Vibrations of an isolated wind turbine blade using the finite element method

Abstract

The finite element method is applied to an isolated and twisted wind turbine blade which is rotating in a vertical plane to determine its structural dynamic characteristics. The equations of motion are formulated for a rotating beam with flap and lead-lag degrees of freedom subjected to nonsymmetric bending. Using a variational approach, a blade finite clement is developed from these equations of motion. Additionally, expressions are formulated for the elastic strain energy and kinetic energy of a rotating wind turbine blade. Lagrange's equation is applied to these energy expressions and an isoparametric finite element based on three dimensional elasticity and quadratic interpolation functions is developed.

Both sets of finite element equations are implemented in a general purpose computer program to solve the structural dynamics eigenvalue problem and results compare favorably with published data for the cases of a nontwisted cantilevered beam both at rest and while rotating. A blade finite element model of a 10KW horizontal axis wind turbine blade is presented and its lowest modes of vibration are calculated for the cases of the blade at rest and in operation at rotor speeds up to 250 RPM.