A mathematical model for wind turbine blades

A mathematical model for an elastic wind turbine blade mounted on a rigid test stand is derived and compared with experimental results. The linear equations of motion describe small rotations of the test stand, blade lateral deflections and rotation of the chord. Warping, extension and tilt of the cross-sections are slaved to the dependent minimal co-ordinates in order to reduce the number of state variables.

Using the principle of virtual work, a procedure is employed which combines the volume discretization of general “solid”, or shell-type finite elements (FE), with the approach of global form functions (stretching over the whole blade length). The equations of motion are solved as an eigenvalue problem and the results are compared with an experimental modal analysis of a 19 m long blade.

The computed eigenfrequencies fit well, but the mathematical model underestimates the pitch motion of the blade chord. Parameter studies show the effect of warping. Despite the few degrees of freedom and uncertainties in the model parameters, the mathematical model approximates the measured blade dynamics well.