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A Dynamic Finite Element for Coupled Extensional-Torsional Vibration of Uniform Composite Thin-Walled Beams

S. M. Hashemi(1*), A. Roach(2)

(1) Department of Aerospace Engineering, Ryerson University, Canada
(2) Department of Aerospace Engineering, Ryerson University, Canada
(*) Corresponding author


DOI: https://doi.org/10.15866/irece.v7i4.10758

Abstract


A Dynamic Finite Element (DFE) formulation for the free vibration analysis of extension-torsion coupled uniform composite thin-walled beams is presented. Employing the exact solutions of the differential equations governing the uncoupled vibrations of a uniform beam element, the analytical expressions for extensional and torsional dynamic trigonometric shape functions are derived. By exploiting the principle of virtual work and the frequency-dependent shape functions, the element dynamic stiffness matrix is developed. The application of the theory is demonstrated by a Circumferentially Uniform Stiffness (CUS) composite circular tube for which the influence of ply fibre-angle on the natural frequencies is studied. A variety of CUS configurations are studied and the correctness of the theory and the superiority of the proposed DFE over the conventional FEM methods are confirmed by numerical checks and the published results.
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Keywords


Composite Beam; Extension-Torsion Couplings; Dynamic Finite Element (DFE); Dynamic Stiffness Matrix (DSM); Finite Element Method (FEM); Materially Coupled Vibrations

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References


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