The behavior of elastic body waves in a dipping layer overlying an elastic medium has been theoretically investigated by a multiple reflection formulation. Although the diffracted wave is not included in this formulation, its importance is studied by investigation of the amplitude discontinuities within the wedge. For a plane SH wave incident at the base of the dipping layer perpendicular to strike, a series solution has been obtained. Numerical values of the amplitude, phase and phase velocity are calculated on the surface. For waves propagating in the up-dip direction the amplitude versus frequency curves for a constant depth to the interface change slowly with increasing dip for dip angles less than 20°. However for waves propagating in the down-dip direction the character of the amplitude curves change rapidly. In these cases, it is found that the diffracted wave plays an important role. In addition to satisfying the boundary conditions at the surface and the lower boundary of the wedge, the diffracted wave must also satisfy additional conditions along a dipping interface between the wedge boundaries due to the geometrical nature of the reflected wave solution. It is found that the phase velocities vary rapidly with both period of the wave and depth to the interface. For incident plane P and SV waves, the complexity of the problem due to the converted waves does not allow the solution to be expressed in series form. However, a computational scheme has been developed which allows the calculation of the disturbance due to the multiply reflected waves. For both incident P and SV waves, numerical values of displacements and displacement ratios are calculated on the surface. It is found that the displacement ratios for incident SV waves are much more sensitive to dip than are there for incident P waves. For incident P and SV waves propagating in the down-dip direction with a propagation direction [symbol omitted],β = 120°, the amplitude ratio versus frequency curves for constant depth to interface do not have significant peaks for dip angles greater than 15°. The maximum discontinuities caused by the outgoing wave are also calculated to determine the role of the diffracted wave. As subsidiary problems the energy relations between waves at an interface between elastic media are determined in terms of propagation direction in a cylindrical system and the complex propagation direction is interpreted using the Rayleigh wave. The final study is to determine by a reflected wave formulation the displacements due to periodic and impulsive line sources of SH waves in the wedge overlying an elastic medium. A formal solution is found by which the contributions due to head and reflected waves are determined by evaluation of the integrals by the method of steepest descent. Using ray paths, the contributions of the integrals have been interpreted. The range of existence of head waves has been examined and the discontinuities associated with diffracted waves studied. In the case of a free or rigid lower boundary of the wedge, the dispersion relation has been determined. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

Experimental results are presented on the propagation of strain waves in long rods of mild steel (type-1020) aluminum (AA2024S) and copper (soft electrolytic). Strain pulses of order 500 μ in/in amplitude were generated by mechanical impact. The average strain rate during loading was of order one per second. The length and diameter of the specimens and the dominant frequencies in the strain pulses were such that one-dimensional conditions prevailed. Budd Metalfilm resistance type strain gauges were used for recording the strain pulses. Electromagnetic disturbances were effectively eliminated by proper grounding and shielding. Elastic wave propagation in mild steel, aluminum, and copper was studied. For the steel specimen, there was no apparent attenuation or dispersion of elastic waves. However, significant attenuation and dispersion were observed in aluminum and copper specimens, a 30 percent reduction in amplitude occurring in aluminum over a distance of 8 feet. Comparison of the Fourier transforms of the strain pulses in copper and aluminum at different positions along each specimen revealed that amplitude decreased exponentially with distance and that phase angle varied linearly with distance. Furthermore, the observed attenuation and phase velocity were frequency dependent. These results conform to the behaviour of strain pulses propagating in linear visco-elastic materials. Complex compliances for aluminum AA2024S and soft electrolytic copper were derived over the frequency range 400-6000 c.p.s. from the variation of attenuation and phase angle measured in these tests. Approximate three-parameter models suitable for estimating internal damping in these two materials were also determined. Plastic wave propagation in statically prestressed rods of aluminum and copper was investigated. In copper, it was observed that strain increments propagate at constant velocity along the rod and that the velocity of propagation decreases with increasing strain. Strain-rate independent theory is thus applicable to the description of plastic wave propagation in copper, but the dynamic stress-strain curve for the material lies well above the quasi-static one. Furthermore, experimentally observed loading-unloading boundaries in copper resemble the shape predicted by Skobeev and calculations based on these boundaries are compatible with the strain-rate independent theory. It was found that annealed aluminum (AA2024S-0) does not possess a smooth quasi-static stress-strain relation and exhibits unstable behaviour under dynamic loading. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The dependence of the point properties at the nucleus, electron density (Qe(0) )and spin density (Qs(0) ), on the nuclear cusp is examined for lithium atomic configuration interaction (CI) wave functions. Several series of CI wave functions with 18 and fewer terms, are studied. Importance of the triplet core spin function to Qs(0) is substantiated. Necessary, but not sufficient, spin and electron integral cusp conditions are applied as linear constraints. For the functions studied, Qs(0) improves on applying the spin cusp constraint if the free variational spin cusp is greater than -Z, but becomes worse otherwise. The electron cusp constraint invariably overcorrects Qe(0). The effect of necessary off-diagonal weighting constraints is also examined. No obvious trends could be found. It is concluded that forcing CI functions with a small number of terms to satisfy necessary diagonal or off-diagonal integral cusp conditions has very limited usefulness. A good Qs(0) can be obtained without constraining by (l) including triplet core spin terms. (2) optimizing orbital exponents. Sufficient nuclear cusp constraints are developed for CI wave functions. The generalized cusp-satisfying CI function has multiconfigurational SCF form with the correct cusp for each orbital. Sample calculations with a small basis set are presented. These simple functions give extremely good Qs(0) expectation values but convergence of Qs(0) with respect to basis set size is yet to be tested. The most interesting discovery is the appearance of Dirac [symbol omitted]-like correction basis orbitals from energy minimization of the orbital exponents. A scheme is depicted classifying previous and present work on cusp constraints in terms of necessity and/or sufficiency. / Science, Faculty of / Chemistry, Department of / Graduate

