Identification of Modal Damping Ratios for a Simplified Wind Turbine Tower Using Fourier Analysis

This paper presents an approach to evaluate the modal damping ratios for a simplified wind turbine tower, using Fourier analysis and linear regression. The model proposed for the wind turbine tower is composed of a flexible tower and rotor blade system, inter-connected using a sub-structuring technique, which facilitates the rotating blade/tower coupling. A model order reduction technique is first used to model each of the two sub-structures (tower/nacelle and rotor system) as single degree-of-freedom systems. The free vibration characteristics of the tower include the effects of a large nacelle mass at the towers free end, and the corresponding properties of the rotating blades include the effects of centrifugal stiffening and axial self-weight, due to rotation. Then, the two reduced order sub systems are then coupled together to form an equivalent two degree-of-freedom coupled tower/blade wind turbine tower model. A wind-induced forced vibration analysis of the coupled tower/blades model is carried out using artificially generated wind drag time-histories obtained as discrete Fourier transform representations of wind drag power spectral density functions. From this analysis, a method is proposed, based on Fourier analysis and the linear regression, to solve the inverse problem for evaluating the first and second modal damping ratios of the coupled system. A numerical example is presented in order to demonstrate the applicability of the proposed approach, where excellent agreement was observed between the originally specified modal damping ratios and the subsequently estimated ones. The proposed method can be extended to obtain the equivalent damping of the system with soil interaction and including aerodynamic damping.