Redirection and Splitting of Sound Waves by a Periodic Chain of Thin Perforated Cylindrical Shells

Abstract

Scattering of sound by finite and infinite chains of equally spaced perforated metallic cylindrical shells in an ideal (inviscid) and viscous fluid is theoretically studied using rigorous analytical and numerical approaches. Due to perforations, a chain of thin shells is practically transparent for sound within a wide range of frequencies. It is shown that strong scattering and redirection of sound by 90 • may occur only for a discrete set of frequencies (Wood's anomalies) where the leaky eigenmodes are excited. The spectrum of eigenmodes consists of antisymmetric and symmetric branches with normal and anomalous dispersion, respectively. The antisymmetric eigenmode turns out to be a deaf mode since it cannot be excited at normal incidence. However, at slightly oblique incidence both modes can be excited at different but close frequencies. The symmetric mode, due to its anomalous dispersion, scatters sound in the "wrong" direction, thus allowing splitting of the incoming signal containing two harmonics into two beams propagating along the chain in the opposite directions. Calculations are presented for aluminum shells in viscous air where the effects of anomalous scattering, redirection, and signal splitting are well manifested.

Poisson-like effect for flexural waves in periodically perforated thin plates

“…In summary, for weak scatterers, the previous results are consistent with the works reported for acoustic waves. 4,6 What happens if we increase the radius of the holes? Figure 4(a) shows the transmittance spectra when a plane wave impinges on an infinite slab containing three layers of free holes.…”

“…Nevertheless, it is emphasized that, thanks to symmetry broken, the coupling of incident waves to the antisymmetric modes is possible at slightly oblique incidence provided the matching condition is satisfied. 6 To prove this, Fig. 8 shows the transmittance spectra for an infinite slab containing three layers of free circular holes with radius r ¼ 3 mm, where the solid and dotted lines represent the results for two incident angles h 0 ¼ 0 and 5 , respectively.…”

“…Redirection of acoustic energy by 90 has been obtained by constructing chains of cylindrical shells. [4][5][6] By using arrays of perforated cylindrical shells, Garc ıa-Chocano and S anchez-Dehesa 4 employed the strategy of wave redirection for the purpose of increasing the propagation path of sound and, thus, enhancing the dissipation loss of the structure. The redirection of acoustic waves was explained in terms of the resonant excitation of a Wood's anomaly; i.e., a leaky guided mode propagating normally to the impinging direction.…”

“…A different mechanism explained this energy redirection, which has been proved to be possible by employing quadrupole resonance of cylindrical shells thanks to the dynamic coupling of normal unidirectional wave motion to the perpendicular one. More recently, Bozhko et al 6 further developed the microscopy theory of wave redirection applied to a linear chain of perforated shells in the air. They demonstrated that, at slightly oblique incidence, the sound waves can be redirected along a periodic chain to one single side provided the symmetric or antisymmetric eigenmode is resonantly excited.…”

Labyrinthine Acoustic Metamaterials with Space-Coiling Channels for Low-Frequency Sound Control

“…Apart from unusual effective properties, the metamaterials offer various possibilities to control propagation of sound or elastic waves at deep sub-wavelength scales [3,4,5]. This can be achieved by incorporating heavy resonators [3], Helmholtz resonators [6,7], tensioned membranes [8,9], or sub-wavelength perforations or slits [10,11,12,13] in a material structure. A class of acoustic metamaterials with internal slits is also known as "labyrinthine".…”