Natural Frequencies of Prestressed Thin-Walled Angle-Ply Composite Beam-Type Structures

This paper introduces an enhanced beam formulation for predicting the natural frequencies of thin-walled composite beam-type structures under initial loading. Each wall of the cross-section is idealized as a thin, symmetric, and balanced angle-ply laminate. The formulation is based on Hooke’s law and a geometrically nonlinear framework, taking into account restrained warping and large-rotation effects, respectively. Shear deformation effects are incorporated by applying the Timoshenko–Ehrenfest beam theory for bending and a modified Vlasov theory for nonuniform torsion. Coupling between transverse shear forces and warping-induced torsional moments arising from cross-sectional asymmetry is explicitly included. A consistent mass matrix, accounting for coupling between translational, rotational, and warping degrees of freedom, is derived using a kinetic-energy-based approach for the thin-walled beam element. Within the framework of Hamilton’s variational principle, the governing equations of the structure in global coordinates are formulated, and the associated eigenvalue problem is derived. The proposed formulation is validated through selected benchmark examples, demonstrating its effectiveness in predicting the natural frequencies of geometrically nonlinear, shear-deformable thin-walled beam and frame structures under initial loading.