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
- SourceAvailable from: hydyn.hanyang.ac.kr[show abstract] [hide abstract]
ABSTRACT: A modeling method for the flapwise bending vibration analysis of a rotating multi-layered composite beam is presented in this paper. For the modeling method, the shear and the rotary inertia effects are considered based on Timoshenko beam theory and hybrid deformation variables are employed to derive the equations of motion. Dimensionless parameters are identified from the equations of motion and the combined effects of the dimensionless parameters on the modal characteristics of the rotating composite beams are investigated through numerical study.Journal of Sound and Vibration 01/2005; 286(4):745-761. · 1.61 Impact Factor
- ARCHIVE Journal of Mechanical Engineering Science 1959-1982 (vols 1-23) 01/1969; 11(1):1-13.
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ABSTRACT: The in-plane and out-of-plane free vibrations of a rotating Timoshenko beam are analyzed by means of a finite element technique. The beam is discretized into a number of simple elements with four degrees of freedom each. The governing equations for the free vibrations of the rotating beam are derived from Hamilton's principle. The effects of hub radius, setting angle, shear deformation and rotary inertia are incorporated into a finite element model for determining the bending frequencies of the rotating beam. Numerical results for uniform cantilever beams with and without the hub radius are given for various values of the rotational speed, and are compared with the available results. It is shown that the present technique offers an accurate and effective method for solving the free vibration problems of rotating beams.International Journal of Mechanical Sciences. 01/1988;