The influence of uncertainties and random noise on the dynamic integrity analysis of a system liable to unstable buckling

Slender structural systems liable to unstable buckling usually become unstable at load levels lower than the linear buckling load of the perfect structure. In some cases, experimental buckling loads can be just a small fraction of the theoretical critical load. This is mainly due to the imperfections present in real structures. The imperfection sensitivity of structures under static loading is well studied in the literature, but little is known on the sensitivity of these structures under dynamic conditions. In a dynamic environment not only geometric imperfections but also initial conditions (disturbances), physical and geometrical system parameters uncertainties and excitation noise influence the bifurcation scenario and basins of attraction. The aim of this work is to investigate the influence of inherent uncertainties of real systems and load noise on the dynamic integrity and stability of their solutions in a dynamic environment. To illustrate the system sensitivity, an archetypal model of slender systems liable to unstable buckling is used. Special attention is given to the influence of uncertainties and random noise on the basins of attraction of the system and consequently on the integrity measures of the unforced and forced system. The Melnikov criterion, erosion profiles based on different integrity measures and stochastic differential equations and polynomial chaos are discussed as possible tools to obtain reliable lower bounds for design.