In a high-precision system that performs measurements or tooling on a workpiece, alignment of the tool and workpiece is of prime importance. To prevent misalignment, which leads to a loss in accuracy and precision, unwanted vibrations in structures must be attenuated. Topology Optimization (TO) is evolving as a mature design tool that provides innovative designs beyond human creativity. This thesis focuses on developing and investigating TO methods for the limitation of response peaks on a flat surface for suspended structures. When optimizing for multiple excitation frequencies at multiple output points, the complexity of the problem increases, and the number of required constraints grows manifold. Thus, for a compact formulation, there is a need for aggregation of peaks in both dimensions, space, and frequency. Furthermore, the application requires the top surface of the suspended structure to remain flat during operation. In such a scenario, where a structure is excited harmonically, the dynamic deformations on the surface become key to quantifying surface flatness. The incorporation of dynamic flatness measures in TO framework is studied and implemented, and the results show that the proposed methods look promising.

Topology optimization has seen increased interest with the development of additive manufacturing (AM) as a manufacturing method, because of its ability to utilize the geometric complexity that AM offers. However AM still imposes some restrictions on the design, most notably on its minimum feature size, overhang, and enclosed voids. Enclosed voids are problematic because for most AM methods it is impossible to remove supports from them, additionally for powder-based AM these enclosed voids trap unmelted powder adding parasitic mass. In this thesis, two new methods have been investigated to alleviate this issue, the eigenfrequency method and the flood fill method. The eigenfrequency method utilizes the eigenfrequency of an inverted density field, which changes enclosed voids to floating masses. These floating masses have rigid body modes, which can then be prevented by applying a minimum eigenfrequency constraint. The eigenfrequency method encountered a large problem in the form of intermediate densities, which were used to satisfy the eigenfrequency constraint instead of the elimination of enclosed voids. The flood fill method utilizes a modified flood fill algorithm, which is a filter with a resulting density field where every enclosed void element is changed to solid. The flood fill method did successfully eliminate enclosed voids in both 2D and 3D problems, at the cost of very little additional computational effort. It also allows for direct control over the location, amount, and size of the void elimination features by varying boundary elements, running additional flood fills, and morphologic operators, respectively.

High performance machines such as those used in the semiconductor industry, robotics or racing engines have lots of fast moving parts. The dynamic properties of these moving parts are crucial to the performance of the machine. Therefore these moving parts have to be carefully designed which is often a very time consuming iterative process. In this thesis a general method to optimize the dynamic properties of a structure utilizing topology optimization is investigated. More specifically, the method will be focused on the optimization of eigenfrequencies whilst achieving specific ratios between eigenfrequencies,
as dynamic performance requirements are often linked to such criteria. We refer to this class of topology optimization problems as problems involving constrained eigenfrequencies. A particular case of interest is the desired multiplicity of two or more eigenfrequencies, that is a ratio of 1. Several crucial aspects of the topology optimization of eigenfrequencies are investigated, these are the material interpolation methods, mode tracking techniques, multiplicity problems and obtaining a discrete design. By comparing different material interpolation methods, a clear view on the effects of different methods is obtained, leading to solid arguments for selecting a linear material interpolation method for topology optimization of eigenfrequencies. A simple yet effective method of tracking the eigenmodes during the optimization process combined with a solution for the multiplicity problems is presented and verified to show similar results as a more complex analytical approach. A new method of obtaining a discrete design without applying penalization or modification of the eigenvalue problem has been developed using a modified objective function. This method shows promising results and is a good candidate for replacing the material interpolation penalization method. By combining these results, a general and capable framework for the topology optimization of constrained eigenfrequencies is obtained. Using the presented framework, a practical application of the method is given by the design of a cantilever used in an atomic force microscope. Feasible and well-performing designs have been generated, both from a functional and manufacturing point of view.