Flapwise non-linear dynamics of wind turbine blades with both external and internal resonances

• Published in: International journal of non-linear mechanics 2014-05, Vol.61, p.1-14
• Main Authors: Li, L., Li, Y.H., Liu, Q.K., Lv, H.W.
• Format: Article
• Language: English
• Subjects: Aeroelasticity; Blades; Dynamical systems; Galerkin methods; Internal resonance; Mathematical models; Modal interaction; Nonlinear dynamics; Nonlinearity; Primary resonance; Vibration; Wind turbine blade; Wind turbines
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2014.01.006

An investigation on the non-linear aeroelastic behavior of a wind turbine blade with both external and internal resonances is presented. The external resonance is a primary resonance that appears at the first flapwise mode; it can cause severe damage to blade. The internal resonance happens at the first two flapwise modes; it can enhance the energy transfer between two modes, and change blade dynamics in primary resonance. Three aspects including blade behavior in pure primary resonance (abbr. PPR; only considering external resonance), blade behavior in combination resonance (abbr. CR; including both external and internal resonances), and the influence of internal resonance (i.e. modal interaction) on external resonance are examined. A simple Bernoulli–Euler beam model, in which geometric non-linearity and unsteady aerodynamic force are considered, is used to describe the flapwise motion of blade. The perturbation method is applied to the infinite-degree-of-freedom discrete system, which is obtained from the original continuous system via Galerkin׳s method, to get dynamic responses. Amplitude–frequency curves of resonance modes in CR and PPR are derived, and the stability of the steady state motion of blade is judged. The strongest modal interaction between two resonance modes is taken into account, and then effects of modal interaction, excitation amplitude, damping and non-linearity on non-linear vibration properties of blade are analyzed. Also, influences of three designing parameters (inflow ratio, setting angle and coning angle) and two detuning on the non-linear behavior of blade are discussed for a concrete downwind turbine. •Non-linear aeroelastic dynamics of blade in 1:1:3 CR and PPR are discussed.•The kinetic energy of blade concentrates on resonance modes in two resonances.•Geometric non-linearity has hardening effect.•Increasing the second damping can reduce the energy transfer between two modes.•Internal resonance can suppress the vibration of blade in external resonance.