General shell model for a rotating pretwisted blade

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A novel dynamic model for a pretwisted rotating compressor blade mounted at an arbitrary stagger angle using general shell theory and including the rotational velocity is developed to study the eigenfrequencies and damping properties of the pretwisted rotating blade. The strain–displacement relation and constitutive model based on the general (thick) shell theory are applied to bring out the strain energy of the rotating blade. Using Hamilton's principle, the variational form of the total energy is derived in order to obtain the corresponding weak form for the numerical simulation. The model is validated by comparing to the literature results and Ansys results, showing good agreement. Parametric analyses are carried out to study the influence of the rotation velocity, the stagger angle and the radius of the disk on the eigenfrequencies of the pretwisted blade. Proportional damping is included into the proposed model to investigate the influence of rotational velocity on the damping characteristics of the pretwisted rotating blade system. It is shown that, due to inertial and Coriolis effects, damping decreases as the rotation velocity increases for the lower part of the velocity range considered and either decreases or increases depending on the mode order for higher velocities. Furthermore, frequency loci veering as a result of the rotation velocity is observed. The proposed model is an efficient and accurate tool for predicting the dynamic behavior of compressor blades of arbitrary thickness, stagger angle and pretwist, potentially during the early designing stage of turbomachinery.