Keywords: composite thin-walled cross-section, unbalanced laminates, consistent mass matrix, natural frequencies, initial load, beam model.

This work presents an improved beam formulation for predicting the natural frequencies of composite thin-walled beam-type structures subjected to initial loading. Each wall of a beam element cross-section is idealised as a thin, symmetric and unbalanced angle-ply laminate. The formulation is based on Hooke’s law and a geometrically nonlinear framework, which accounts for restrained warping of the cross section and large rotation effects, respectively. Shear deformation effects are included by applying the Timoshenko-Ehrenfest beam theory for bending and a modified Vlasov theory for torsion. A consistent mass matrix of a beam element is derived using a kinetic-energy-based approach, accounting for coupling between translational, rotational, and warping degrees of freedom. The governing equations of motion of the beam element are formulated within the framework of Hamilton’s variational principle, leading to the corresponding eigenvalue problem. The proposed formulation is verified through selected examples, demonstrating its effectiveness in predicting the natural frequencies of geometrically nonlinear, thin-walled beam-type structures under initial loading.

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