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arXiv 2410.04549physics.app-ph
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广义一维声子晶体的色散关系

Dispersion relations of generalized one-dimensional phononic crystals

Universitat Politècnica de València(瓦伦西亚理工大学);Imperial College London(伦敦帝国学院)

Mario Lázaro, Richard Wiltshaw, Richard V. Craster, Vicent Romero-García

AI总结:

本文提出了一种通用方法,用于计算一维声子晶体的色散关系,通过调整参数考虑不同波和散射体,并通过数值示例验证了方法的高效性和通用性。

摘要:

我们提出了一种全面的方法,用于确定一维共振声子晶体的精确和近似色散关系,适用于各种结构,无论其具体特性如何。该通用框架采用一种统一的数学模型,称为广义一维(1D)声子晶体,在其中通过调整某些参数可以考虑不同类型的波和散射体/谐振器。广义1D声子晶体由一个具有物理性质以矩阵形式表示的均匀弹性材料作为基质,以及任意数量的散射体(在单元胞内),包括谐振器(离散和连续)、小材料掺杂或横截面积的变化组成。基于一般假设,并施加周期性和布洛赫解,我们开发了一种基于矩阵的算法,利用平面波展开法来推导解。此外,我们提出了一种迭代程序,能够提供一阶和二阶项的解析表达式,特别是在弱散射背景下特别有用。该方法的收敛条件被严格定义。通过几个数值示例展示了该方法的效率,突显了其在不同波导配置和散射场景中的通用性。

英文摘要:

We present a comprehensive method for determining {both exact and approximate} dispersion {relations} for one-dimensional {resonant phononic} crystals, applicable to a wide range of structures, regardless of their specific characteristics. This general framework employs a unified mathematical model, referred to as generalized {one-dimensional (1D) phononic crystal}, in which {different} types of {waves} and scatterers{/resonators} {can be} {considered} by adjusting certain parameters. The generalized {1D phononic crystal} consists of both a host {one-dimensional} homogeneous elastic {material} with physical properties represented in matrix form and an arbitrary set of scatterers {within the unit cell,} including resonators (discrete and continuous), small material inclusions, or variations in cross-sectional area. Based on general assumptions, {and imposing the periodicity and Bloch solutions} we develop a matrix-based algorithm utilizing the plane wave expansion method to derive the solution. Additionally, we propose an iterative procedure that provides analytical expressions for the first- and second-order terms, particularly useful in the context of weak scattering. The convergence conditions of the method are rigorously defined. The {efficiency of the} approach is demonstrated through several numerical examples, highlighting its versatility in different waveguide configurations and scattering scenarios.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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