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

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Abstract

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.

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Notes

  1. Generally speaking, we obtain a family of equivalent periodic structures with proportional parameters and the same frequency spectrum

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ACKNOWLEDGMENTS

The author thanks Prof. Yu.I. Bobrovnitskii for discussion of the work.

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  1. Mechanical Engineering Research Institute, Russian Academy of Sciences, 101990, Moscow, Russia

    L. Ya. Banakh

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  1. L. Ya. Banakh
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Banakh, L.Y. Propagation of Elastic Waves in Dynamically Self-Similar Structures (Dynamic Fractals). Acoust. Phys. 66, 250–256 (2020). https://doi.org/10.1134/S1063771020020013

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