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: Jie Yuan[Show abstract] [Hide abstract]
ABSTRACT: The work introduces a novel reduced order model (ROM) technique to describe the dynamic behavior of turbofan aeroengine blades. We introduce an equivalent 3D frame model to describe the coupled flexural/torsional mode shapes, with their relevant natural frequencies and associated modal masses. The frame configurations are identified through a structural identification approach based on a simulated annealing algorithm with stochastic tunneling. The cost functions are constituted by linear combinations of relative errors associated to the resonance frequencies, the individual modal assurance criteria (MAC), and on either overall static or modal masses. When static masses are considered the optimized 3D frame can represent the blade dynamic behavior with an 8% error on the MAC, a 1% error on the associated modal frequencies and a 1% error on the overall static mass. When using modal masses in the cost function the performance of the ROM is similar, but the overall error increases to 7%. The approach proposed in this paper is considerably more accurate than state-of-the-art blade ROMs based on traditional Timoshenko beams, and provides excellent accuracy at reduced computational time when compared against high fidelity FE models. A sensitivity analysis shows that the proposed model can adequately predict the global trends of the variations of the natural frequencies when lumped masses are used for mistuning analysis. The proposed ROM also follows extremely closely the sensitivity of the high fidelity finite element models when the material parameters are used in the sensitivity.Mechanical Systems and Signal Processing 03/2015; DOI:10.1016/j.ymssp.2015.02.015 · 2.47 Impact Factor
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ABSTRACT: Twisting chirality is widely observed in artificial and natural materials and structures at different length scales. In this paper, we theoretically investigate the effect of twisting chiral morphology on the mechanical properties of elastic beams by using the Timoshenko beam model. Particular attention is paid to the transverse bending and axial buckling of a pre-twisted rectangular beam. The analytical solution is first derived for the deflection of a clamped-free beam under a uniformly or periodically distributed transverse force. The critical buckling condition of the beam subjected to its self-weight and an axial compressive force is further solved. The results show that the twisting morphology can significantly improve the resistance of beams to both transverse bending and axial buckling. This study helps understand some phenomena associated with twisting chirality in nature and provides inspirations for the design of novel devices and structures.Acta Mechanica Sinica 08/2014; 30(4):507-515. DOI:10.1007/s10409-014-0067-0 · 0.62 Impact Factor
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ABSTRACT: Analytical solutions for the vibration of a beam with axial force subjected to generalized support motion are obtained in this paper. The finite element method (FEM) is introduced to validate the analytical solution obtained by an analytical approach. The dynamic responses of clamped–clamped, pinned–pinned and clamped–pinned beams with axial tension or compression are obtained via analytical approach and FEM. Comparing results show that the analytical approach is effective. The analytical analysis shows that the resonance will occur in general when the oscillatory frequency of transverse motion or rotation of any support end is equal to the natural frequency of the beam. Moreover, several cases in which the resonance disappears even if the frequencies of support excitations are equal to the natural frequencies of the beam are detected and are validated by the FEM solution.Journal of Sound and Vibration 03/2015; 338. DOI:10.1016/j.jsv.2014.11.004 · 1.86 Impact Factor