Wave barriers are a common mitigation measure when dealing with environmentally induced vibrations. These wave barriers generally consist of stiff vertical walls buried in the soil to impede waves on their path from the source to the receiver. The geometries of the wave barriers that are used in practice are very simple. More complex geometries have not often been considered as it is difficult to estimate which changes would increase the effectiveness. In literature, topology optimization was explored as a method to design wave barriers. This method was applied while modelling the soil as a homogeneous elastic half-space. The resulting wave barriers showed a significant increase in the achieved vibration reduction. However, the designs were often very complex and hard to manufacture. In this thesis the method was improved by introducing a layered soil and by ensuring the manufacturability of the designed wave barriers. The improved method was then applied to multiple situations in order to investigate aspects of wave barrier design and effectiveness. Optimization of a wave barrier for a two-layered soil model showed the significance of implementing a layered soil model. The interface between two layers resulted in reflections that could diminish the effectiveness of a wave barrier if not accounted for. The optimization algorithm responded to these reflections by placing material in the path of waves that would otherwise reflect back to the surface. A wave barrier optimized for a three-layered soil model that consisted of a softer layer embedded in a stiff layer and a stiff half-space showed a different approach to reflections. The wave barrier appeared to use the softer layer as a waveguide in order to reduce the energy at the surface. The manufacturability was increased by adding constraints. This resulted in wave barriers with a more manufacturable design at the cost of a decrease in vibration reduction. In three of the four cases, the optimized wave barrier still performed significantly better than the reference wave barrier. In one case, the final design reverted back to the reference wave barrier when the manufacturability conditions were applied. The goals set at the start of the thesis were largely accomplished. The model was able to more accurately reflect soil profiles found in practice by using a layered soil model and the topology optimization algorithm resulted in wave barriers that are relatively easy to manufacture while still showing a significant improvement over the standard reference wave barriers. The possible use of soft embedded layers as waveguides was discovered during the optimization. Future research into this possibility could prove valuable. Some concerns are posited with regards to the reliability of the wave barriers. In some cases, the optimized wave barrier appeared to abuse the idealized representation of the interface between layers. An initial investigation showed that in those cases, the effectiveness of the wave barrier was sensitive to changes of the interface depth. Further investigation would be required to determine the sensitivity of the designed wave barriers to other parameters related to the idealized representations of the interfaces.

As offshore wind turbines are moving further from the coast, floating wind turbines are being considered. These structures need to be able to endure high dynamic loads while remaining as still as possible in order to minimize internal stresses and maximize the efficiency of the turbine. To find ways to combat large responses, the effectiveness of tuned mass dampers (TMDs) and tuned liquid dampers (TLDs) has been widely researched. While both systems have been shown to be effective, these damping systems are being used separately. This thesis investigates the effectiveness of vertical TMDs combined with a TLD by analysing three barge-turbine structures. The first system is the undamped structure, which works as a control. The second system combines vertical TMDs with a TLD. These damping systems are not directly linked. The third system interdependently combines vertical TMDs with a TLD by stacking the damping systems. This makes the TMD displacement determine the shape of the TLD tank, which causes the system to be significantly nonlinear. The analysis of the three systems begins with the development of a program that creates the frequency response function for each of these systems. The basis for these programs is a linear modal analysis. The nonlinearity of the third system is accounted for by Newton iteration. The effectiveness of each damping system is determined by the performance index, which is based on the integral of the frequency response function. The damping parameters of the independent TMD and TLD are optimized. Due to computational difficulties no parameter optimization is performed for the interdependent damping system. In order to judge possible performance improvement for this system, a rough sensitivity study is performed on the damping parameters of this system. The results of the optimization and sensitivity study show that the independently damped system performs best of all three systems when using these particular parameters. The interdependently damped system has unknown damping potential. It is not possible to definitively conclude from this research whether the TMDs and TLD damp more effectively when they work either separately or interdependently. Both damped systems are able to perform better than the undamped system with the correct damping parameters. The developed programs give reasonable frequency response spectra for all three systems. From this it is concluded that the programs of the three systems work as intended, including the nonlinear part.

