# Dynamics and Aeroelasticity of Flexible Rotor Blades

Since aspect ratios of wind turbine rotor blades are high, they can be regarded as slender beams. Modelling of rotor blades as flexible, infinitely thin beams is sufficient for most dynamic problems. Although in reality infinite number of modes could be used to describe dynamics of a wind turbine rotor blade, sufficient approximation of the behavior can be made with the aid of the primary dominant modes. The method of assumed modes belongs to the group of global methods and represents a fairly popular way of solving for the motion of rotor blades. A series of functions (mode shapes) are used for the first approximation of blade shape. Lagrange’s method and the Raleigh-Ritz method are some of the most typical of methods of assumed modes. They allow estimation of modal shapes and corre­sponding modal frequencies. However Galerkin’s method which is based on energy considerations represents most popular of these methods. It is widely used as it can be used in the case of nonslinear or non-conservative problems that both Lagrange’s and Raleigh-Ritz methods cannot solve (Bramwell et al. 2001). In Galerkin’s method, an approximation function is substituted into the partial dif­ferential equation of blade motion. The most significant aspect of Galerkin’s method applied to wind turbine rotors is that range of aerodynamic models of the loading and inflow dynamics can be incorporated into the analysis. If n different mode shapes and frequencies are considered, it is transformed into a system of n ordinary differential equations (Bramwell et al. 2001). The blade natural fre­quencies and actual mode shapes are determine from these equations. Thus, the complete set of linear equations may be obtained by combining the linear struc­tural dynamic equations of motion with the expressions for the linearized aero­dynamic loads. One may obtain a typical set of root loci for different rotor speeds (Fig. 4.8) or with different inflow velocities (Fig. 4.9).

 Fig. 4.7 Definition of coordinates for thin-walled sections

 Fig. 4.8 Blade root locus for changing rotor speeds, with the CG and tension axis offsets equal to zero

 Fig. 4.9 Blade root locus for increasing inflow velocities, with the CG and tension axis offsets equal to zero

 Blade Flutter Root Locus with variable inflow

 -60

 -40

 -20

 0