Structural Vibration Analysis of Large-scale Wind Turbines Considering Periodically Time-Varying Parameters

Dynamics of the wind turbine, which is a rotor system possessing a number of rotor blades, is characterized by a set of linear differential equations with periodically time-varying parameters. And the periodic terms in the equation-of-motion leads to difficulties in investigating the wind turbine dynamics by means of the ordinary dynamic analysis methods for time-invariant system. In the present paper, a coordinate transformation approach, which employs the Hill’s infinite order determinant, is proposed to take the periodic parameters into consideration in the analysis for the wind turbine by extending the periodic system matrices into equivalent time-invariant matrices of infinite dimension. For a typical three-bladed horizontalaxis wind turbine, the eigenvalue and directional spectral analyses are treated as a numerical example that demonstrates the proposed approach provides more precise analysis results than given by the conventional method commonly adopted in the field of wind turbines.