Low frequency attenuation of acoustic waves in a perforated pipe

Abstract

This paper presents new experimental and numerical evidence that perforations in a pipe wall result in a low-frequency bandgap within which sound waves rapidly attenuate. These perforations are modelled as an acoustically soft boundary condition on the pipe wall and show that a low frequency bandgap is created from 0 Hz. The upper bound of this bandgap is determined by the dimensions and separation of the perforations. An analytical model based on the transfer matrix method is proposed. This model is validated against numerical predictions for the pipe with varying perforation geometries. A numerical study is undertaken to model the effect of perforations with ideal acoustically soft boundary conditions and surrounded with an air gap. Close agreement is found between the numerical and analytical models. Experimental evidence shows that the width of the bandgap is accurately predicted with the numerical and analytical models.

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“…As observed from the experimental measurements, by opening the peripheral holes, a band gap is formed at a very low frequency range from the infrasounds up to 2.9 kHz. According to previous works 53,54 , the direct connection of the incident pressure wave to the external air through the peripheral holes results in significant suppression of the pressure at the position of the peripheral holes, leading to backward reflection of the wave. This leads to the elimination of any passbands in the frequency range up to 2.9 kHz and to the appearance of the low frequency gap (see Methods section for further details).…”

“…Particularly, the first resonance triplet is now replaced by a pass band between 2.9 kHz and 3.5 kHz, shifting the lower edge of the first band gap from 2 kHz to 3.5 kHz. This shift reveals the existence of an extended band gap below the first passband that goes down to the infrasounds, which is related to the periodically arranged soft scatterers emerging by opening the peripheral holes 53,54 . Moreover, the appearance of the passband with the fivefold resonant feature predicted by the simulation between 14 kHz and 19 kHz is validated by the measurement.…”

“…Sound hard boundaries impose zero acceleration on the normal component of the fluid (air) at the position of the holes, which describes the case where the holes are blocked and do not directly communicate with the ambient air. For the case of open holes where there is a direct connection between the air conduits of the structure and the ambient air, it is known that the pressure at the position of the holes goes to zero 53,54 . This results to strong reflection of the propagating pressure wave in the low frequencies, which is known to lead to the formation of a low-frequency stopband, as the one observed in the experiments of the cylindrical structure with open holes.…”

“…This results to strong reflection of the propagating pressure wave in the low frequencies, which is known to lead to the formation of a low-frequency stopband, as the one observed in the experiments of the cylindrical structure with open holes. As know from previous works 53,54 , such a scenario is precisely modeled by sound soft boundaries, which impose zero pressure at the position of the holes. Finally, along the X direction Bloch-Floquet periodic boundary conditions were used.…”