations and normal mode equations for all six common types of simple, finite beams in closed form for the first time. The...

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Bibliographic Details
Published in:Journal of sound and vibration 2014-07, Vol.333 (14), p.3332-3337
Main Author: Kang, Jae-Hoon
Format: Article
Language:English
Subjects:
Bending
Clamping
Exact solutions
Mathematical analysis
Mathematical models
Ritz method
Timoshenko beams
Vibration
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Summary:The author has discovered several errors which are not typographical in the frequency equations for a Timoshenko beam clamped at both ends by Huang who presented the frequency equations and normal mode equations for all six common types of simple, finite beams in closed form for the first time. The exact frequency equations in closed form for Timoshenko beams clamped at both ends are derived based on his analysis. And then in order to justify the amended solutions of Huang, two versions of the closed form exact method and the Ritz method are applied. The frequency equations by the previous researcher present frequencies for only the flexural modes, while the closed form exact method and the Ritz method give ones for the thickness–shear modes as well as the bending modes. The purpose of the present study is to reveal the errors, correct them, and give some numerical results.
ISSN:0022-460X
1095-8568
DOI:10.1016/j.jsv.2014.02.027