Spectral element analysis of the axial-bending-shear coupled vibrations of composite Timoshenko beams

Abstract

This article presents a spectral element model for the axially loaded axial-bending-shear coupled vibrations of composite laminated beams, which are represented by the Timoshenko beam models based on the first-order shear deformation theory. The variation approach is used to formulate the frequency-dependent spectral element matrix (often called exact dynamic stiffness matrix) for the present spectral element model. As the spectral element matrix is formulated from exact wave solutions satisfying the frequency domain governing equations of motion transformed by the use of discrete Fourier transform theory, the present spectral element model cannot only provide extremely accurate solutions with using only a minimum number of degrees of freedom but also contribute to improving the computation efficiency. The high accuracy of the present spectral element model is numerically verified by comparing its solutions with exact analytical solutions available from references as well as with the solutions obtained by conventional finite element method. The effects of the axial loading and damping are also numerically investigated. For the numerical verification, the finite element model is also provided for the axially loaded axial-bending-shear coupled composite laminated Timoshenko beams.