A consistent concept for high- and low-frequency dynamics based on stochastic modal analysis

Accurate expressions for the kinetic energy in substructure excited by white noise and broad-band spectra, based on classical random vibration theory and modal analysis, are presented. The approach is accurate, general and valid for all frequency ranges, since no simplifying are needed to arrive at the presented power flow relations. Strong coupling, local energies and energies in substructures can be analyzed for uncorrelated as well as for correlated excitation. The results are compared with statistical energy analysis (SEA) which is applicable for the high-frequency range. It is shown, that the SEA representations is only suitable for very weak coupling between substructures, while an inverse representation does not show the observed limitations. Energies in substructures are not sensitive to variations of the eigenfrequencies or mode shapes due to the summation over frequency ranges and over the domain of the substructure. Hence, modal analysis will lead to accurate estimates even in case FE analysis fails to provide accurate eigenfrequencies and mode shapes, since the coupling between substructures is still represented with acceptable accuracy. Uncertain structural properties will affect the coupling between substructures and therefore the power flow. It is suggested to assess this influence by using Monte Carlo simulation.