Coupled horizontal-rocking vibration of partially embedded pile groups and its effect on resonance of offshore wind turbine structures

The partially embedded pile groups bear tremendous moments generated by wind loads due to the large height of the offshore wind turbine structures. It is of great importance to consider the rocking vibration of the foundations in the lateral vibration analyses of wind turbine structures. In order to avoid resonance, which is very dangerous to high structures, the first-order natural frequencies of the wind turbine structures are always designed as away from 1P and 3P(2P) ones, so it is very important to calculate the natural frequencies of the wind turbine structures accurately during the design procedures. At present, the methods for calculating the dynamic characteristics of the wind turbine structures, including the natural frequencies, are usually based on the assumption of base fixity. Inaccuracies may occur in these methods for not considering the impedance of foundations. In this work, the coupled horizontal-rocking impedance of the pile group is derived and its impact on the resonance characteristics of the wind turbine structures is studied. First, a simplified method to determine the horizontal-rocking impedance of the pile group with dynamic Winkler model is proposed and verified by comparison against some published accurate solutions. Second, a lateral vibration equation for the wind turbine structures is derived with the consideration of the foundation impedance. Finally, through an example of wind turbine structure, the influence of the foundation impedance on the resonance characteristics of the structure is studied, and the proposed simplified method is verified by use of the finite element method.