Complex Modal Analysis of Non-Modally Damped Wind Turbine Blade

Abstract

The vibration model of a wind turbine blade can be approximated as a rotating pretwisted nonsymmetric beam, with damping and gravitational and aeroelastic loading. In this work, the out-of-plane (flapwise) and in-plane (edgewise) motion are examined with simple aeroelastic damping effects. The aeroelastic model used is based on a simple quasisteady blade-element airfoil theory. The linear velocity dependent terms are isolated and incorporated into the damping, which then turns out to be generally non modal (non Caughey). The complex modes are analyzed while neglecting the effects of rotation to single out the effect that aerodynamic damping may have on the modes. The analysis is done by first discretizing the system with assumed modes, and then solving an eigenvalue problem for the state-variable description of the discretized system. The eigen modes are recombined with the assumed mode functions to approximate the modes in the original system. The analysis is performed on the National Renewable Energy Laboratory (NREL) 23-meter blade, the NREL 63-meter blade, and the Sandia 100-meter blade. The effects of nonproportional damping are seen to become more significant as the blade size increases. The results provide some experience for the validity of making modal damping assumptions in blade analyses.