Analytical Estimation of Natural Frequencies of Offshore Monopile Wind Turbines

A comprehensive analytical solution for the estimation of natural frequencies of monopile supported Offshore Wind Turbines (OWTs) is proposed in this paper. The solution is based on the non-dimensional equations established using the Euler-Bernoulli beam theory and relevant boundary conditions. The equations of motion for above water and underwater are separated to compensate for the effect of added mass. Therefore, three equations of motion are established to simulate the motion of the monopile underwater, above water, and tower. The tower is considered a tapered tubular structure that linearly varies in diameter from bottom to top. Four sets of boundary conditions are also established at the seabed, seawater, platform, and nacelle levels. The seabed boundary conditions are to model the effect of the monopile section under the seabed by using the coupled springs. The seawater and platform level boundary conditions are the continuity conditions to link the monopile underwater, above water, and tower. The translational and rotational masses of the nacelle-rotor assembly are also included in the boundary conditions at the nacelle level. The non-dimensional equations are solved for a DTU 10 MW OWT case, and the results are compared to similar works. Besides, the 1st natural frequency of the system is evaluated for different values of monopile length and cross-section. The proposed method can easily be programmed to estimate the natural frequencies of the OWT structures.