Barros D F, Costa A E B, de Moura F A B F
Instituto de Física, Universidade Federal de Alagoas, Maceió-AL 57072-970, Brazil.
J Phys Condens Matter. 2011 Aug 31;23(34):345404. doi: 10.1088/0953-8984/23/34/345404.
In this paper we study the propagation of acoustic waves in a one-dimensional medium with a short range correlated elasticity distribution. In order to generate local correlations we consider a disordered binary distribution in which the effective elastic constants can take on only two values, η(A) and η(B). We add an additional constraint that the η(A) values appear only in finite segments of length n. This is a generalization of the well-known random-dimer model. By using an analytical procedure we demonstrate that the system displays n - 1 resonances with frequencies ω(r). Furthermore, we apply a numerical transfer matrix formalism and a second-order finite-difference method to study in detail the waves that propagate in the chain. Our results indicate that all the modes with ω ≠ ω(r) decay and the medium transmits only the frequencies ω(r).
在本文中，我们研究了声波在具有短程相关弹性分布的一维介质中的传播。为了产生局部相关性，我们考虑一种无序二元分布，其中有效弹性常数只能取两个值，即η(A)和η(B)。我们添加了一个额外的约束条件，即η(A)值仅出现在长度为n的有限段中。这是著名的随机二聚体模型的一种推广。通过使用一种解析方法，我们证明该系统呈现出n - 1个频率为ω(r)的共振。此外，我们应用数值转移矩阵形式和二阶有限差分方法来详细研究在链中传播的波。我们的结果表明，所有ω≠ω(r)的模式都会衰减，并且介质仅传输频率为ω(r)的波。
