Along-wind response of a wind turbine tower with blade coupling subjected to rotationally sampled wind loading

This paper proposes an approach to investigate the along-wind forced vibration response of a wind turbine tower and rotating blades assembly subjected to rotationally sampled stationary wind loading. The wind turbine assembly consists of three rotating rotor blades connected to the top of a flexible annular tower, constituting a multi-body dynamic entity. The tower and rotating blades are each modelled as discretized multi-degree-of-freedom (MDOF) entities, allowing the free vibration characteristics of each to be obtained using a discrete parameter approach. The free vibration properties of the tower include the effect of a rigid mass at the top, representing the nacelle, and those of the blade include the effects of centrifugal stiffening due to rotation and blade gravity loadings. The blades are excited by drag force time-histories derived from discrete Fourier transform (DFT) representations of rotationally sampled wind turbulence spectra. Blade response time-histories are obtained using the mode acceleration method, which allows for the quantification of base shear forces due to flapping for the three blades to be obtained. This resultant base shear is imparted into the top of the tower. Wind drag loading on the tower is also considered, with a series of spatially correlated nodal force time-histories being derived using DFTs of wind force spectra. The tower/nacelle is then coupled with the rotating blades by combining their equations of motion and solving for the displacement at the top of the tower under compatibility conditions in the frequency domain. An inverse Fourier transform of the frequency domain response yields the response time-history of the coupled system. The response of an equivalent system that does not consider the blade/tower interaction is also investigated, and the results are compared.