Abstract
PurposeThe size of wind turbines is increasing because efficiency of the power production increases, but with the increasing blade lengths, weights and tower heights, vibration problems are also becoming important and challenging. Dynamic analysis of blades only may not be sufficient; flexibility of tower and foundation should also be considered for more accurate vibration analysis of the big size HAWT systems.MethodsIn this paper, coupled vibration of an onshore horizontal axis wind turbine is studied. Tower of the turbine is considered as Rayleigh beam which is having flexible foundation that has rocking and horizontal flexibilities. Nacelle mass, rotor-blade system mass, and inertia are taken into account. Tower fore-aft and side-to-side first three modes are considered. The orthogonal modes of Euler-Bernoulli beam having fixed-free boundary conditions are assumed. By using Lagrange equation, ten degrees of freedom dynamic equations are derived. Non-dimensionalized equations are obtained, two types of foundations are considered; one is the embedded in-stratum over bedrock and the other is the on-stratum over bedrock.ResultsIt is shown that rotor-bearing system inertias are lowering the tower fore-aft and side-to-side natural frequencies up to 35%. Rocking and horizontal flexibilities for different geometries of the tower footing are found and respective system natural frequencies are calculated. It is shown that footing geometry affects the tower fore-aft and side-to-side natural frequencies up to 5%, rocking natural frequencies of the system up to 50%, and horizontal natural frequencies of the system up to 40%.ConclusionsAlthough the effect of tower footing is not significant on the tower fore-aft and side-to-side flexible vibrations, systems horizontal and rocking natural frequencies are affected by the tower footing geometries significantly and cannot be ignored.