A new energy approach to the analysis of complex and uncertain system

A new approach for predicting the response of a complex and uncertain structural-acoustic system was developed, namely the Time Asymptotic ensemble Energy Average (TAE). This approach belongs to the class of the energetic methods, since the system dynamic is described in terms of global parameters (the energies of a subset of the system) and a statistical approach is developed by introducing random natural frequencies, whose variability is due to stochastic perturbations of physical and geometrical parameters of the system. The developed method allows the evaluation of the energy sharing among two or more subsystems, for both weak and strong coupling. The originality of this method lies in the development of an asymptotic expansion technique, which permits to evaluate the energy distribution among the subcomponents of a system in both transient and steady state conditions in terms of only few modes of the system and the related marginal probabilities, determined with a low computational cost. The proposed method has been experimentally validated for two different configurations: a twoplate and a three-plate assemblies. The typical experiment consists in a transient excitation on a subcomponent of the structure and a measure of the dynamical responses of the plates at different locations upon all the subsystems, in order to derive a space-average value of the vibrational energies.