General 3D solution to the free vibration of offshore wind turbines supported on multiple foundations

Dynamic characterization of offshore wind turbines (OWTs) is an important design consideration dictating two Limit States: Serviceability Limit State (SLS), and the Fatigue Limit State (FLS). Hence determining the natural frequency of the system considering Soil-Structure-Interaction, is an important design parameter and is also necessary in preliminary concept design. Currently, OWTs are planned to be installed in deeper waters where support structures (for example Jackets and seabed frames) are founded on multiple foundations. This paper presents a general 3D solution to obtain the natural frequencies of OWTs supported on multiple foundations. A mechanical idealization is presented, and mass and stiffness matrices were derived using the Euler-Lagrange method. This method will enable designers to study the natural frequency of the system under different conditions where the foundation supports may have different mass and stiffness properties and is compared to the Finite Element method. Using the derived formulations critical front-end design considerations are provided such as the effect of soil spatial variability, the effect of aspect ratio, and effect of foundation mass.