Advanced Numerical Free Vibration Analysis of FG Thin-Walled I-Beams Using Refined Beam Models

This paper presents a numerical analysis of the free vibration of thin-walled composite and functionally graded material (FGM) I-beams, considering the effects of bending-torsional behavior using refined beam theory models RBT and RBT* built on the 3D Saint-Venant (SV) solution. The models enable a realistic analysis of beams with arbitrary cross-sections, overcoming the limitations inherent in classical beam theories. They incorporate a set of 3D displacement modes, representing cross-sectional deformations, which are derived from 2D FEM calculations. These modes are then applied to solve the beam problem using a 1D FEM, providing the 3D vibration modes and natural frequencies. The mechanical properties of the FGM thin-walled beams are varied according to different material distributions across the cross-section. A numerical comparison of the natural frequencies and 3D mode shapes of the thin-walled beams is carried out to validate the proposed models against available results from the literature and 3D FEM calculations. The results confirm that the RBT models provide accurate and efficient analysis of thin-walled I-beams subjected to various boundary conditions.