Non-Linear Vibration of Rotating Co-Rotational Two-Dimensional Beams With Large Displacement

In order to achieve better performances and reduce fuel consumption, the new generation of turbomachines uses larger and lighter design, for instance the “open-rotor” concept, and is conceived to rotate at higher speeds. Parts of the structure become then even more likely to undergo large amplitude vibrations. Consequently, the conception of future aero-engine requires a sound and robust technique to predict the rotating machine vibrations considering geometrical nonlinearities (large displacements and large deformation). In this paper, the nonlinear vibrations of rotating beams with large displacements is investigated by the use of the Co-Rotational (C-R) finite element method. In the C-R approach, the full motion of each element is decomposed into a rigid body part and a pure deformational part by introducing a local coordinate system attached to the element. The utilization of the C-R method offers the possibility to treat geometrical nonlinearity directly with pre-extracted rigid body motion displacements. 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.