Abstract
The purpose of this paper is to extend a previously published beam model of a turbine blade including the centrifugal force field and root flexibility effects on a finite element model and to demonstrate the performance, accuracy and efficiency of the extended model for computing the natural frequencies. Therefore, only the modifications due to rotation and elastic root are presented in great detail. Considering the shear center effect on the transverse displacements, the geometric stiffness matrix due to the centrifugal force is developed from the geometric strain energy expression based on the large deflections and the increase of torsional stiffness because of the axial stress. In this work, the root flexibility of the blade is idealized by a continuum model unlike the discrete model approach of a combination of translational and rotational elastic springs, as used by other researchers. The cross-section properties of the fir-tree root of the blade considered as an example are expressed by assigning proper order polynomial functions similar to cross-sectional properties of a tapered blade. The correctness of the present extended finite element model is confirmed by the experimental and calculated results available in the literature. Comparisons of the present model results with those in the literature indicate excellent agreement.
Highlights
Pre-twisted beams with aerofoil cross-section are used in several types of engineering structures, such as turbine blades, helicopter blades, aircraft propellers, and wind turbine blades
Cross-section properties of the pre-twisted part of the blade given in tabular form at nine discrete cross-sections along the Z-axis in [15,20] are formulated by assigning the polynomial functions as given in [20]
The cross-sectional data of the root are expressed as fourth-order polynomial functions determined by curve fitting
Summary
Pre-twisted beams with aerofoil cross-section are used in several types of engineering structures, such as turbine blades, helicopter blades, aircraft propellers, and wind turbine blades. If the centroid and shear center are not coincident as in the pre-twisted beam with an aerofoil cross-section, the flexural vibrations in two planes and torsional vibrations are inevitably coupled. Blade failure due to vibrations at or near a resonant condition has led to appreciable research in this field to avoid such undesired results. Many researchers have reported results on the vibrations of rotating pre-twisted beams of rectangular cross-section but few have discussed the same problem for an asymmetrical aerofoil cross-section. Since there is no analytical solution for the vibration of rotating pre-twisted beam with an aerofoil cross-section, semi-analytical or numerical methods are utilized to solve this problem
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