Computation of the modes and polar moment of inertial of the blades of an HAWT

The coupled differential equations of motion of the blades of a horizontal axis wind turbine are solved numerically, permitting the optimization of the design at relatively low cost. The equation of motion is transformed into a set of first order equations and solved with fourth order Runge-Kutta integrators. This technique is applied to a twisted, tapered blade of variable cross section and stiffness including discontinuities. The first six natural frequencies and mode shapes are obtained. The polar moment of inertia of the blades is obtained as a function of frequency and rotational speed.