Topology optimization for suppression of vibrations in suspended structures and achieving dynamic global flatness

Abstract

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.