A three-degree-of-freedom model for vortex-induced vibrations of turbine blades

A new three-degree-of-freedom model simulating vortex-induced vibrations (VIVs) of turbine blades is proposed. Equations of motions include the coupling for bending and torsion of a blade as well as the fluid-blade interactions, which is described by a van der Pol oscillator. The 1:1 internal resonance analysis is carried out with the multiple scale method, and modulation equations are derived. Bifurcation curves for responses with respect to the detuning parameter and dimensionless freestream velocity are obtained. Effects of the system parameters including the lift and moment coefficients, structural damping, cubic nonlinearity and coupling parameters on the responses are investigated. It is found that dynamic behaviours such as the saddle-node and Hopf bifurcations can occur for certain values of the system parameters. The approximate solutions obtained by the multiple scale method are validated by a direct numerical simulation. The results indicate that the proposed three-degree-of-freedom model can be useful to explain the dynamic response characteristics of blades and to optimize the blade design.