Nonlinear Vibration of Rotating Co-Rotational 2D Beams with Large Displacement

[+] Author and Article Information
Zihan Shen

Ecole Centrale de Lyon, LTDS UMR 5513, 69130 Ecully, France; ANSYS France, 69100 Villeurbanne, France

Benjamin Chouvion

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

Fabrice Thouverez

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

Aline Beley

ANSYS France, 69100 Villeurbanne, France

Jean-Daniel Beley

11 Avenue Albert Einstein Lyon, Select State/Province 69100 France

1Corresponding author.

ASME doi:10.1115/1.4041024 History: Received June 26, 2018; Revised July 10, 2018


In this paper, the Co-Rotational (C-R) finite element method derived from a rotating reference frame is proposed to investigate the nonlinear vibration of rotating 2D beams with large displacement. This method has been widely applied for static analysis with very large displacement. However, at present, the application of the C-R method in the non-linear dynamic analysis is relatively limited, especially in rotating machinery simulations. The consideration of C-R method provides us with the possibility to treat geometrical nonlinearity directly with pre-extracted rigid body motion displacements. Moreover, it re-activates the existing linear finite element library, as the pure deformational displacements are also extracted. In this work, the Euler-Bernoulli beam hypotheses are used but the extension to other beam theory should not be an issue. The accuracy of the C-R formulation is examined by a convergence theoretical study by comparing the approximated strains in local C-R frames with exact ones derived in Total Lagrangian formulations. In our proposed C-R formulation, starting from the consistent expression of kinematic energy, the governing equations for nonlinear vibration are obtained by using Lagrange's equations, in which the constant angular velocity is taken into consideration. By this way, the geometrical nonlinearity of large displacement is perfectly dealt with. To enhance the numerical simulations, the mass, the Coriolis, and the tangent stiffness matrices are derived analytically. The proposed formulations are used in modal and temporal simulations comparing with results from Total-Lagrangian formulations.

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