Simplified Calculation Method for the Natural Frequencies of the Offshore Wind Turbine Structures with Monopile Foundations Based on Euler–Bernoulli Beam Theory

The wind and wave loads on the offshore wind-turbine (OWT) structures with monopile foundations occur at specific frequencies. When these excitation frequencies are close to the natural frequencies of OWT structures, resonance can disturb the proper operation of the power-generation equipment and shorten the service life of the structural system. Therefore, to ensure safe and efficient operation, the natural frequencies of the OWT structures with monopile foundations must be determined. To this end, a calculation method for the natural frequencies of the OWT structures with monopile foundations is proposed. This method, which considers the mass ratio (the ratio of the lumped mass on the top of the tower to the total mass of the tower, the transition piece, and the monopile above the mudline) as well as the nonuniform moment of inertia of the structures above the mudline and the soil–structure interaction (SSI), is derived using the Euler–Bernoulli beam differential equation and slope-displacement equation of a monopile according to the flexibility matrix, stiffness equivalent principle, and virtual work principle. Finally, the natural frequency calculation method is compared with finite element simulation and other calculation methods.