An estuary is a semi-enclosed coastal body of water, having both a free connection to the open sea and a connection to fresh water coming from land-regions. Cook Inlet is an estuary in Alaska, and a major part of the Alaskan citizens live near its shores. The inlet is an important shipping route for oil, gas and petroleum products, and the port of Anchorage, near the head of the estuary, serves approximately 80\% of the Alaskan population.

The tidal waves and currents in Cook Inlet can be quite strong. To ensure the safety of local communities and to assess the risks of the transport of goods and raw materials through Cook Inlet, it is important that the local water velocity and tidal currents can be predicted. However, Cook Inlet is often covered by ice, and the influence of ice on the tidal water motion is not thoroughly investigated yet. The ice cover varies seasonally, and with climate change, these variations will be even larger. To increase our understanding of the influence of ice on the tidal water motion in high-latitude estuaries such as Cook Inlet, this thesis will focus on modelling and analysing the ice-water interaction within estuaries. To investigate the most important processes that determine the ice-water interactions, an idealised modelling approach is used.

In estuaries, one generally distinguishes two types of ice: landfast ice, and ice floes. Landfast ice is a stationary type of ice that finds itself on the surface of the estuary. This type of ice causes a frictional force at the interface between the water and the ice. Ice floes are drifting sheets of ice, that interact with both the water and each other. In this thesis, we focus on the effect of ice floes that drift relatively freely, so that the interaction between floes is negligible, and their velocity is close to the velocity of the water.

The effect of landfast ice and ice floes on the water motion are analysed separately, and the time-dependency of both model both models is solved by a Fourier/method. The model for landfast ice allowed for analytical solutions to be found under the assumption of and exponentially converging estuary-width and a constant estuary-depth. Using these analytical solutions, the effect of the percentage of landfast ice coverage in general estuaries is analysed. This analysis led to the conclusion that landfast ice covers can either increase or decrease the height of tidal waves, depending on the length of the estuary and the convergence of its width.

The model for ice floes without vertical stresses cannot be solved analytically, since the horizontal viscosity can no longer be neglected due to the presence of ice floes. As a first step, the depth is assumed to be constant. In the numerical solution method, the vertical structure of the longitudinal water velocity is approximated by depth-dependent eigenfunctions. The surface level and amplitudes of the eigenfunctions, which vary over the longitudinal coordinate, are solved using a finite difference method. The effect of the percentage of ice floe coverage in general estuaries is analysed using these approximations. It is found that an increased ice cover could either attenuate or amplify the waterlevel, depending on the length of the estuary.

Within this report, an analytical research will be performed on the effectivity of Tuned Mass Dampers (TMDs) and Viscoelastic Dampers (VEDs), and a conclusion will be drawn as to which is most effective in damping the oscillations of an earthquake. First of all, a simple model of second-order differential equations describing the oscillations of each floor within a building of n floors is derived, in which no frictional forces are taken into account. The solution to this model is derived for a building of two floors, which demonstrates the characteristics of oscillations in this model and which shows how resonance is represented mathematically, and what patterns of oscillations look like. Then, a TMD and VED are added to the model of one floor to expose what their working principles are. Subsequently, the methods of adding these dampers to the models for two, five and ten floors are given. For varying earthquake-frequencies, the maximum displacement within 5 seconds is determined, which shows the effect of TMDs and VEDs for different positions within the building. The conclusion from these results is that the effect of the TMDs is always that at the eigenfrequencies, the oscillations of the building are no longer resonating. However, the building will start resonating for other eigenfrequencies due to the TMD. The VED is more consistent, though its damping-effect on resonating frequencies is smaller than for the TMDs. The conclusion is that VEDs are most effective, though more dampers have to be added to improve its effectiveness. After this, a new model is introduced, which does contain a friction force: air resistance. Based on the new model, it is concluded that even oscillations for resonating frequencies are eventually damped out, though they do still grow large. Again, TMDs and VEDs are added to the model, and similar conclusions about the effectivity of the dampers as for the first model were drawn.