Investigating the influence of structural components on the natural vibrations of structures is of great interest in many fields of application including mechanical engineering, aerospace, construction and optics. Shells of marine protozoa show an enormous diversity of regular and irregular honeycomb and lattice structures which often fulfill different functions. The silicate shells of diatoms, for example, are characterized by a high stiffness at low mass and serve already as inspiration for lightweight designs. Furthermore, the irregular diatom structures are expected to have a positive influence on vibration characteristics. In this study, a magnet underframe structure (girder) of a particle accelerator was replaced by bio-inspired lattice structures in order to achieve a high first natural frequency and stiffness. The parametrically constructed structures were based on algorithms, which generated the bio-inspired structures. Multi-objective optimizations using evolution strategy allowed the discovery of best possible parameter combination to achieve the desired properties. The results indicated a high potential of lattice and honeycomb structures to influence the vibration characteristics. The irregular structures led to significantly higher natural frequencies and stiffness than regular structures. Moreover, structures of equal stiffness and different first natural frequencies were generated, whereby the masses always remained within permitted values. Regarding the girder structure, the bio-inspired structures showed a simultaneous increase of the first natural frequency by a factor of 1.4 and the stiffness of 1.9 compared to the reference structure.