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A continuum-based formulation is reported for torsional dynamics of gravity-base, monopile and suction caisson foundations supporting offshore wind turbines (OWTs). The applicability of the formulation for OWT foundations is verified with rigorous formulations in the literature, and applicable to conventional foundations – shallow footings, pile foundations and caissons. From this study, it is found that the present analysis is accurate, although the foundation-base is treated approximately. Further, the formulation is employed to obtain the foundation-head stiffness for gravity-base, monopile and suction caissons. This stiffness is obtained for a wide range of dimensionless frequency, and foundation–soil stiffness and slenderness ratios. From the results, it is found, the frequency has a reasonable effect on the foundation-head stiffness, and should be incorporated in the design of the OWT–foundation system, of course, based on the loading frequency and design requirements. These results can be used to describe the foundation at the base of the OWT structure above the seabed level, and subsequently calculate its natural frequency. The advantage of the results reported is that an integrated analysis for the OWT–foundation system is not required.

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