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

A new method to determine the shear coefficient of Timoshenko beam theory
A new method to determine the shear coefficient of Timoshenko beam theory
The frequencies 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 , where m is the mode number: . The coefficients A4 and A6 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 for any cross-section. The result agrees with the consensus best values in the literature, and provides a derivation of that does not rely on physical assumptions.
0022-460X
3488-3497
Chan, K.T.
7d33b162-af28-4970-9080-3de063cec990
Lai, K.F.
717fe179-ea58-45f2-8482-986075f631bb
Stephen, N.G.
af39d0e9-b190-421d-86fe-28b793d5bca3
Young, K.
33daac74-a29f-4676-9a99-c86ab703ecd8
Chan, K.T.
7d33b162-af28-4970-9080-3de063cec990
Lai, K.F.
717fe179-ea58-45f2-8482-986075f631bb
Stephen, N.G.
af39d0e9-b190-421d-86fe-28b793d5bca3
Young, K.
33daac74-a29f-4676-9a99-c86ab703ecd8

Chan, K.T., Lai, K.F., Stephen, N.G. and Young, K. (2011) A new method to determine the shear coefficient of Timoshenko beam theory. Journal of Sound and Vibration, 330 (14), 3488-3497. (doi:10.1016/j.jsv.2011.02.012).

Record type: Article

Abstract

The frequencies 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 , where m is the mode number: . The coefficients A4 and A6 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 for any cross-section. The result agrees with the consensus best values in the literature, and provides a derivation of that does not rely on physical assumptions.

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Submitted date: 8 February 2011
Published date: 4 July 2011

Identifiers

Local EPrints ID: 174639
URI: https://eprints.soton.ac.uk/id/eprint/174639
ISSN: 0022-460X
PURE UUID: af0bf660-331f-4387-ac9a-db129f89fd20

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Date deposited: 16 Feb 2011 11:18
Last modified: 19 Jul 2019 23:11

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