Flexural vibrations of circular beams

摘要

For circular cylindrical beams, the Timoshenko theory, which includes shear and rotary effects, can be applied by introducing a constant K' = 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. (C) 1998 Academic Press Limited. [References: 10]