Bloch spectra for high contrast elastic media
Bloch spectra for high contrast elastic media
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DOI：
10.1016/j.jde.2022.05.021
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发表时间：
2021-10
影响因子：
2.4
通讯作者：
R. Lipton;R. Perera
中科院分区：
文献类型：
--
作者：
R. Lipton;R. Perera
本文给出了描述高对比度夹杂周期性弹性晶体能带结构的解析表达式和幂级数。我们使用与结构谱相关的无源模来表示声子晶体内Lamé系统的解算子。利用这些表示公式，得到了Bloch波谱的收敛幂级数。通过包含阵列的结构谱和包含阵列的Dirichlet谱，给出了收敛半径的一个显式界。对于任何固定的准动量色散关系的光谱分支分离的充分条件被确定。一个条件是足够的带隙的出现。
Analytic representation formulas and power series are developed to describe the band structure inside periodic elastic crystals made from high contrast inclusions. We use source free modes associated with structural spectra to represent the solution operator of the Lamé system inside phononic crystals. Convergent power series for the Bloch wave spectrum are obtained using the representation formulas. An explicit bound on the convergence radius is given through the structural spectra of the inclusion array and the Dirichlet spectra of the inclusions. Sufficient conditions for the separation of spectral branches of the dispersion relation for any fixed quasi-momentum are identified. A condition is found that is sufficient for the emergence of band gaps.