This thesis investigates water particle kinematics and the wave forces exerted on a slender rigid vertical cylinder in regular bidirectional wave fields. The instrumented portion of this cylinder is partitioned into nine independent segments enabling measurement of the vertical profile of hydrodynamic loading both in-line and transverse to the direction of wave propagation. Experiments conducted at the Hydraulics Laboratory of the National Research Council in Ottawa are described and some results are compared with the predictions of a wave force model based on the Morison equation and linear fluid kinematics. The influence of the crossing angle between the two wave components on the forces experienced by the column is determined. These experiments consider short-crested wave behavior in intermediate and deep water resulting from the interaction of two identical regular wave trains crossing at angles of 30, 60 and 90 degrees. The limit corresponding to unidirectional monochromatic waves is also investigated to provide a reference condition for comparison with the short-crested results. Conditions at the location of maximum short-crested wave height are of primary interest, however, forces at locations between the anti-node and node of the flow are also examined. In all, water surface elevations, flow velocities, and wave forces were measured in 24 short-crested and 8 different long-crested wave conditions spanning the range of Keulegan-Carpenter number between 4 and 24. The results of this study confirm the findings of previous researchers that short -crested waves with a certain period travel faster and rise higher before breaking than do their long-crested counterparts, but that in-line wave forces are not necessarily increased. Lift force maxima equal to half the maximum in-line force were measured; these forces can contribute significantly to the magnitude and direction of the total force resultant. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

No description available.

No description available.

In the first part of this thesis, the nonlinear Schrodinger equation for inviscid cross-waves near onset is found to be modified by viscous linear damping and detuning. The accompanying boundary condition at the wavemaker is also modified by damping from the wavemaker meniscus. The relative contributions of the free-surface, sidewalls, bottom, and wavemaker viscous boundary layers are computed. It is shown that viscous dissipation due to the wavemaker meniscus breaks the symmetry of the neutral curve. In the second part, existence and stability of steady solutions to the nonlinear Schrodinger equation are examined numerically. It is found that at forcing frequency above a critical value, f(c), only one solution exists. However, below f(c), multiple steady solutions, the number of which is determined, are possible. This multiplicity leads to hysteresis for f < f(c), in agreement with observation. A Hopf bifurcation of the steady solutions is found. This bifurcation is compared with the transition from unmodulated to periodically modulated cross-waves observed experimentally.

Thèse -- Université de Paris.

No description available.

No description available.