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.