Probability density analysis of nonlinear stochastic dynamics of horizontal axis wind turbine blades

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Wind turbine blades with horizontal axis are frequently subjected to cyclic and random loads during operation, which may decrease blade stability and impair power generation efficiency. In this paper, the finite element method (FEM) is mainly used to investigate the nonlinear stochastic dynamics of turbine blades and assess blade operation stability. The harmonic excitation and Gaussian white noise are combined to represent the external stimulation of the Mathieu-Duffing equation describing blade vibration, the Fokker-Planck (FP) equation is formulated and numerically solved using the FEM and the Crank Nicholson method to obtain the transient joint probability density function (PDF) and marginal PDF. The findings show that the blade's PDF exhibits an unstable split phenomenon in one vibration cycle, meaning that the blade's motion may jump randomly and has some uncertainty, potentially affecting blade operating stability and power generation efficiency. Furthermore, the sensitivity of blade stability to excitation strength is examined. The form and position of the PDF vary when the intensity of the harmonic excitation or noise is strong, increasing the random jump probability of blade vibration and compounding the instability and uncertainty of blade motion. Under severe circumstances, the blades may lose stability or even damage, endangering the safety and efficacy of blade operation. The current study might be used to evaluate blade stability and the overall safety of turbines. • The nonlinear stochastic dynamics of a horizontal axis wind turbine blade subjected to a combination excitation of harmonic and Gaussian white noise is investigated from the aspect of probability density. • The Fokker-Planck equation and transient probability density function of the blade vibration are numerically solved using the finite element method and the Crank-Nicolson time difference scheme, yielding the complete probability information of the blade in motion. • The findings demonstrate that the nonlinear stochastic vibration of the blade has unstable bifurcation features, which means that the blade may jump randomly, making its motion unpredictable and unstable, affecting the operation stability and power generation efficiency of the blade. • The effects of harmonic excitation and white noise intensity on blade vibration are studied. The results reveal that the higher the harmonic amplitude or white noise intensity, the easier the random jump of blade, and the blade may lose stability or possibly be destroyed, affecting the overall performance of the turbine.