A phase-gradient acoustic metasurface for broadband duct noise attenuation in the presence of flow

Reconfigurable and Phase‐Engineered Acoustic Metasurfaces for Broadband Wavefront Manipulation

“…The GSL is then harnessed as a guide of the element arrangement with periodicity, which can be rewritten considering the diffracted wave as [ 53–55,58 ] $$$$\begin{equation} \sin {\theta}_{\mathrm{re}}-\ \sin {\theta}_{\mathrm{in}}=\ m\frac{\lambda}{2\pi}\frac{d\mathrm{\Phi}\left(x\right)}{\textit{dx}} \end{equation}$$$$where m denotes the diffracted order stemming from the periodicity of the structure. Supposing that the metasurface in a period is constructed by arranging the elements in the sequence, that is, elements #1, #2, #3, …, #8, then the factor $$\frac{{d\Phi ( x )}}{{dx}}$$ can be simplified as 2π/ D owing to the linear variation of Φ( x ), in which D is the periodic length of the metasurface.…”

“…In previous studies, numerous metasurfaces designed for acoustic wave manipulation are constructed by the elements with a representative configuration, that is, the cavity-like structure, [52,53] for instance, the uniform cavities varying with heights, [54,55] and the uniform coiled-up channels with diverse internal dimensions. [5,7] The latter can also be regarded as the uniform cavities holding different cross-sectional areas (s 1 ) and heights (l 1 ) by the conversion of incident area (s 0 ), as shown in Figure 1a.…”

“…Moreover, the analytical and numerical results are in good agreement with each other, demonstrating the correctness of the analytical model. The GSL is then harnessed as a guide of the element arrangement with periodicity, which can be rewritten considering the diffracted wave as [53][54][55]58] sin…”