Bending vibrations of a rotating non-uniform beam with tip mass and an elastically restrained root

Abstract

The influence of taper ratio, elastic root restraints, tip mass, setting angle and rotating speed on the pure bending vibration of rotating non-uniform beams is investigated. The characteristic equation is derived in term of the four fundamental solutions of the system. The three different non-uniform beams considered are the tapered beams with linearly varying width and constant depth, constant width and linearly varying depth, and linearly varying width and depth. The results indicate that the effect of taper ratio on the first natural frequencies of the three different tapered beams is less significant than those on the second and third natural frequencies, besides the beam with linearly varying width, constant depth and without tip mass. The tip mass can depress the effect of taper ratio on the first natural frequencies. For the second and third natural frequencies, as the taper ratio is increased, there exists a cross-over between the natural frequencies of the rotating beams with and without tip mass. While changing the rotational and translational elastic spring constants, there may also exist a cross-over between the third natural frequencies of the rotating beam with and without tip mass.