Free vibration analysis of a von Koch beam

In this paper, the free undamped motion of a cantilever von Koch beam is investigated. The reduction of the stiffness and mass matrices leads to simple analytical recursive relationships depending on the fractal dimension of the structure. Results are then extended to perform a detailed modal analysis, which suggests peculiar scaling laws for the natural frequencies and modal shapes of the structure. Energy considerations are also provided. Finally, the potentiality of the von Koch beam as a fractal antenna is examined in terms of resonant frequencies.