论文标题
二维Helmholtz谐振阵列。第一部分I
Two-dimensional Helmholtz resonator arrays. Part I. Matched asymptotic expansions for thick- and thin-walled resonators
论文作者
论文摘要
我们提出了一种新型的多极公式，用于计算圆柱旋转器的二维阵列的带结构。该公式是通过将现有的理想圆柱阵列与匹配的渐近扩展方法相结合的现有多极方法来得出的。我们构建了第一带表面的分散方程的渐近封闭表示，校正并扩展了已建立的最低阶（各向同性）导致薄壁谐振阵列的文献。我们为第一频带获得的描述在相对较宽的频率和Bloch矢量范围内是准确的，而不仅仅是在长波长和低频方向上，就像许多经典处理中一样。至关重要的是，我们能够捕获第一条带的特征，例如低频各向异性，在较大的填充分数，壁厚和光圈角度。除了描述第一个频带外，我们还使用公式来计算厚和薄壁的谐振器的第一个频段隙，并发现较厚的谐振墙既对应于第一个频段隙的狭窄，又对应于中央频段隙频率的增加。
We present a novel multipole formulation for computing the band structures of two-dimensional arrays of cylindrical Helmholtz resonators. This formulation is derived by combining existing multipole methods for arrays of ideal cylinders with the method of matched asymptotic expansions. We construct asymptotically close representations for the dispersion equations of the first band surface, correcting and extending an established lowest-order (isotropic) result in the literature for thin-walled resonator arrays. The descriptions we obtain for the first band are accurate over a relatively broad frequency and Bloch vector range and not simply in the long-wavelength and low-frequency regime, as is the case in many classical treatments. Crucially, we are able to capture features of the first band, such as low-frequency anisotropy, over a broad range of filling fractions, wall thicknesses, and aperture angles. In addition to describing the first band we use our formulation to compute the first band gap for both thick- and thin-walled resonators, and find that thicker resonator walls correspond to both a narrowing of the first band gap and an increase in the central band gap frequency.
