Abstract

Vibrations and waves are investigated in periodic systems that consist of identical subsystems having an arbitrary structure. Spectral regularities are found for such systems. Their dispersion curves are shown to consist of branches, each of which corresponds to its own mode shape of elastic vibrations of the subsystem. The presence of band gaps in such systems, in which a harmonic signal cannot be transmitted, was revealed, and their boundaries were determined. The mode shapes of vibrations in various frequency ranges are obtained. Modulated waves are shown to arise in the system due to modulation by lower frequencies, which correspond to system vibrations without taking into account the elastic properties of the constituent subsystems.

中文翻译：

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由任意结构的相同子系统组成的周期系统的振动

摘要

在由具有任意结构的相同子系统组成的周期系统中研究振动和波。发现此类系统的光谱规律。它们的色散曲线由分支组成，每个分支对应于子系统弹性振动的其自身模态形状。人们揭示了此类系统中存在带隙（谐波信号无法在其中传输），并确定了带隙的边界。获得了不同频率范围内的振动模态形状。由于较低频率的调制，系统中出现了调制波，这对应于系统振动，而不考虑组成子系统的弹性特性。