Redirection of sound in straight fluid channel with elastic boundaries

Abstract

A fluid channel clad between two solid plates is an acoustic waveguide where excitation of elastic waves at the channel boundaries has been usually neglected. This work develops a rigorous theory of scattering of sound by a finite-length fluid channel which takes into account excitation of elastic eigenmodes of two plates acoustically coupled through a fluid channel. The theory predicts an evidently contradictory result that the transmission and reflection coefficients of a non-dissipative channel do not sum up to one. Moreover, they both exhibit deep minima at the same series of frequencies. It is shown that conservation of acoustic energy occurs due to redirection of sound, since part of the acoustic flux escapes into the solid plates. This scattering becomes possible because the bf uniform flatness of the boundaries of a straight channel is broken by vibrations. Theoretical predictions are supported by the experiments with ultrasound transmission through a narrow slit obtained between two brass or aluminum plates submerged in water. Measured transmission spectra exhibit deep minima exactly at the frequencies where the theory predicts strong redirection of sound.

On the use of aerogel as a soft acoustic metamaterial for airborne sound

“…Accounting for the leakage through the use of Eqs. ( 21) and (22), this observed difference in the reflectance can fres (Hz) E (MPa) ρ (kg/m 3 ) 1420 0.569 107 TABLE I. Measured values for the flexural resonance frequency, Young's modulus E and density ρ for the silica aerogel examined in this work.…”

“…It is expected that the elasticity of the materials defining the metamaterial structure might play a fundamental role in order to understand the phenomena observed in sound transmission and reflectance through the channels defined by the structure. In fact, the role of the elastic properties is paramount for the case of structures embedded in water, as it has been recently demonstrated [22]. Although some recent work has begun to incorporate the elastic effects into the metamaterial structure, many of these designs continue to have the primary dynamic element consisting of mass-spring resonators which are affixed to an elastic plate as structural support [19,20].…”

Transparent Gradient-Index Lens for Underwater Sound Based on Phase Advance

“…Although the strength of the space-coiling design is the ability to significantly modify a phase within a confined space, there is a drawback that it can only delay the phase over a lengthened path; similar to rubbers in water, the effective sound speed of these devices is less than the background fluid. The space-coiling design has not yet been demonstrated in water, where common solids such as steel that might be used to confine the coils cannot be assumed to be perfectly rigid due to their significantly smaller density contrast with water-thus introducing the challenge of elastic coupling [37] that must be incorporated into any design strategy. Although the kinematic viscosity of water is less than that of air [23], recent measurements of air-borne space-coiled metamaterials [36] demonstrate significant attenuation, and we caution that viscous effects should not be neglected in aqueous designs.…”

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

“…the initial flux of energy is partially redirected by 90 • . The effect of redirection of acoustic energy was recently predicted not only for periodic systems of scatterers [16,19,22] but also for a narrow fluid channel in a solid elastic plate [23,24].…”