A dynamic finite element for the free vibration analysis of extension-torsion coupled composite beams

Abstract

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