There are two classes of phononic structures that can support elastic waves with non-conventional topology, namely intrinsic and extrinsic systems. The non-conventional topology of elastic wave results from breaking time reversal symmetry (T-symmetry) of wave propagation. In extrinsic systems, energy is injected into the phononic structure to break T-symmetry. In intrinsic systems symmetry is broken through the medium microstructure that may lead to internal resonances. Mass-spring composite structures are introduced as metaphors for more complex phononic crystals with non-conventional topology. The elastic wave equation of motion of an intrinsic phononic structure composed of two coupled one-dimensional (1D) harmonic chains can be factored into a Dirac-like equation, leading to antisymmetric modes that have spinor character and therefore non-conventional topology in wave number space. The topology of the elastic waves can be further modified by subjecting phononic structures to externally-induced spatio-temporal modulation of their elastic properties. Such modulations can be actuated through photo-elastic effects, magneto-elastic effects, piezo-electric effects or external mechanical effects. We also uncover an analogy between a combined intrinsic-extrinsic systems composed of a simple one-dimensional harmonic chain coupled to a rigid substrate subjected to a spatio-temporal modulation of the side spring stiffness and the Dirac equation in the presence of an electromagnetic field. The modulation is shown to be able to tune the spinor part of the elastic wave function and therefore its topology. This analogy between classical mechanics and quantum phenomena offers new modalities for developing more complex functions of phononic crystals and acoustic metamaterials.

We consider two one-dimensional harmonic chains coupled along their length via linear springs. Casting the elastic wave equation for this system in a Dirac-like form reveals a directional representation. The elastic band structure, in a spectral representation, is constituted of two branches corresponding to symmetric and antisymmetric modes. In the directional representation, the antisymmetric states of the elastic waves possess a plane wave orbital part and a 4x1 spinor part. Two of the components of the spinor part of the wave function relate to the amplitude of the forward component of waves propagating in both chains. The other two components relate to the amplitude of the backward component of waves. The 4x1 spinorial state of the two coupled chains is supported by the tensor product Hilbert space of two identical subsystems composed of a non-interacting chain with linear springs coupled to a rigid substrate. The 4x1 spinor of the coupled system is shown to be in general not separable into the tensor product of the two 2x1 spinors of the uncoupled subsystems in the directional representation. (C) 2017 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

We address questions related to the parameterization of two distinct types of seismic sources: earthquakes and underground nuclear explosions. For earthquakes, we focus on the improvement of location parameters, latitude and longitude, using relative measurements of spatial cluster of events. For underground nuclear explosions, we focus on the seismic source model, especially with regard to the generation of surface waves. We develop a procedure to improve relative earthquake location estimates by fitting predicted differential travel times to those measured by cross-correlating Rayleigh- and Love-wave arrivals for multiple earthquakes recorded at common stations. Our procedure can be applied to populations of earthquakes with arbitrary source mechanisms because we mitigate the phase delay that results from surface-wave radiation patterns by making source corrections calculated from the source mechanism solutions published in the Global CMT Catalog. We demonstrate the effectiveness of this relocation procedure by first applying it to two suites of synthetic earthquakes. We then relocate real earthquakes in three separate regions: two ridge-transform systems and one subduction zone. In each scenario, relocated epicenters show a reduction in location uncertainty compared to initial single-event location estimates. We apply the relocation procedure on a larger scale to the seismicity of the Eltanin Fault System which is comprised of three large transform faults: the Heezen transform, the Tharp transform, and the Hollister transform. We examine the localization of seismicity in each transform, the locations of earthquakes with atypical source mechanisms, and the spatial extent of seismic rupture and repeating earthquakes in each transform. We show that improved relative location estimates, aligned with bathymetry, greatly reduces the localization of seismicity on each of the three transforms. We also show how improved location estimates enhance the ability to use earthquake locations to address geophysical questions such as the presence of atypical earthquakes and the nature of seismic rupture along an oceanic transform fault. We investigate the physical basis for the mb-MS discriminant, which relies on differences between amplitudes of body waves and surface waves. We analyze observations for 71 well-recorded underground nuclear tests that were conducted between 1977-1989 at the Balapan test site near Semipalatinsk, Kazakhstan in the former Soviet Union. We combine revised mb values and earlier long-period surface-wave results with a new source model, which allows the vertical and horizontal forces of the explosive source to be different. We introduce a scaling factor between vertical and horizontal forces in the explosion model, to reconcile differences between body wave and surface wave observations. We find that this parameter is well correlated with the scaled depth of burial for UNEs at this test site. We use the modified source model to estimate the scaled depth of burial for the 71 UNEs considered in this study.

This research investigates the effects of beam diffraction from a source of finite width on nonlinear Rayleigh wave propagation in an elastic half space. Previous work has shown that nonlinear ultrasonic Rayleigh waves can be used to evaluate material damage due to plastic deformation and fatigue. In this measurement, a relatively small wedge transducer is employed to launch Rayleigh surface waves in the specimen and the first and second harmonic amplitudes are measured in the far field as a function of propagation distance. In order to obtain a reliable set of measurement data, one needs to make numerous points in a wide range of distance, which can be impractical in many cases. This research investigates model is employed and the computation results are compared with experiment ones. This research will make measurements on 7075-T651 aluminum as a specimen, compensate the diffraction effects and then, will compare the feasibility of the method proposed in this research in the results of normalized second harmonic amplitude vs propagation distance.

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Bibliography: leaves 135-151 / v, 151 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.)--University of Adelaide, Dept. of Applied Mathematics, 1991

Thesis (Ph.D.)--University of Tulsa, 1988. / Bibliography: leaves 121-123.

Thesis (Ph.D.)--University of Tulsa, 1993. / Includes bibliographical references (leaves 91-96).

Thesis (Ph.D.)--University of Tulsa, 1993. / Includes bibliographical references (leaves 91-96).