An improved high-order finite element method for nonlinear vibration of a rotating flexible hub-beam

Abstract

This work investigates the nonlinear chordwise vibration characteristics of a rotating flexible hub-beam under gravitational loading using an improved high-order finite element (HFE) method. A geometrically exact dynamic model is established using slope angle variables and Hamilton’s principle, incorporating geometric nonlinearity, rotational effects (Coriolis force, centrifugal force, and rotational inertia), and material damping. The model is discretized using the HFE method with an improved integration element technique that subdivides each finite element into sub-elements to precompute integral values at their nodes. Subsequently, a piecewise Hermite interpolation is employed to obtain integral values over the element. This method effectively eliminates computationally intensive double integrals and enhances efficiency without compromising accuracy. Validation through a flexible pendulum example demonstrates the high accuracy and computational efficiency of the method. The Incremental Harmonic Balance (IHB) method is employed to analyze the nonlinear periodic responses of the rotating flexible hub-beam, while the Floquet theory is utilized to assess stability of these periodic solutions. The analysis reveals rich nonlinear phenomena, including jump phenomena, period-doubling bifurcations, subharmonic and superharmonic resonances. Parametric studies further indicate that increased beam length or reduced damping intensifies nonlinear effects, whereas a larger hub radius enhances stiffness, raises resonance frequencies, and suppresses bifurcations, though expanding instability regions at higher frequencies.