Acoustic performance of boundaries having constant phase gradient

In this paper, inhomogeneous boundaries having constant phase gradient are investigated. In principle, such a theoretically proposed boundary is dispersionless. In practice, however, when the boundary is realized by a subwavelength-structured tubes array, the impedance discretization brings about sub-reflections at high frequencies. Moreover, determined by the longest duct in the array, a realized boundary is impractically thick. Therefore, a finite-thickness boundary is further proposed by truncating and periodizing the tubes in the array. In this paper, the theoretical analysis agrees well with the numerical simulations. By appropriately choosing its phase gradient and target frequency, the finite-thickness boundaries have potential applications in noise control.

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