Propagation of Elastic Waves in Dynamically Self-Similar Structures (Dynamic Fractals)

The concept of a dynamically self-similar structure (dynamic fractal) is introduced, consisting in the similarity of the dynamic parameters of the cell generatrices. Elastic wave propagation in unbranched dynamically self-similar structures is investigated. It is shown that such structures are equivalent in frequency to a periodic structure with additional fixation; however, the nature of wave propagation in them significantly differs. A dynamic fractal can feature both attenuated waves and waves that increase along the length of the structure; the intensity of wave attenuation is stronger than in a periodic structure.