Traveling waves and their tails in locally resonant granular systems
Traveling waves and their tails in locally resonant granular systems
复制标题
局部共振颗粒系统中的行波及其尾部
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
A. Stefanov
中科院分区：
文献类型：
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作者：
H. Xu;P. Kevrekidis;A. Stefanov
在目前的研究中，我们重新审视了局部共振颗粒晶体系统中的波传播主题，也被称为质量中质量系统。我们使用三种不同的方法来识别相关的行波。第一种是行波问题的直接解。第二个是问题的傅里叶变换变量的解，或者更准确地说，是它在实空间中的卷积重新表述（基于傅里叶反变换）。最后，我们的第三种方法将限制考虑到有限域，利用傅里叶级数的概念，因为重要的技术原因，即避免共振，这将被详细讨论。这三种方法都可以用于位移或应变公式。在有限域的典型计算结果是孤波在计算域的两端具有对称的不灭尾。然而，重要的是，一个可数无限的反共振条件集被确定，其中解具有真正快速衰减的尾。
In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as mass-in-mass systems. We use three distinct approaches to identify relevant traveling waves. The first consists of a direct solution of the traveling wave problem. The second one consists of the solution of the Fourier tranformed variant of the problem, or, more precisely, of its convolution reformulation (upon an inverse Fourier transform) in real space. Finally, our third approach will restrict considerations to a finite domain, utilizing the notion of Fourier series for important technical reasons, namely the avoidance of resonances, which will be discussed in detail. All three approaches can be utilized in either the displacement or the strain formulation. Typical resulting computations in finite domains result in the solitary waves bearing symmetric non-vanishing tails at both ends of the computational domain. Importantly, however, a countably infinite set of anti-resonance conditions is identified for which solutions with genuinely rapidly decaying tails arise.