Parametric Vibration and Combined Resonance of A Bending-Torsional Coupled Turbine Blade With A Pre-Set Angle

The parametric vibration and combined resonance of a turbine blade with a pre-set angle subjected to the combined effect of parametric and forced excitation were investigated. The blade was modeled as a rotating beam considering the effects of centrifugal, gyroscopic, and bending-torsion coupling. The instability region of the corresponding linear system with parametric excitation was analyzed using Floquet theory, and the effect of blade parameters on this region was discussed. Notably, the parametric vibration of the torsional degree of freedom caused by parametric excitation of the bending degree of freedom has been found. The results show that the size and position of the parameter resonance region are affected by the blade aspect ratio and preset angle, respectively. Furthermore, the multi-scale method was employed to solve the blade equation under the combined action of parametric and forced excitation to study the combined resonance caused by forced excitation and gyroscopic item. The effect of blade parameters and excitation characteristics on regions of combined resonance were investigated. The phenomenon of heteroclinic bifurcation was observed due to changes in the excitation frequency, and the harmonic components that accompanied the bifurcation changed. Specifically, a multi-period response dominated by the excitation frequency and subharmonic components shifted to a single-period response dominated by subharmonic components. This study provides a theoretical explanation for the non-synchronous resonance of blades and the subharmonic signals in blade vibration and guides blade parameter design, especially for wind turbines.