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Research Papers

Nonlinear Vibration of Rotating Corotational Two-Dimensional Beams With Large Displacement

[+] Author and Article Information
Zihan Shen

Ecole Centrale de Lyon,
LTDS UMR 5513,
Ecully 69130, France;
ANSYS France,
Villeurbanne 69100, France
e-mail: zihan.shen@doctorant.ec-lyon.fr

Benjamin Chouvion, Fabrice Thouverez

Ecole Centrale de Lyon,
LTDS UMR 5513,
Ecully 69130, France

Aline Beley, Jean-Daniel Beley

ANSYS France,
Villeurbanne 69100, France

1Corresponding author.

Manuscript received June 26, 2018; final manuscript received July 10, 2018; published online December 7, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(5), 051008 (Dec 07, 2018) (8 pages) Paper No: GTP-18-1365; doi: 10.1115/1.4041024 History: Received June 26, 2018; Revised July 10, 2018

In this paper, the nonlinear vibrations of rotating beams with large displacements are investigated by the use of the co-rotational (C-R) finite element method. In the C-R approach, the full motion is decomposed into a rigid body part and a pure deformational part by introducing a local coordinate system attached to the element. The originality we propose in this study is to derive its formulation in a rotating reference frame and include both centrifugal and gyroscopic effects. The nonlinear governing equations are obtained from Lagrange's equations using a consistent expression for the kinetic energy. With this formulation, the spin-stiffening effect from geometrical nonlinearities due to large displacements is accurately handled. The proposed approach is then applied to several types of mechanical analysis (static large deformation, modal analysis at different spin speeds, and transient analysis after an impulsive force) to verify its accuracy and demonstrate its efficiency.

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Figures

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Fig. 1

Kinematics of rotating deformed beam: (a) global kinematics and (b) local kinematics

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Fig. 2

Static large deformation analysis: (a) Cantilever beam under different tip moment (0, 0.2Mcr, 0.4Mcr, 0.6Mcr, 0.8Mcr, and Mcr) and (b) rolled-up rotating cantilever beam with different spin speed (η = 0, 2, 4, 6, 8, 10)

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Fig. 3

Convergence analysis for C-R formulation

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Fig. 4

Large amplitude vibration of cantilever beam: (a) vertical displacement and (b) horizontal displacement

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Fig. 5

Vertical tip response to an impulsive force

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