Fibonacci sequence for modelling stop bands in random microstructure

In this paper the mathematical concept of the Fibonacci sequence has been introduced as an accurate and reliable tool to model randomness in a heterogeneous material. It is also argued, that this randomness plays an important role and can control the response of a heterogeneous material, subjected to dynamic loading, here an elastic wave propagating through the material. A particular dynamic phenomenon, the presence of band gaps, has been analysed. It has been shown that randomness, modelled using the Fibonacci sequence, introduced into the material's structure, increases the range of stop band frequencies.