Structures can be characterized by their natural vibration. If the associated eigenfrequencies correspond to external, exciting vibration frequencies, high vibration amplitudes can occur which might cause structural damage. Therefore, heavy and costly damping mechanisms are often employed to prevent high vibration amplitudes. Natural structures are often highly optimized. The silicate shells of marine plankton organisms, for example, serve already as inspiration for lightweight construction owing 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. In this investigation, the eigenfrequencies of different plates with regular patterns were compared to irregular plates of Voronoi cells. The irregular Voronoi plates were designed using evolutionary strategic optimization. The results showed significantly higher first eigenfrequencies of the irregular structures compared to regular structures of the same mass.