Wave component analysis of energy flow in complex structures – Part III: two coupled plates

A statistical, wave-based approach to the analysis of energy flow in structures is applied to example structures comprising two, regularly or irregularly coupled, rectangular plates. The approach, which is developed in two companion papers, is based on the expression of the response in terms of energy-bearing ‘wave components’ and a description of the structure in terms of subsystem and junction wave component scattering matrices, S and T. Uncertainty in the properties of the structure is taken into account by assuming that the structure is drawn from an ensemble of structures which vary randomly in detail. A ‘scalar random phase’ ensemble is defined in terms of a random distribution of the eigenvalues of the global scattering matrix product ST. Analytical expressions enable the ensemble mean and variance of energy responses over this ensemble to be found at low computational cost. Scalar random phase ensemble-based estimates of these statistics for regularly and irregularly coupled plate structures are found to be in good agreement with the results of Monte Carlo simulations.