Redirection and splitting of sound waves by a periodic chain of thin perforated cylindrical shells

Abstract

A line of perforated cylindrical shells in air is practically transparent for sound since each individual unit is a weak scatterer. However, strong scattering occurs due to the coupling to the acoustic eigenmodes of the chain. Here we develop an analytical theory of sound transmission and scattering at a linear chain of perforated shells and predict strong anomalous effect for oblique incidence. The chain eigenmodes are weakly decaying, with symmetric profile and anomalous dispersion, or with antisymmetric profile and normal dispersion, and their excitation leads to deep minima in the transmission and 90̊-redirection of the external sound. At normal incidence, only the symmetric eigenmode can be excited, otherwise both modes are excited at close frequencies. Moreover, the wave which resonates with the normal-dispersion mode is redirected along the “right” direction, whereas the wave resonating with the anomalous-dispersion mode is redirected in the “wrong” direction. Thus, a periodic chain of perforated shells may serve not only as a 90̊-redirecting antenna but also as a splitter of sound waves with close frequencies. For example, an acoustic signal containing two frequencies around 3 kHz can be split into monochromatic components propagating in opposite directions along the chain, if the beat frequency is ≈500 Hz.