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.

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The thesis examines thinking about, and experiences of, gender roles and family relationships for the gentry and nobility, particularly through the process of marriage formation. The study draws on a range of sources, including collections of family letters, personal memoirs and prescriptive literature. Some chapters pursue a case study approach to correspondence. Others consider the relationship between published advice and personal attitudes and experience. The study explores whether there were contradictions in thinking on family life, gender, love and marriage, as some historians have claimed, and seeks to disentangle the overlaps and inter-relationships between these broad themes. While family and gender roles were multi-layered and multi-faceted, thinking and practice were neither incoherent nor conflicting. Rather, they were highly complex and treated as such. How marriages were forged and male and female roles in this process and in marriage itself required the balancing of many factors. Prescription recognised this and practice reinforced the need for pragmatism. Moreover, advice was not monolithic, but nuanced according to its purpose and intended audience. Gender roles, family relationships and marriage were varied and manifold within both the realms of rhetoric and experience. There was a strong elision of gender roles, affording women significant scope for decision-making. Family relationships were fluid, underpinned by a heavy dependence on, respect for, and emotional investment in, the extended family. Marriage formation was informed by recognition of the importance of a moral, disciplined love for sustaining marriages and families. The thesis highlights the intricacies of relatively new (although increasingly wellresearched) areas of study for historians. It seeks to undermine a simplistic division between prescription and practice, and between advisers and the advised, and to raise the importance of considering men within the family and facets of female authority.

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An evolving design philosophy for port structures in many seismically active regions reflects the observations that: -The deformations in ground and foundation soils and the corresponding structural deformation and stress states are key design parameters. -Conventional limit equilibrium-based methods are not well suited to evaluating these parameters. -Some residual deformation may be acceptable. Performance-based design is an emerging methodology whose goal is to overcome the limitations present in conventional seismic design. Conventional building code seismic design is based on providing capacity to resist a design seismic force, but it does not provide information on the performance of structure when the limit of the force-balance is exceeded. If we demand that limit equilibrium not be exceeded for the relatively high intensity ground motions associated with a rare seismic event, the construction cost will most likely be too high. If forcebalance design is based on amore frequent seismic event, then it is difficult to estimate the seismic performance of the structure when subjected to ground motions that are greater than those used in design. In this thesis a case study will be carried out on a typical port structure to show the performance evolution aspects and its comparison with damage criteria and performance grade in performance-based methodology.