Dynamic stability analysis of non-linear structures with geometrical imperfections under random loading

This article presents selected research results in the field of stochastic dynamic stability problems. Both the geometrical properties and the loading conditions are supposed to be random in nature. The stability behavior of structures excited by time-dependent loads can be described by the maximum Lyapunov exponent. This exponent turns positive for unstable systems and can be computed by a non-linear time integration with simultaneous stability analysis. Alternatively, an approximation can be obtained by investigating a linearized version of the structural model. The non-linear time integration of large structures requires a huge numerical effort, thus this method is limited by available computer capacities. In this article both methods are applied and the respective results are compared for geometrically perfect and imperfect systems of different sizes.