Pretwist and Shear Flexibility in the Vibrations of Turbine Blades

A theory is developed for pretwisted beams with finite shear flexibility. The effect of pretwist is accounted for via the axial derivative of the St. Venant warping function. The shear flexibility relies on a decomposition of the shear stresses into torsion and shear contributions, and the normalized strain energy of the latter is expressed in terms of the shear flexibility tensor. An explicit approximation for the shear flexibility tensor is derived for cross sections of moderate wall thickness. A special Legendre transformation is used to obtain a consistent discretization, which is then cast in the form of a finite beam element. The accuracy of the method is illustrated by comparison with experimental results for a steam turbine blade, and the effects of pretwist and shear flexibility are discussed.