Refined tower mass coefficient for natural frequency of offshore wind turbines with SSI and P–Δ

One of the most critical aspects in the dynamic design of offshore wind turbines is the accurate determination of the first natural frequency. A key factor in this analysis is the inclusion of the tower mass in the dynamic model through appropriate mass-participation coefficients. In previous studies, these coefficients were derived under similar assumptions and have typically shown close numerical values. In the present study, the proposed coefficient differs by approximately 8–12 % from those reported in the literature and has been validated using data from turbines with various rated capacities, ranging from early designs to modern large-scale systems. The analysis further demonstrates that, when soil effects are considered, this coefficient should not be treated as a constant but rather as a function of soil stiffness and foundation displacement. Additionally, the influence of increasing rotor diameters—associated with higher rotor–nacelle–assembly (RNA) mass—and taller tower geometries is investigated in relation to the P–Δ effect (i.e., the global second-order geometric nonlinearity caused by axial load acting on the laterally displaced tower). Although these effects vary with tower dimensions and rated power, their overall influence on the natural frequency remains below 3 %. The findings indicate that the proposed coefficient enables more accurate estimation of the dynamic behavior of next-generation offshore wind turbines and can serve as a reliable correction parameter for preliminary design and resonance-free frequency assessment.