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Title: Coupled bending-bending-torsion vibration of a pre-twisted beam with aerofoil cross-section by the finite element method
Authors: Yardımoğlu, Bülent
Inman, Daniel J.
Keywords: Vibrations
Transverse displacements
Convergence of numerical methods
Finite element method
Kinetic energy
Torsional stress
Issue Date: 2003
Publisher: Hindawi Publishing Corporation
Source: Yardımoğlu, B., and Inman, D. J. (2003). Coupled bending-bending-torsion vibration of a pre-twisted beam with aerofoil cross-section by the finite element method. Shock and Vibration, 10(4), 223-230. doi:10.1155/2003/354074
Abstract: The present study deals with a finite element model for coupled bending-bending-torsion vibration analysis of a pretwisted Timoshenko beam with varying aerofoil cross-section. The element derived in this paper has two nodes, with seven degrees of freedom at each node. The nodal variables are transverse displacements, cross-section rotations and the shear angles in two planes and torsional displacement. The advantage of the present element is the exclusion of unnecessary derivatives of fundamental nodal variables, which were included to obtain invertable square matrix by other researchers, by choosing proper displacement functions and using relationship between cross-sectional rotation and the shear deformation. Element stiffness and mass matrices are developed from strain and kinetic energy expressions by assigning proper order polynomial expressions for cross-section properties and considering higher order coupling coefficients. The correctness of the present model is confirmed by the experimental results available in the literature. Comparison of the proposed model results with those in the literature indicates that a faster convergence is obtained. The results presented also provide some insights in the formulation by clearly indicating that higher order coupling terms have considerable influence on the natural frequencies.
ISSN: 1070-9622
Appears in Collections:Mechanical Engineering / Makina Mühendisliği
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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