The vibrations of pre-twisted rotating Timoshenko beams by the Rayleigh–Ritz method
ABSTRACT A modeling method for flapwise and chordwise bending vibration analysis of rotating pre-twisted Timoshenko beams is introduced.
In the present modeling method, the shear and the rotary inertia effects on the modal characteristics are correctly included
based on the Timoshenko beam theory. The kinetic and potential energy expressions of this model are derived from the Rayleigh–Ritz
method, using a set of hybrid deformation variables. The equations of motion of the rotating beam are derived from the kinetic
and potential energy expressions introduced in the present study. The equations thus derived are transmitted into dimensionless
forms in which main dimensionless parameters are identified. The effects of dimensionless parameters such as the hub radius
ratio, slenderness ration, etc. on the natural frequencies and modal characteristics of rotating pre-twisted beams are successfully
examined through numerical studies. Finally the resonance frequency of the rotating beam is evaluated.
KeywordsModal characteristics–Pre-twisted rotating Timoshenko beams–Hybrid deformation variables–Dimensionless parameters–Rayleigh–Ritz method