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Two-dimensional phononic crystals with time-varying properties: a multiple scattering analysis

机译:具有时变特性的二维声子晶体:多重散射分析

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摘要

Multiple scattering theory is a versatile two-and three-dimensional method for characterizing the acoustic wave transmission through many scatterers. It provDEes analytical solutions to wave propagation in scattering structures, and its computational complexity grows logarithmically with the number of scatterers. In this paper we show how the 2D method can be adapted to include the effects of time-varying material parameters. Specifically, a new T-matrix is defined to include the effects of frequency modulation that occurs in time-varying phononic crystals. Solutions were verified against finite difference time domain (FDTD) simulations and showed excellent agreement. This new method enables fast characterization of time-varying phononic crystals without the need to resort to lengthy FDTD simulations. Also, the method of combining T-matrices to form the T-supermatrix remains unchanged provDEed that the new matrix definitions are used. The method is quite compatible with existing implementations of multiple scattering theory and could be readily extended to three-dimensional multiple scattering theory.
机译:多重散射理论是一种通用的二维和三维方法,用于表征通过许多散射体的声波传输。它为散射结构中的波传播提供了解析解,其计算复杂度随着散射体的数量呈对数增长。在本文中,我们展示了如何将2D方法修改为包括随时间变化的材料参数的影响。具体而言,定义了一个新的T矩阵,以包括随时间变化的声子晶体中发生的频率调制的影响。解决方案针对时域有限差分(FDTD)仿真进行了验证,并显示出极好的一致性。这种新方法可以快速表征随时间变化的声子晶体,而无需进行冗长的FDTD模拟。同样,假设使用新的矩阵定义,则组合T矩阵以形成T超级矩阵的方法保持不变。该方法与多重散射理论的现有实现方式完全兼容,并且可以容易地扩展到三维多重散射理论。

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