Structures can be characterized by their natural vibration. A correspondence of the associated eigenfrequencies with frequencies of external vibrations may result into resonance phenomena. Therefore, extensive and costly damping mechanisms are often applied to prevent high vibration amplitudes. Consequently, a direct eigenfrequency adjustment is of great interest to avoid additional damping mechanisms. Natural structures also exhibit eigenfrequencies. The silicate shells of marine plankton organisms, for example, serve already as inspiration for lightweight construction due to their high stiffness and strength at low mass. Moreover, the irregularities of their honeycomb and lattice structures are expected to have a strong impact on the vibration characteristics. First studies indicated significantly higher eigenfrequencies of irregular lattice structures compared to regular lattice structures of the same mass. Bio-inspired lattice structures shall be applied to magnet underframe structures (girders) of particle accelerators. A high first eigenfrequency and stiffness as well as a low mass are required. Improving the girder structure by using topology optimization and bio-inspired lattice structures leads to higher eigenfrequencies and stiffness at low mass as shown in first numerical calculations. The resulting high magnet stability causes high beam brilliance which allows high resolution X-ray microscopy.