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Shock and Vibration
Volume 11, Issue 5-6, Pages 637-646

Coupled Bending-Bending-Torsion Vibration of a Rotating Pre-Twisted Beam with Aerofoil Cross-Section and Flexible Root by Finite Element Method

Bulent Yardimoglu1 and Daniel J. Inman2

1Department of Mechanical Engineering, Izmir Institute of Technology, 35430, Urla, Izmir, Turkey
2Department of Mechanical Engineering, Center for Intelligent Materials and Structures, Virginia Tech, Virginia, MC 0261, Blacksburg, VA 24061, USA

Received 2 January 2004; Revised 7 April 2004

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.