Abstract
For circular cylindrical beams, the Timoshenko theory, which includes shear and rotary effects, can be applied by introducing a constantK′=0·9. The study presented here takes into account the actual configuration and thus makes it an integral part of the analysis. A variational approach previously used [7] is followed. A simplification of the three-dimensional problem is obtained using the inverse method due to St. Venant. A biquadratic equation yields numerical results for the natural frequencies of the first three modes for the following cases: simply supported, fixed–fixed, free–free and fixed–free.
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