Nonlinear Buckling and Vibration Analysis of Thin-Walled Fiber Reinforced Polymer T-Section Beams

Resumo

Thin-walled beams with open cross-sections are highly sensitive to lateral-torsional buckling due to their low torsional and lateral stiffness. This instability is strongly influenced by material properties, bracing conditions, load distribution, boundary constraints, and cross-sectional geometry. Fiber-reinforced polymer (FRP) thin-walled members, increasingly used in civil engineering, offer high strength-to-weight ratios but present complex nonlinear behaviors that demand refined analysis. This study investigates the static and dynamic lateral-torsional buckling of FRP beams with monosymmetric T-sections, a common geometry in practical applications. The analysis is based on a modified Vlasov theory, incorporating large displacements, torsion angles, warping, axial shortening, and flexural-torsional coupling. The governing equations are discretized via the Galerkin method, and solved using path-following techniques to trace pre- and post-buckling responses. The nonlinear oscillatory behavior of FRP beams, sparsely explored in the literature, is comprehensively analyzed using Poincaré maps and bifurcation diagrams obtained via continuation methods and brute-force simulations, complemented by Poincaré sections, phase portraits, time histories, and basins of attraction. The impact of load eccentricity - a critical factor in thin-walled beam performance - is also systematically evaluated. Results demonstrate that dynamic loading can substantially reduce the structural load-bearing capacity, triggering large-amplitude coupled flexural-torsional vibrations. These findings underscore the necessity of accounting for dynamic effects and load eccentricity in the design of FRP thin-walled structures operating in dynamic environments.