Experimental investigation of underwater locally multi-resonant metamaterials under high hydrostatic pressure for low frequency sound absorption
Introduction
In recent years, viscoelastic composites have been widely applied into underwater vehicles or constructions such as underwater anechoic layers for absorbing unwanted sounds or acoustic stealth. According to different sound absorption mechanisms and practical application requirements, various underwater acoustic materials or structures have been investigated and developed [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], i.e. pure polymer composites [11], particle-filled polymer composites [12], cavity-resonant polymer composites containing periodically distributed inner holes [13], [14], woodpiles [15], phononic glass [16] or locally resonant metamaterials [17] et al. Herein, we mainly focus on locally resonant metamaterials for underwater acoustic absorption. The locally resonant metamaterials are typically gratings of dense metallic spheres or cylinders which are coated with soft materials in a host polymer matrix [18]. The soft coating layer and the heavy core (e.g., dense metallic spheres or cylinders) are responsible for the locally resonant phenomenon, which forms scattering resonances. The locally resonant mechanism induces transmission dips or stop bands at low frequencies corresponding to acoustic wavelengths much larger than the dimension of the scatterers or even the spacing between the scatterers. Therefore, the local resonators can have strong reactions when the frequencies of waves are near their natural frequencies; while the bandwidth of the resonance gap remains narrow.
In order to broaden the bandwidth of resonance gaps to achieve broadband sound reflecting or absorbing performance, a variety of methods have been developed [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], i.e. using the local resonators with multi-coaxial cylindrical inclusions [24] or using multilayered locally resonant scatterers [27] et al. Wen et al. [28] studied the effect of the locally resonant mode on underwater sound absorption. Results showed that the localized resonance leads to the absorption peak, and the mode conversion from longitudinal to transverse waves at the second absorption peak is more efficient than that at the first one. Shi et al. [29] studied the effect of the geometric structure of steel plate backing on the sound absorption characteristics. Results showed that the steel plate backing has a significant effect on the sound absorption characteristics of the acoustic metamaterials in the low frequency range. Sharma et al. [31], [32] numerically investigated the acoustic performance of a locally resonant phononic crystal comprising steel cylindrical scatterers arranged periodically in a viscoelastic medium. Results showed that dipole resonance of the cylinders as well as constructive interference between waves scattered by the cylinders and reflected from the steel backing plate were shown to lead to high sound absorption.
In addition, there are also studies on underwater sound absorption using smart materials [33], [34], [35], [36], [37], [38], [39]. Zhang et al. [33] investigated an underwater semi-active composite anechoic coating with periodic subwavelength piezoelectric arrays to broaden the low-frequency absorption bandwidth and improve the absorption coefficient. Change regulations of seven critical parameters on the sound absorption characteristics of the coating were investigated for revealing the multiple energy dissipation mechanisms of the overburden in the whole research frequency range. Jin et al. [38] studied a resonant structure of a hard-core coated by piezoelectric composite materials as an acoustic metamaterial. Results showed that the multi-unit acoustic metamaterial offers the advantages of broadening the double-negativity domain, while the cut-up frequency remains the same as that of the single-unit cell acoustic metamaterial.
However, most of the previous studies focused on theoretically investigating the sound absorbing performance of locally resonant metamaterials under no hydrostatic pressure. There are few experimental researches on underwater locally multi-resonant metamaterials under high hydrostatic pressure. In this research, a new underwater acoustic metamaterial in which every unit cell includes multiple harmonic oscillators is proposed. The effects of high hydrostatic pressure on local resonance mechanism are investigated experimentally. The effects of different practical methods for fabricating the locally multi-resonant metamaterial structure on the underwater sound absorption performance are also investigated. Multiple small bandgaps are superimposed by several local resonance units due to strong coupling and multiple scattering effects among lots of harmonic oscillators. By this way, the proposed acoustic metamaterial can achieve the broadband low-frequency underwater sound absorbing effect under high hydrostatic pressure.
Section snippets
Overview of the proposed underwater acoustic metamaterial
Fig. 1 shows the composition and schematic diagram of unit cell of the proposed acoustic metamaterial. Specifically, the proposed metamaterial is composed of a steel array including 12 small steel cylinders of the same size, a RTV (Room Temperature Vulcanization) silicone rubber cylinder and a viscoelastic polymer cube. The RTV silicon rubber cylinder is located at the center of the viscoelastic polymer matrix as shown in Fig. 1. The steel array is included in the RTV silicon rubber cylinder as
Experiments
For the convenience of the experiments, the host matrix of the viscoelastic polymer is in a shape of a cylinder which meets the experimental requirements of an acoustic standing wave tube. Herein, the underwater sound absorption performance of the proposed acoustic metamaterial is only considered within unit cell. Three experimental samples are fabricated in the research as shown in Fig. 3. The radius of the samples is equal to 59 mm. The experimental sample 0 is a pure viscoelastic polymer
Band structure analysis for the proposed metamaterial
In order to reveal the underlying physical mechanism of the proposed metamaterial, band structure of the proposed metamaterial is calculated by sweeping the reduced Bloch wave vector along the border line of the Brillouin zone depicted on the right of the band structure as shown in Fig. 7. There are 450 branches obtained in the band structure.
Starting with the fourth branch, the remaining 446 branches are approximately flat bands in the investigated frequency range. For a clearer display,
Performance comparison between two fabrication methods
In an actual production process of the RTV silicone rubber cylinder including 12 small steel cylinder cores, it is difficult to cover the 12 steel cores with two-component RTV (Room Temperature Vulcanization) silicone rubber and ensure the accurate three-dimensional position of the steel cylinder array at one time. It is inevitable to use the method of bonding. In order to explore the effect of fabrication methods of the silicone rubber cylinder with 12 steel cores on the sound absorption
Conclusion
In summary, a new underwater locally resonant metamaterial is proposed and fabricated by introducing multi-scatterers into the unit cell for broadband low-frequency underwater sound absorption performance. The underwater sound absorption performance of the proposed acoustic metamaterial is experimentally investigated in an acoustic standing wave tube under different hydrostatic pressure conditions. Results show that the average sound absorption coefficient of the proposed acoustic metamaterial
CRediT authorship contribution statement
Yinghong Gu: Conceptualization, Methodology, Software, Validation. Haibin Zhong: Investigation, Data curation, Validation. Bin Bao: Conceptualization, Supervision, Writing - original draft, Visualization. Quan Wang: Writing - review & editing. Jiuhui Wu: Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
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