Scattering by wave-bearing surfaces under fluid loading.
PhD thesis, University of Nottingham.
Wave-bearing surfaces and compressible fluids are often adjacent, the subsequent interactions are of substantial interest in structural acoustics, acoustic microscopy, seismology and many other fields. Here we take a broad view and discuss a variety of problems, both time harmonic and transient, which are amenable to exact solution. These in turn highlight physical effects and can additionally form the basis of asymptotic solutions.
In structural acoustics the interaction of plate waves with defects is Cl major source of underwater noise. A model problem of two semi-infinite elastic plates (made of different material) joined in a variety of ways is considered for obliquely incident flexural plate waves. Asymptotic results for 'light' and 'heavy' fluid loading are extracted. In addition reciprocity and power flow relations, besides being of independent interest, provide a useful check on the results.
There are many closely related problems involving a fluid loaded elastic solid. The situation here is somewhat similar, but often more complicated, due to the number of waves that an elastic solid supports, mode conversion at interfaces, and interfacial waves.
We first address the scattering effects of low frequency waves by very small interfacial defects, that is, small relative to a typical wavelength. In this limit, and in related water wave or acoustic work, matched asymptotic expansions are used. An important aspect, that has not been noticed before, is the natural separation that occurs in the inner problem into fluid and solid pieces. A matching argument may now be used to give a useful physical interpretation of these defects and far field directivity patterns show the distinctive beaming that occurs along the Rayleigh angles in the light fluid loading limit.
In many areas of interest embedded defects are imaged by pulses and we therefore require a transient analysis. In this case our problem involves a combination of compressional and shear source loadings beneath a fluid-solid interface. The exact solution is found and a full asymptotic analysis of this solution is performed with an emphasis upon wavefront expansions and leaky waves, and in particular, for 'light' and 'moderate' fluid loading. In some situations, when the sources are near the interface, a pseudo-compressional wavefront is generated and the limit as the loading approaches the interface is investigated. These non-geometric wave arrivals may be important in seismology and elastic wave studies related to the non-destructive evaluation of structures.
This study is generalised to investigate the dynamic stress loading of subsurface cracks in either homogeneous or non-homogeneous media. An iterative method of solution based on physical considerations is developed and quantities of interest such as the scattered displacement fields and the stress intensity factors are determined.
The problems considered here are ideally suited to analysis by transform methods and the Wiener-Hopf and Cagniard-de Hoop techniques.
Thesis (University of Nottingham only)
||Q Science > QA Mathematics > QA299 Analysis
||UK Campuses > Faculty of Science > School of Mathematical Sciences
||26 Jun 2014 13:52
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