Mode acceleration approach for rotating wind turbine blades

Abstract

This paper presents a time-domain analytical approach for evaluating the displacement response in the flapping direction of rotating wind turbine blades subjected to stationary stochastic wind loading. This approach includes the effects of rotational sampling of the wind spectra on the blades. The blades are modelled as discrete multi-degree-of-freedom systems, consisting of tapered beams of rectangular hollow cross-section built using the finite element software code ANSYS. ANSYS is used to obtain the stiffness matrices of the blades, allowing the free vibration characteristics of the rotating blades to be determined by analytical formulation. A geometric stiffness matrix is included in the free vibration solution allowing for the centrifugal stiffening effects experienced by the blades to be included. Once the natural frequencies and mode shapes are obtained, the mode acceleration technique is employed to predict nodal responses to the prescribed wind loading. Nodal wind loading is obtained by generating artificial drag force time-histories, which have elevated energy at frequencies corresponding to integer multiples of the blade rotational frequency, in order to replicate realistic blade loading conditions. Blade nodal displacements based on rotationally sampled and nonrotationally sampled spectra are obtained for varying rotational frequencies. Blade response is also obtained in the frequency domain and used to verify the time-domain results.