Structures can be characterized by their natural vibrations. If the eigenfrequencies lie in the range of external, exciting frequencies, resonance phenomena can occur. Additional damping mechanisms are often employed to prevent increased vibration amplitudes. To avoid damping, a direct adjustment or maximization of structural eigenfrequencies would be of great interest. In nature, there are highly optimized structures. The shells of marine plankton organisms (diatoms, radiolarians), for example, show a variety of regular and irregular honeycomb and lattice structures, which often fulfill several functions simultaneously. The silicate shells of diatoms are characterized by a high stiffness at low mass and already serve as inspiration for lightweight structures. Furthermore, it is expected that the structural irregularities have a high impact on the vibration characteristics. The use of biologically inspired lattice structures leads to improved vibration characteristics. First studies show that increasing structural irregularities result into an eigenfrequency increase. In cooperation with the German Electron Synchrotron (DESY), optimized magnet girder structures of a new particle accelerator will be developed by using biologically inspired optimization and lattice structures. The objectives are to achieve high eigenfrequencies and high rigidity at low mass. First numerical results show that the use of bio-inspired structures leads to improved structural properties.