Geometric Stiffness Models
Geometric stiffening models account for changes in structural response due to structural deflection from the reference (not deflected) state. Bladed provides models that include contributions from element axial and shear internal forces.
Geometric stiffness due to element axial forces
Traditional geometric stiffness models account for the effect of element internal axial forces on structural stiffness. This is illustrated schematically in Figure 1. Centrifugal loads in the structural elements lead to a restoring load that tends to increase the stiffness of the blade. A linear finite element model for an initially straight blade is illustrated on the left side of Figure 1. A centrifugal force applied to the blade in its deflected position does not cause a bending moment along the blade. This is normal for linear finite element (FE) models as deflections are assumed to be small. On the right side of the diagram, the effect of geometric stiffness is illustrated. As the centrifugal load is applied in the deflected blade position, a bending moment is generated in the blade. This extra bending moment can change the blade flapwise and edgewise frequencies.
Geometric stiffness forces in the axial direction are responsible for the well-known “centrifugal stiffening” effect, where blade vibrational frequencies increase with rotor speed.
Geometric stiffness due to element shear forces
There are also geometric stiffening forces associated with element internal shear forces. Figure 2 illustrates how torsion moments can be generated in the blade by application of shear forces to the blade in its displaced position. On the right side of the diagram, as the drag or lift load is applied in the deflected blade position, a torsional moment is generated in the blade. This extra torsional moment can affect the blade torsional dynamics.
When evaluating the geometric stiffness effect of shear forces, it is important to account for the change in orientation of the torsion axis of the blade elements due to deflection. This is illustrated in Figure 3, where the difference in internal torsional load between the “reference” and deflected coordinate system is shown. Whether this affect is included depends on whether IgnoreAxesOrientationDifferencesForShear is set true or false. For more details see the theory section about Translation and orientation offset between neutral and shear axes.
