A new method to determine the shear coefficient of Timoshenko beam theory |
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Authors: | K.T. Chan |
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Affiliation: | a Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong, PR China b Department of Physics, The Chinese University of Hong Kong, Hong Kong, PR China c School of Engineering Sciences, Mechanical Engineering, University of Southampton, Highfield, Southampton SO17 1BJ, UK |
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Abstract: | The frequencies ω 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=mπ/L, where m is the mode number: ω2=A4q4+A6q6+?. 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 κ for any cross-section. The result agrees with the consensus best values in the literature, and provides a derivation of κ that does not rely on physical assumptions. |
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