Variability of the coupling loss factor between two coupled plates

Within statistical energy analysis (SEA), the coupling loss factor (CLF) is a statistical quantity defined in terms of the average behaviour of an ensemble of similar systems. Thus, the 'effective' CLF for a given realization may differ from the ensemble average. The effective CLF of two coupled plates with low modal density and low modal overlap fluctuates significantly compared with the ensemble average CLF. Accordingly, the CLF is the main parameter expected to determine the confidence intervals in the SEA prediction. The aim of the present paper is to quantify the variability of the effective CLF for the case of two finite rectangular plates. Extensive parameter investigations have been performed by using the dynamic stiffness method (DSM) and a 'numerical' power injection method (PIM) using the SEA power balance equations. The effects of frequency bandwidth and the number of modes in a band were separated by using frequency averages at a series of constant bandwidths rather than one-third octave averages, while the modal overlap is made independent of frequency by setting the damping loss factor to be inversely proportional to frequency. Finally, an improved empirical model for the variability of the CLF is derived, from these numerical results, in terms of the modal overlap factor and the number of modes in a frequency band. This model can subsequently be used to evaluate the uncertainty of the CLF of such a system.