Parametric Instability and Bifurcation of Thin-Walled Axially Compressed Long FRP Columns

Abstract

AbstractIn the present work, the nonlinear oscillations and parametric instability of a long simply supported column with a channel section made of fiber-reinforced polymer is investigated. The nonlinear equations of motion of the thin-walled column are here derived in terms of the two flexural displacements and the torsion angle, taking into account large displacements, warping, and shortening effects. The governing nonlinear equations of motion are discretized in space using the Galerkin method and solved by the Runge-Kutta method. Using the tools of nonlinear dynamics, bifurcation diagrams and basins of attraction are obtained, thus permitting the identification of the parametric instability boundaries in force control space and the bifurcation phenomena connected with these boundaries. The parametric analysis shows how the material characteristics and geometric properties of the column influence its nonlinear vibrations and dynamic instability.KeywordsParametric instabilityFiber-reinforced polymerThin-walled column