A Rayleigh-Ritz solution for high order natural frequencies and eigenmodes of monopile supported offshore wind turbines considering tapered towers and soil pile interactions

Abstract

Offshore wind turbines may be exposed to extreme or accidental loads during the service life, such as extreme water slamming, ship collisions, earthquakes, extreme winds, ice loads, etc. Under the action of such loads, they will respond not only in the primary eigenmode, but also high order modes. This paper presents a Rayleigh-Ritz solution for high order natural frequencies and eigenmodes of monopile supported offshore turbines. The model considers explicitly tapered wind turbine towers and soil-pile interactions. Different soil conditions are considered using equivalent cross coupled springs at the mudline. The proposed Rayleigh-Ritz solution is applied to the DTU 10 MW wind turbine mounted on a monopile foundation. The predicted natural frequencies and eigenmodes are compared with nonlinear finite element simulations using USFOS. The results show excellent agreement for the first 3 eigenmodes. Even higher eigenmodes than the 3rd order are also calculated but are not presented. They can be readily obtained if needed.

High order natural frequencies and eigenmodes using the proposed Rayleigh-Ritz solution can, together with the Duhamel's integral, be well utilized in the buckling and collapse analysis and design of monopile supported offshore wind turbines in Ultimate Limit States (ULS) and Accidental Limit States (ALS). In addition, the high accuracy of the predicted primary natural frequency makes it a useful design tool to help avoid undesired resonance from external excitation loads and to reduce resonance related fatigue effects in Fatigue Limit States (FLS).