Abstract

Wave propagation behavior within 1D granular chain has been a much-studied topic in the past decades due to its novel physical wave phenomena. The initial motivation of the present study was prompted by how to construct a granular system with desired wave properties and particle motions. Here, we systematically report the methodology to construct equivalent systems (systems with identical output) using theoretical analysis, experiments and numerical simulation. We investigate the properties of Nesterenko solitary wave supported by one-dimensional granular chains and achieve an equivalent wave transmission among various materials and dimensions. The results of typical experiments and finite element analysis fully support the established theoretical predictions based on Hertz contact and long wavelength approximation theory, which yields a broad class of equivalent systems. Finally, an instructive mechanism map, containing various equivalent systems, is proposed to clarify the relationship between geometric parameters and material properties, providing insights into designing a desired nonlinear dynamic system and guidance for potential engineering applications.

Graphic abstract

中文翻译：

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Nesterenko孤立波传输的等效系统的通用设计定律

摘要

一维颗粒链中的波传播行为由于其新颖的物理波现象而在过去几十年中一直是人们研究的热点。本研究的最初动机是由如何构建具有所需波特性和粒子运动的颗粒系统引起的。在这里，我们通过理论分析，实验和数值模拟，系统地报告了构建等效系统（具有相同输出的系统）的方法。我们研究了一维颗粒链支撑的Nesterenko孤波的特性，并实现了在各种材料和尺寸之间的等效波传输。典型实验和有限元分析的结果完全支持基于赫兹接触和长波长近似理论的既定理论预测，这产生了各种各样的等效系统。最后，提出了一个包含各种等效系统的指导性机制图，以阐明几何参数与材料特性之间的关系，为设计所需的非线性动力系统提供了见识，并为潜在的工程应用提供了指导。

图形摘要