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

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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