| Summary: | Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution May 1989 The problem of a low-frequency acoustic plane wave incident upon a free surface coupled to a semi-infinite elastic plate surface, is solved using an analytic approach based on the Wiener-Hopf method. By low-frequency it is meant that the elastic properties of the plate are adequately described by the thin plate equation (kH ≲ 1). The diffraction problem relates to issues in long range sound propagation through partially ice-covered Arctic waters, where open leads or polynya on the surface represent features from which acoustic energy can be diffracted or scattered. This work focusses on ice as the material for the elastic plate surface, and, though the solution methods presented here have applicability to general edge diffraction problems, the results and conclusions are directed toward the ice lead diffraction process. The work begins with the derivation of an exact solution to a canonical problem: a plane wave incident upon a free surface (Dirichlet boundary condition) coupled to a perfectly rigid surface (Neumann boundary condition). Important features of the general edge diffraction problem are included here, with the solution serving as a guideline to the more complicated solutions presented later involving material properties of the boundary. The ice material properties are first addressed using the locally reacting approximation for the input impedance of an ice plate, wherein the effects of elasticity are ignored. This is followed by use of the thin plate equation to describe the input impedance, which incorporates elements of elastic wave propagation. An important issue in working with the thin plate equation is the fluid loading pertaining to sea ice and low-frequency acoustics, which cannot be characterized by simplifying heavy or light fluid loading limits. An approximation to the exact kernel of the ...
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