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.

中文翻译：

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动态自相似结构（动态分形）中弹性波的传播

摘要

引入了动态自相似结构（动态分形）的概念，其中包括细胞谱系的动态参数的相似性。研究了弹性波在无分支动态自相似结构中的传播。结果表明，这种结构在频率上等同于带有附加固定的周期性结构。但是，它们中的波传播性质却大不相同。动态分形既可以具有衰减波，也可以沿结构长度增加波。波衰减的强度比周期性结构强。