Nonlinear vibrations and parametric instability of pultruded angle section columns

The nonlinear vibrations and parametric instability of pultruted fiber-reinforced polymer (FRP) angle columns are investigated in this work. The equal and unequal-leg angle sections are modeled as two interconnected plates using von Kármán's nonlinear plate theory for orthotropic materials. To account for bending about the major and minor axes, as well as torsion, suitable interpolating functions for in-plane and transverse displacements are employed. These functions satisfy the simply supported boundary and continuity conditions while incorporating nonlinear modal couplings and interactions. The continuous system is discretized using the Ritz method to obtain reliable reduced-order models (ROMs). The stability of the column under harmonic axial loading is then analyzed, with parametric instability regions identified based on the frequency and magnitude of the harmonic excitation. The effects of material properties, damping, and geometry on the parametric instability boundaries are also examined. Bifurcation diagrams are generated using both the brute-force method and continuation techniques to identify bifurcations in the parametric instability boundaries within the force-control space and to detect the presence of coexisting solutions. Also, basins of attraction for these coexisting solutions are determined to evaluate the dynamic integrity of the stable solution. The results indicate that the column may lose stability at load levels significantly lower than the static buckling load. Consequently, designers must exercise caution when working with structures exposed to time-varying axial loads to ensure safety and stability.