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<p>Variable-pitch control can markedly improve the aerodynamic performance of vertical-axis wind turbines (VAWTs), yet it also introduces strong geometric nonlinearity, time-varying stiffness modulation, and cross-modal coupling in blade dynamics. This study develops a unified modeling–analysis framework for variable-pitch VAWT blades based on a three-dimensional coupled Euler–Bernoulli beam formulation with geometrically exact kinematics. Using Lagrangian energy methods, the governing equations are derived to capture pitch-induced parametric modulation and nonlinear stiffness effects. A Galerkin discretization combined with a multiple-scales perturbation procedure is employed to obtain closed-form amplitude–frequency response relations and detuning evolution laws, and stability boundaries are determined via analytical criteria; time-domain Runge–Kutta simulations are used for verification. The results show that pitch amplitude primarily controls the onset and width of the parametric instability tongue, while rotational speed mainly shifts its location. Multi-mode simulations further reveal a pronounced directional asymmetry in energy transfer: low-order modes readily excite higher-order modes once a finite threshold is exceeded, whereas high to low back-coupling is comparatively weak and requires stricter near-resonance conditions. The proposed framework provides quantitative stability maps and mechanistic insights to support robust controller tuning and structural safety assessment for variable-pitch VAWTs.</p>

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Nonlinear dynamic behavior and stability analysis of variable-pitch blades in vertical axis wind turbines

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Cong Xiong,
  • Liang Li,
  • Hongbang Wen,
  • Jingyi Cao,
  • Hongwei Zhou,
  • Weidong Zhu,
  • Long Wang,
  • Yinghui Li

摘要

Variable-pitch control can markedly improve the aerodynamic performance of vertical-axis wind turbines (VAWTs), yet it also introduces strong geometric nonlinearity, time-varying stiffness modulation, and cross-modal coupling in blade dynamics. This study develops a unified modeling–analysis framework for variable-pitch VAWT blades based on a three-dimensional coupled Euler–Bernoulli beam formulation with geometrically exact kinematics. Using Lagrangian energy methods, the governing equations are derived to capture pitch-induced parametric modulation and nonlinear stiffness effects. A Galerkin discretization combined with a multiple-scales perturbation procedure is employed to obtain closed-form amplitude–frequency response relations and detuning evolution laws, and stability boundaries are determined via analytical criteria; time-domain Runge–Kutta simulations are used for verification. The results show that pitch amplitude primarily controls the onset and width of the parametric instability tongue, while rotational speed mainly shifts its location. Multi-mode simulations further reveal a pronounced directional asymmetry in energy transfer: low-order modes readily excite higher-order modes once a finite threshold is exceeded, whereas high to low back-coupling is comparatively weak and requires stricter near-resonance conditions. The proposed framework provides quantitative stability maps and mechanistic insights to support robust controller tuning and structural safety assessment for variable-pitch VAWTs.