Two-dimensional phononic crystals studied using a variational method: Application to lattices of locally resonant materials
- 2 April 2003
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 67 (14), 144301
- https://doi.org/10.1103/physrevb.67.144301
Abstract
A variational method is introduced to study the propagation of elastic waves in two-dimensional periodic systems. First, it has been applied to a binary system consisting of an array of high-density cylinders in an epoxy background, where the advantages of the method are pointing out in regard with the well-known plane-wave expansion formalism. Second, a comprehensive study is performed for the two-dimensional counterpart of the ternary systems recently studied by Liu et al. [Z. Liu et al., Science 289, 1734 (2000)]. Numerical simulations predict that subfrequency gaps also appear because of the soft polymer that coats the cylinders. A simple mechanical model is introduced to give a physical insight of the phenomenon responsible for our findings.Keywords
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