The upper bound of the fundamental bending frequency of a rotating uniform Timoshenko beam with general elastically restrained root is derived via Rayleigh’s principle. Comparing the upper bound with the results in the existing literature and those obtained by the transfer matrix method reveals that the upper bound is quite reliable. It can be found that as the rigidities of the elastic at root are decreased, the difference between the fundamental bending frequency evaluated for a Timoshenko beam and that evaluated for a Bernoulli-Euler beam is decreased. In addition, the effect of rotational speed and slenderness ratio on the error of the upper bound and the influence of root elastic restraints on the fundamental bending frequency are examined.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Acoustics and Ultrasonics
- Mechanics of Materials
- Mechanical Engineering