Nonlinear Dynamics, Safety, and Control of Structures Liable to Interactive Unstable Buckling

摘要

The nonlinear dynamics of two archetypal structural systems exhibiting interactive modal post-buckling behavior is addressed, the discrete Augusti's model and a reduced-order model of the axially loaded cylindrical shell. The uncoupled models exhibit a stable post-buckling response. However, the modal interaction leads to unstable post-buckling paths that entail a complex dynamic behavior and imperfection sensitivity, with a marked influence on the dynamic integrity and safety. Perfect and imperfect Augusti's models are investigated in terms of static buckling, linear vibrations, nonlinear normal modes, local and global nonlinear response to harmonic excitation, dynamic integrity, control of global bifurcations aimed at increasing the load carrying capacity. Then, as an example of a continuous system exhibiting strong modal coupling and interaction, a two-degree-of-freedom model of the thin-walled cylindrical shell is investigated in terms of global behavior and dynamic integrity. The influence of uncertainties on the nonlinear response and dynamic integrity is also shortly addressed. The chapter shows how a judicious use of the tools of nonlinear dynamics sheds light on the actual safety of structural systems liable to unstable buckling under static and dynamic loads.