Wave component analysis of energy flow in complex structures – Part I: a deterministic model

A wave-based method is developed for the analysis of vibrational energy flow in built-up structures. The structure is divided into a network of interconnected subsystems and its response to external forcing is expressed as the time-averaged energies of these subsystems. The flow of energy between subsystems is described in terms of generalised ‘wave components’. These propagate perpendicularly to cross-sections of the structure—generally defined at the interfaces between subsystems and the junctions between subsystems—and have characteristic patterns of amplitude variation over the cross-sections which correspond to local eigenfunctions. Reflection and transmission of wave components is described in terms of two global scattering matrices, which are systematically constructed from local coefficients associated with individual subsystems and junctions. The method forms the deterministic basis for an alternative, statistical approach to the analysis of vibrations in complex, uncertain structures, which is described in two companion papers.