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A theoretical non-hydrostatic model is developed to describe the dynamics of a two-layer shallow water system in the presence of viscous and Coriolis effects. The Navier-Stokes equations are integrated over the water depth in each layer to obtain the layer-mean equations. To close the resulting equation set, perturbation expansions of the vertical momentum equation are used and the dynamic pressures are solved in terms of wave elevations and horizontal velocities. A preliminary analysis is also carried out and a result for the quasigeostrophic problems is given based on an previous study. Our final model is of the Bousinesq class which is nonlinear and dispersive, and includes the effects of surface wind stress, bottom friction, eddy diffusion and earth rotation. It is shown that our new model can be readily reduced to previous inviscid non-hydrostatic models. Our model can be used in numerical simulations to study real ocean problems such as hurricane generated waves, tidal induced current, and interactions among surface waves, internal waves and variable topographies. / Thesis (M. S.)--University of Hawaii at Manoa, 1995. / Includes bibliographical references (leaves 55-59). / UHM: Has both book and microform. / U.S. Geological Survey; project no. 06; grant agreement no. 14-08-0001-G2015

Statistically-based estimation techniques are presented in this study. These techniques incorporate structural test data to improve finite element models used for dynamic analysis. Methods are developed to identify optimum values of the parameters of finite element models describing structures. The parameters which may be identified are : element area, mass density, and moment of inertia; lumped mass and stiffness; and the Rayleigh damping coefficients. A technique is described for incorporating hydrodynamic effects on small bodies by identifying equivalent structure mass, stiffness, and damping properties. Procedures are presented for both the free vibration problem and for forced response in the time domain. The equations for parameter identification are formulated in terms of measured response, calculated response, the prior estimate of the parameters, and a weighting matrix. The form of the weighting matrix is presented for three identification schemes : Least Squares, Weighted Least Squares, and Bayesian. The weighting matrix is shown to be a function of a sensitivity matrix relating structural response to the parameters of the finite element model. Sensitivities for the forced vibration problem are derived from the Wilson Theta equations, and are presented for the free vibration problem. The algorithm used for parameter identification is presented, and its implementation in a computer program is described. Numerical examples are included to demonstrate the solution technique and the validity and capability of the identification method. All three estimation schemes are found to provide efficient and reliable parameter identification for many modeling situations. / Graduation date: 1993

This thesis is concerned with the prediction of the vibro-acoustic response of structures with uncertain properties in the mid frequency region. The motivation for this research is the growing need of engineers to understand the responses of a group of similar structures ranging from vehicles, aircraft and aerospace structures, to household whitegood appliances. These structures are complex in geometry and may possess variability in their material or geometric properties, as well as variation arising from the assembly and manufacturing processes. Small variations can have a significant effect on a dynamic response of a structure, and the effect of structural uncertainties increases as the frequency increases. Deterministic modelling techniques such as finite element analysis are only suitable to model complex structures at low frequencies. Furthermore, FEA cannot easily account for uncertainty or randomness in structural parameters. High frequency dynamic predictive techniques such as Statistical Energy Analysis can account for structural uncertainty but is limited to structures with high modal density. There exists a frequency range between the two methods in which neither technique can be applied with great confidence. The objective of this thesis is to investigate predictive techniques for mid frequency vibration analysis of dynamic systems with structural uncertainties. The first part of this work is to numerically characterise the effect of a range of uncertainties on the modal statistics of structures. The degree of uncertainty required to achieve universality of the statistical properties is investigated. This is achieved by examining the modal statistics of dynamic systems with a range of uncertainty, corresponding to uncertainty due to mass and stiffness perturbations, uncertainty at the boundaries of a structure, uncertainty in the coupling between structures, uncertainty in the material properties of a structure and uncertainty in the geometry of a structure. Several structures are examined corresponding to a plate with masses and/or linear springs added at random locations, a plate with torsional springs attached at random locations along its boundary edges, two plates coupled by linear springs at random locations, a mass-loaded coupled L-shaped plate, a mass-loaded frame-plate structure, and a plate with varying Young's modulus, density and thickness. The natural frequencies of the aforementioned structures have been derived using either the Lagrange-Rayleigh-Ritz technique, finite element analysis, or the use of interval analysis in conjunction with FEA. The natural frequency statistics of structures with uncertain properties are observed using two statistical measures; the statistical overlap factor and the probability density function of the spacing between successive natural frequencies. The statistical overlap factor is defined by the variation in a natural frequency from its mean value measured across an ensemble of nominally identical structures with uncertainty. For a single ensemble member, the probability density function of the spacing between successive natural frequencies is compared to a Rayleigh distribution of the mean frequency spacing. A Rayleigh distribution of modal spacings is a feature of the universality exhibited by structures with uncertainty. To further investigate the effect of structural uncertainty on the vibrational characteristics of structures, the interval analysis is applied to finite element models of a plate with uncertainty in its material properties and dimensions. Using this method, the Young's modulus, density and thickness of a rectangular plate were set to vary by a small amount within predefined bounds. Using finite element equations, the natural frequencies and modeshapes of the structure were then determined in terms of the Young's modulus, density and plate thickness. For the mass and spring loaded plates, the springs were shown to affect the lower order modes while the masses had a significant effect on the higher order modes. As the frequency increased, only a small amount of perturbation was sufficient to affect the natural frequencies of a structure. Using the interval analysis method, the variation of the natural frequencies from their deterministic value increased as the frequency increased. An ergodic hypothesis was used to examine the responses statistics of structures with uncertainty. Three structures have been computationally studied corresponding to two plates coupled by springs, an L-shaped plate and a frame plate structure. Uncertainty has been generated for the two coupled plates by locating the springs randomly across the surface of the two plates. For the L-shaped plate and a frame plate structure, uncertainty was generated by randomly positioning small masses across the plates. Using the ergodic hypothesis, the frequency averaged response on one member of an ensemble is compare with the ensemble averaged response. It was found that the ensemble averaged response was well predicted by a frequency averaged response of a single ensemble member. The width of the frequency averaging band was shown to have a large influence on the quality of the match between the frequency and ensemble averaged responses. Results were significantly improved using a frequency averaging bandwidth which varies proportionally to frequency. Finally, experiments have been conducted on an L-shaped plate, a frame plate structure and a vehicle to validate the computational results for the natural frequency and response statistics.

Typescript (photocopy) / 106 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.) Dept. of Mechanical Engineering, University of Adelaide, 1984

Typescript (photocopy) / 106 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.) Dept. of Mechanical Engineering, University of Adelaide, 1984

M.Ing. / In this study it is shown that numerical analysis, and more specifically computational fluid dynamics can be used to investigate, compare, predict and design lining/cooling system combinations for blast furnaces’ in order to ensure longer campaign life and better performance. Three currently available cooling systems namely, copper staves are investigated. These combined with four different refractory materials, namely high alumina, silicon carbide, semi-graphite and graphite, stated in order of increasing thermal conductivity.