| Summary: | Research Doctorate - Doctor of Philosophy (PhD) Real-world phenomena are often modelled using differential equations. A sub-class of differential equations known as partial differential equations (PDEs) are used to model fluid-flow, deformation of solids, heat-transfer, etc. This thesis focuses on fluid-structure interaction problems, arising from two applications: 1) vibrations of ice-shelves and icebergs; and 2) fluid-flow through railway ballast. To solve the resulting governing equations, we use the finite element method. We obtain the solution to the problem of the vibration of an ice shelf of constant thickness using the eigenfunction matching method in water of finite depth, and accounting for the draught of the shelf. We validate the eigenfunction matching solution against a solution found using the finite element method. We then compare the finite-depth solution with the shallow-water solution, and show that the finite-depth and shallow-water solutions differ for periods below 50–100 s and significantly differ for periods below 20 s. In real life, it is observed that the shape of the cavity and the shelf-thickness varies greatly along the horizontal axis. Hence the simplified thickness/depth averaged models may not be sufficient to describe the ice-shelf vibrations. For such cases, we develop a mathematical model for predicting the vibrations of ice shelves based on linear elasticity for the ice-shelf motion and potential flow for the fluid motion. No simplifying assumptions such as the thinness of the ice-shelf or the shallowness of the fluid are made. We model the ice-shelf as a two-dimensional elastic body of an arbitrary geometry under plane-strain conditions. We then solve the model using a coupled finite element method incorporating an integral equation boundary condition to represent the radiation of energy in the infinite fluid. In the next section of the thesis, we illustrate the use of the mathematical model developed earlier to real-life scenarios. In the first part, we perform a ...
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