Equipartition and mean-square responses in large undamped structures

It is shown that the smoothed spectral energy density at one point in a large complex structure may be approximated in a simple manner as proportional to the frequency-smoothed admittance at the receiver and at the source, and inversely proportional to the global modal density. Thus, the mean-square response may be estimated with little computational burden, knowing only the local properties at source and receiver and the size of the system. The approximate predictions are compared with the results of direct numerical simulations and found to be accurate except in the presence of Anderson localization.