Analysis of Coupled Vibration Characteristics of Wind Turbine Blade Based on Green’s Functions

This paper presents the analysis of dynamic characteristics of horizontal axis wind turbine blade, where the mode coupling among axial extension, flap vibration (out-of-plane bending), lead/lag vibration (in-plane bending) and torsion is emphasized. By using the Bernoulli-Euler beam to describe the slender blade which is mounted on rigid hub and subjected to unsteady aerodynamic force, the governing equation and characteristic equation of the coupled vibration of the blade are obtained. Due to the combined influences of mode coupling, centrifugal effect, and the non-uniform distribution of mass and stiffness, the explicit solution of characteristic equation is impossible to obtain. An equivalent transformation based on Green’s functions is taken for the characteristic equation, and then a system of integrodifferential equations is derived. The numerical difference methods are adopted to solve the integrodifferential equations to get natural frequencies and mode shapes. The influences of mode coupling, centrifugal effect, and rotational speed on natural frequencies and mode shapes are analyzed. Results show that: (1) the influence of bending-torsion coupling on natural frequency is tiny; (2) rotation has dramatic influence on bending frequency but little influence on torsion frequency; (3) the influence of bending-bending coupling on dynamic characteristics is notable at high rotational speed; (4) the effect of rotational speed on bending mode is tiny.