Finding the optimal structural design to avoid resonance has been a goal for decades as it is of high interest in many technical areas. Lightweight design structures, in particular, show a high susceptibility to vibration. One approach is to increase (maximise) the structural eigenfrequencies, i.e., to ’detune’ the system. In this work, a detailed literature review on technical lightweight structures and structural optimisations focusing on vibration characteristics is presented. Subsequently, different studies investigate the application of biologically inspired structures and methods to increase eigenfrequencies. It has been observed that diatom shells are shaped according to their vibration mode shapes, which leads to the assumption that these structures are optimised for vibratory loads. Applying this mode shape adaptation strategy to axially constrained beams (1D) and plates (2D) results in strong eigenfrequency increases at constant mass. In addition, the increase of multiple eigenfrequencies is possible. The mode shape adaptation results are compared to evolutionary strategic optimisations and, in the case of the plate, also to topography optimisations. The optimisations using commercially available optimisers successfully increase the targeted eigenfrequencies. However, the single eigenfrequency increases are generally lower than those generated by the mode shape adaptation method, while the evolutionary strategic optimisations lead to higher multiple eigenfrequency increases. With regard to the complex honeycomb and lattice structures found in aquatic plankton organisms, the impact of the structural complexity on the eigenfrequencies is studied. The 1st eigenfrequency of a 2D cellular plate significantly rises using irregular structures. In addition, the application of the mode shape method to the studied cellular plates raises the 1st eigenfrequency even further. Regarding lattice structures, a strong 1st eigenfrequency increase with rising structural complexity is obtained likewise. Additional design constraints allow the development of vibration optimised lattices that can be additive manufactured without support structures. As an example of biologically inspired vibration optimisation, a girder used in synchrotron radiation facilities to support the magnets and to assure a stable particle beam is studied. It is focused on the girder design for the currently planned synchrotron radiation facility upgrade PETRA IV at DESY (German Electron Synchrotron, Hamburg, Germany). In a parametric study, the impact of different boundary conditions on the magnet-girder assembly is investigated, involving varying loading conditions, girder support definitions, and material properties of the girder and bases. Afterwards, a development process for a girder structure installed in a synchrotron radiation facility is generated. Based on a topology optimisation, a parametric beam-shell model including biologically inspired structures is created. The subsequent cross section optimisation using evolutionary strategic optimisation reveals an optimum girder structure. Vibration experiments of the casted girder structure validated the numerical results. Future changes in the specifications can be implemented in the development process to obtain further adapted girder structures.