Nonlinear Vibrations and Dynamic Buckling of an Imperfect Thin-Walled I-Beam

Thin-walled beams with open cross-sections are prone to lateral-torsional buckling, often exhibiting unstable post-buckling behavior and significant imperfection sensitivity. Consequently, for loads below the critical threshold, the safe pre-buckling state is bounded by saddles connected to the unstable post-buckling paths. The depth of this safe basin is highly dependent on both load and geometric imperfections, profoundly influencing the load-carrying capacity of dynamically loaded beams—a topic that remains under-explored in the literature. This study investigates the nonlinear vibrations and dynamic buckling of an imperfect thin-walled beam with a bisymmetric I-section, considering both load and combined geometric imperfections. The analysis begins with a static buckling assessment, highlighting the beam's imperfection sensitivity and the corresponding erosion of the safe basin of attraction. Subsequently, the nonlinear dynamic response under harmonic excitation is examined using bifurcation diagrams of the Poincaré map, basins of attraction, phase space projections, and time responses. The bifurcation analysis delineates stability boundaries in the force control space, revealing the most sensitive regions and elucidating the influence of flexural-torsional coupling on the structural load capacity.