Comparison of two non-probabilistic approaches for the energy flow uncertainty in structural vibrating system

Two non-probabilistic, set-theoretical methods for determining the energy flow between two structural multimodal systems coupled by a joint with uncertain parameters are presented. They are based on the theories of interval mathematics and convex models. The uncertain parameters of the joint are assumed to be a convex set, hyper-rectangle or ellipsoid. For both non-probabilistic methods, less prior information about the uncertain nature is required than that which is required concerning the probabilistic model. The properties of the standard interval arithmetic, the interval Taylor expansion, the convex models and the Monte Carlo Method solutions are investigated and compared.