4.7 Article

A new method to determine the shear coefficient of Timoshenko beam theory

Journal

JOURNAL OF SOUND AND VIBRATION
Volume 330, Issue 14, Pages 3488-3497

Publisher

ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jsv.2011.02.012

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The frequencies omega of flexural vibrations in a uniform beam of arbitrary cross-section and length L are analysed by expanding the exact elastodynamics equations in powers of the wavenumber q = m pi/L, where m is the mode number: omega(2) = A(4)q(4) + A(6)q(6) + ... . The coefficients A(4) and A(6) are obtained without further assumptions; the former captures Euler-Bernoulli theory while the latter, when compared with Timoshenko beam theory rendered into the same form, unambiguously yields the shear coefficient kappa for any cross-section. The result agrees with the consensus best values in the literature, and provides a derivation of K that does not rely on physical assumptions. (C) 2011 Elsevier Ltd. All rights reserved.

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