Effects of Periodic Pitch Motion on the Nonlinear Frequency Characteristics of a Rotating Wind Turbine Blade

To investigate the nonlinear vibration characteristics of rotating wind turbine blades under periodic pitch excitation, this study establishes a coupled flapwise–edgewise aeroelastic dynamic model incorporating unsteady aerodynamic effects. Based on Greenberg’s unsteady aerodynamic theory, the blade pitch angle is expressed as the superposition of a static installation angle and a periodic dynamic pitch component. The governing equations are discretized using modal superposition and the Galerkin method, yielding generalized equations of motion with periodically time-varying coefficients. Fourier expansion and the method of multiple scales are subsequently employed to analyze the resulting parametric system, and the first-order approximate modal responses and amplitude–phase evolution equations are derived under non-resonant conditions. The results show that periodic pitch motion modulates the aerodynamic stiffness, equivalent structural stiffness, and modal coupling coefficients of the blade. Quantitatively, within the investigated parameter range, variation in the pitch amplitude causes changes of approximately 15.4%–26.6% in the first three flapwise nonlinear frequencies and 1.3%–36.4% in the corresponding edgewise frequencies, whereas the variations induced by the pitch frequency and initial phase remain below approximately 0.2%. Among the investigated pitch parameters, the pitch amplitude therefore has the strongest influence on the nonlinear frequency response. Moreover, the two bending directions exhibit distinct modulation characteristics: the flapwise modes predominantly show frequency hardening, whereas the edgewise modes tend to exhibit frequency softening. These results demonstrate that periodic pitch excitation produces a direction-dependent nonlinear frequency modulation of the rotating blade within the investigated non-resonant regime.