Wave component analysis of energy flow in complex structures – Part II: ensemble statistics

A wave-based method is presented for the analysis of high-frequency vibrations in complex structures. The response of the structure to external forcing is described in terms of generalised, energy-bearing wave components, and the structure is represented by global 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 that differ randomly in detail. A ‘scalar random phase’ ensemble is defined in terms of random eigenvalues of the product ST of the scattering matrices, and analytical expressions are derived for the average and variance of the energy responses over this ensemble. The scalar random phase ensemble is thought to be a reasonable approximation to many practical ensembles and the approach provides a means for estimating response statistics at relatively low computational cost.