Spectral Element Model for the Vibration of a Bending-Shear-Torsion Coupled Composite Timoshenko Beam

In this paper, a spectral element model is developed for axially loaded bending-shear-torsion coupled composite laminated beams. The composite laminated beams are represented by the Timoshenko beam model based on the first-order shear deformation theory. The spectral element model is formulated by using the variational method from frequency-dependent dynamic shape functions. The dynamic shape functions are derived from exact wave solutions to the governing differential equations of motion which are transformed into the frequency-domain by using the DFT theory. The numerical results show that the present spectral model provides extremely accurate natural frequencies for an example problem when compared to the results obtained by using the conventional finite element model which is also presented in this paper.