Keywords: wind turbine tower, along-wind response, soil-structure interaction, simple models, fast Fourier transform.

This paper investigates the along-wind forced vibration response of a wind turbine tower subjected to stationary random wind loading and includes the dynamic interaction effects between the foundation of the tower and the underlying soil. 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. Each of the two sub-structures (tower/nacelle and rotor system) are first separately modelled 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. The two sub systems are then coupled together to form a two degree-of-freedom coupled tower/blade wind turbine tower model.

The foundation of the structure is modelled as a circular footing, whose movement is related to the surrounding elastic soil by means of a complex translational impedance function. The impedance function is dependant on the shear wave velocity and Poisson's ratio of the soil medium. The soil impedance function used in this paper is that presented by Velestos and Verbic [1] in which the foundation is modelled as a rigid massless circular disk, resting on an elastic halfspace.

Transfer functions for displacement at the top of the tower due to the presence of a unit harmonic load are derived including and excluding soil/structure interaction effects. These transfer functions are then used to estimate the along-wind forced vibration response at the top of the tower. Time-histories of wind drag loading are generated from discrete Fourier transform representations of wind drag power spectral density functions using the technique outlined in Murtagh et al [2], and the fast Fourier transform of these are used as input to the transfer functions. The response of the system may then be computed from the inverse fast Fourier transform of the output, where the effects of soil/structural interaction are observed.

A numerical example is presented to qualitatively illustrate the effects of soil-structure interaction on the two degree-of-freedom wind turbine tower model, with representative geometry. Figures contrasting the inclusion and exclusion of soil-structure interaction effects on the transfer functions are presented separately for both modes. It is observed from these transfer functions that soil-structure interaction has the effect of decreasing the natural frequency of the structure (lengthening the natural period) and also adds a consider amount of damping to the system. This is further substantiated by comparing the along-wind response time-histories simulated at the top of the tower including and excluding soil-structure interaction.

1

A.S. Veletsos, B. Verbic, "Vibration of viscoelastic foundations", Earthquake Engineering and Structural Dynamics, 2, 87-102, 1973. doi:10.1002/eqe.4290020108

2

P.J. Murtagh, B. Basu, B.M. Broderick, "Wind force time-history generation by Discrete Fourier Transform (DFT)", 3rd International Symposium on Multi-body Dynamics: Monitoring and Simulation Techniques, Loughborough, UK, 147-154, 2004.

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