Modal Dynamics of Wind Turbines with Anisotropic Rotors

Equations of motion for wind turbines contain periodic terms due to the rotor rotation. For a three-bladed isotropic rotor the traditional approach for conducting modal analysis is to use the Coleman transformation to yield a time-invariant system. Eigenvalue analysis of this system produces frequencies, damping and mode shapes. When the rotor is anisotropic, e.g. due to a difference in blade stiffness, the periodic terms are not completely removed by the Coleman transformation and an eigenvalue problem cannot be set up in this way. Modal analysis can be performed using Floquet analysis or using Hill’s method where the equation system is expanded to obtain eigenvalues and-vectors of a selected number of terms in a Fourier series. The modal solutions for the isotropic rotor contain harmonic terms of the eigenfrequency and terms with frequencies of the rotor speed plus and minus the eigenfrequency. Applying an anisotropy on the rotor creates additional harmonic terms in the solutions. Through a numerical example of a simple structural model of a wind turbine the modal dynamics are illustrated using the different methods. I