To reduce the environmental impact or cost of a civil engineering structure their designs are optimized. A promising method to optimize are iterative optimization algorithms. If both the design calculations and the iterative optimization algorithm are automated, an optimized design solution can be found within a feasible timeframe. To be able to automate the design calculations they need to be fully parameterizable. In this context it becomes interesting to research whether yet unparameterizable calculation processes can be made parameterizable. One of these processes is the determination of the locations in which the fatigue resistance has to be determined in a steel orthotropic bridge deck. This location is the location where the first fatigue crack is expected. Therefore, Antea Group requested if a study could be performed with the objective to answer the following research question: How can the determination of the location of the first fatigue crack in the deck, at a stiffener to deck plate weld toe, be parameterized? To answer the research question, the (in the Netherlands active) regulations are studied. Based on the regulations the process of determining fatigue damage of a point in the bridge can be understood. As well as the reason why, this process is too computational demanding and complex to be able to be applied to all points in all welds. In response to this an alternative method is proposed. This method reduces the complexity and the computational budget that is needed, by using 1D elements instead of the currently prescribed 2D elements. To determine if this method can be used it was decided to apply it on a case study. The bridge which served as the case study was the Goereese bridge. The alternative method was applied to determine the expected distribution of fatigue damages in all welds in the case study. Based on this obtained distribution a limited number of interesting locations in the deck could be identified. At these points to regulatory required method was used to obtain results which can be compared with the alternative method. It is concluded that the predicted location of the first fatigue crack of both methods is directly next to each other. However, the distribution of the remaining points suggest by the alternative method does not agree with the obtained results of the regulatory method. Remarkable enough, both these methods predict a location which is counter intuitive to the structural engineers participating in the research. Therefore, the following general recommendations are given:- Research if the regulatory method, to determine the location of the first fatigue crack, can be simplified. - Research the cause(s) of the differences between the regulatory method and the alternative method. - Increase the awareness of structural engineers regarding their intuition on the location of the first fatigue crack.

The instability of a moving mass / oscillator due to surpassing the velocity of the minimum group wave velocity (in a continuous homogeneous structure) has been studied extensively and is well understood. In contrary to that, Parametric Instability of a moving mass / oscillator on a continuous periodic structure has been studied less extensive and therefore the mechanism behind the instability is unknown. Literature that is avaiable on this topic mainly focuses on continuous periodic inhomogeneous structures, namely where the foundation is modeled as a continuous periodic inhomogeneous structure. Even less well studied are models where instead of a continuous periodic inhomogeneous foundation discrete periodic supports have been used. So far as known to the author there has also been no studies where the discrete supports are coupled through a medium. In order to solve the transition curves discerning the stable and unstable domains concerning the parametric instability of a moving mass / oscillator the analogy with the Mathieu equation is used, which tells us that the solution on those transition curves will be periodic with once or twice the period of the parametric excitation. In this thesis we have focussed on studying the use of the analogy on continuous structures founded upon periodic supports. The Mathieu equation describes the motion of a parametric oscillator, for example a pendulum with a length that periodically varies over time. The theory that predicts the solution to the Mathieu equation is called Floquet theory and ascociated with the solution are the Floquet exponents, these exponents dictate whether the solution will be periodic and bounded or unbounded. By solving for the Floquet exponents of the Mathieu one sees that for an increase of the amplitude of the parametric excitation the system will experience a greater exponential growth. For a greater mistuning between the parametric excitation and the natural frequency of the equivalent non-parametrically forced equation we see that the system will experience a smaller exponential growth. Outside the instability domains the solutions will be bounded and periodic and contain a wide variety of frequencies. When damping is introduced, the value of the damping coefficient (if written in the canonical form of a viscously damped single degree of freedom equation) will be subtracted from the value of the undamped Floquet exponents and by that result in an upward shift and narrowing of the transition curves. Furthermore, outside the instability domains we will see two regions: the first lies close the the transition curves and is asymptotically stable with a period equal to that of the transition curve, the second covers the remaining stable region and is asymptotically stable and periodic with a wide variety of frequencies. Regarding the Parametric Instability of a moving mass / oscillator we have studied three different models: a continuous Euler-Bernoulli beam on periodic spring supports, a continuous Euler-Bernoulli beam on periodic supports that are complex (i.e. modeled as an oscillator between two springs), and a continuous Euler-Bernoulli beam on periodic supports that are founded upon a 2-dimensional lattice. Of these models we have conducted a parametric study as to study what the effects are of the various parameters. We have seen that whenever the ratio between the stiffness of the supports and that of the beam is increased, the instability domains will shift to higher velocities and become wider. For certain combinations also 'islands' of instability may appear, where these 'islands' indicate stable areas between regions of instability. If damping is introduced into the system, this will generally narrow the instability domains and shift them to higher values of the mass and lower values of the velocity. However, for certain parameter combinations adding damping will lead to a widening of the instability domain. In the case of a moving oscillator the instability domains will narrow and be shifted to lower values. If the support is modeled with a mass it will affect the general trend of the transition curves through its own resonance, hence for a complex structure it is advised to model the supports with the correct dynamic equations. Last but not least, if the supports are coupled through a medium (a 2-dimensional lattice in this case) one will generally see a similar effect as adding damping has. In this thesis we have also studied three real world cases: a regular railway track, a high-speed railway slab-track, and the Hyperloop. In the first case we have seen that Parametric Instability will most likely have no influence. For the slab-track, being much more stiff, Parametric Instability will be important. However, a more extensive study with several cases must confirm this. In the last case, namely the Hyperloop, we have seen that for a moving mass the instability domains are relatively large as compared with the other cases. We have also studied the Parametric Instability of a test-pod, which showed that its instability domains that are negligible. Of course, this was merely a test-pod not capable of transporting people, hence when a larger pod is studied it may be expected that the instability domains may not be neglected.