The influence of taper ratio, elastic root restraint, setting angle and rotational speed on the bending natural frequencies of a rotating non-uniform beam is investigated using a semi-exact numerical method. One observes that the influence of taper ratio on the second and third natural frequencies of a rotating beam with constant width and linearly varied depth and a double-tapered beam is greater than that of a beam with constant depth and linearly varied width. For a beam with rotational flexibility only, the first three natural frequencies of the rotating beam are greater than those of the non-rotating beam. The second and third natural frequencies of a rotating beam with translational flexibility are greater than those of the non-rotating beam. However, the fundamental natural frequency of the rotating beam can be less than that of the non-rotating beam. In particular, when the translational rigidity of the root is relatively low and the setting angle and rotational speed of the beam are relatively high, the value of the natural frequency becomes pure imaginary and the phenomenon of divergence instability occurs. The natural frequencies are decreased when the setting angle is increased, and the influence of the setting angle on the natural frequencies becomes very significant when the phenomenon of divergence instability is about to occur.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanics of Materials
- Acoustics and Ultrasonics
- Mechanical Engineering