Dynamic modeling and free vibration analysis of horizontal axis wind turbine blades in the flap-wise direction

Abstract

The dynamic modeling and free vibration analysis of horizontal axis wind turbine (HAWT) blades in the flap-wise direction are addressed in this paper. Blade kinetic and potential energy are evaluated while taking into account the influences of gravity force, centrifugal force, and the blade rotary inertia. Using Hamilton's principle, a nonlinear partial differential equation with time and space varying coefficients together with appropriate boundary conditions is derived as a novel and comprehensive dynamic model for the blade vibration in the flap-wise direction. After linearizing and simplifying the nonlinear model, the Rayleigh-Ritz method is employed to find natural frequencies and their associated mode shapes. Furthermore, the National Renewable Energy Laboratory (NREL) 5-MW reference wind turbine is chosen to investigate the effects of the rotary inertia, angular velocity, hub radius, pitch and precone angles on its dynamic characteristics. It is shown that increasing the hub radius and the angular velocity or decreasing the rotary inertia, significantly increases the natural frequencies while design parameters such as pitch or precone angles slightly affect the dynamic characteristics of the blades. The accuracy of the simplified model is also verified by comparing results for natural frequencies with some existing data in the literature.