Nonlinear dynamic analysis of parked large wind turbine blade considering harmonic inertial excitation using continuum mathematical model

Abstract

In this paper, an investigation on the nonlinear dynamics of parked large wind turbine blades considering harmonic inertial excitation is presented. The investigation is based on the continuum mathematical model which is derived using the extended Hamilton principle. Employing the Euler–Bernoulli beam model, the equations of motion are derived by considering the flap-wise and edge-wise deformations as well as the cubic nonlinearity. The proposed model is validated through comparisons with both published results and numerical simulations. The nonlinear dynamics of the NREL 5-MW wind turbine blade is investigated numerically using a bifurcation toolbox MATCONT. The steady state primary resonances of the first three modes are compared and analyzed with varying excitation frequency and excitation direction. Results show that for parked blades the aerodynamic damping increases with the increase of inflow wind speed, and the response under low wind speed becomes more unfavorable than high wind speed. The blade response can suddenly jump up or down when the excitation direction varies slightly because of the saddle node bifurcation. The 3:1 internal resonance between the 1st and 3rd modes is also observed in this study, suggesting the possible interaction of the two modes during large amplitude vibration. Quasi-periodic motions can also be induced because of the Hopf bifurcation in the case of negative aerodynamic damping.