Spectral Element Formulation for General Anisotropic Beams with Elastic Couplings

Unlike the time-domain formulation, the spectral element method describes the structural system exactly with a single dynamic or spectral element matrix, rather than separate mass and stiffness matrices. In this work, a fully anisotropic Timoshenko-like beam element is formulated as a spectral element system, solved in the frequency domain. A key feature of the spectral element formulation is the elimination of the time derivative from the governing equations, which are instead transformed into frequency-dependent terms that can be solved in parallel at discrete frequencies. The results are evaluated for a composite box beam with and without elastic couplings. The frequency-dependent wavenumbers, describing the spectrum relations, are computed in an analytical form to capture the propagation of all wave modes along the beam length. The influence of bending-torsion coupling on the spectrum relations is also identified.