Statistical energy analysis of engineering structures
This thesis examines the fundamental equations of the branch of linear oscillatory dynamics known as Statistical Energy Analysis (SEA). The investigation described is limited to the study of two, point coupled multi-modal sub-systems which form the basis for most of the accepted theory in this field. Particular attention is paid to the development of exact classical solutions against which simplified approaches can be compared. These comparisons reveal deficiencies in the usual formulations of SEA in three areas, viz., for heavy damping, strong coupling between sub-systems and for systems with non-uniform natural frequency distributions. These areas are studied using axially vibrating rod models which clarify much of the analysis without significant loss of generality. The principal example studied is based on part of the structure of a modem warship. It illustrates the simplifications inherent in the models adopted here but also reveals the improvements that can be made over traditional SEA techniques. The problem of heavy damping is partially overcome by adopting revised equations for the various loss factors used in SEA. These are shown to be valid provided that the damping remains proportional so that inter-modal coupling is not induced by the damping mechanism. Strong coupling is catered for by the use of a correction factor based on the limiting case of infinite coupling strength, for which classical solutions may be obtained. This correction factor is used in conjunction with a new, theoretically based measure of the transition between weakly and strongly coupled behaviour. Finally, to explore the effects of non-uniform natural frequency distributions, systems with geometrically periodic and near-periodic parameters are studied. This important class of structures are common in engineering design and do not posses the uniform modal statistics commonly assumed in SEA. The theory of periodic structures is used in this area to derive more sophisticated statistical models that overcome some of these limitations.