Design of Acoustic Meta-surfaces for Underwater Stealth in Low Frequency Ranges

doi:10.21203/rs.3.rs-3470346/v1

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Design of Acoustic Meta-surfaces for Underwater Stealth in Low Frequency Ranges

https://doi.org/10.21203/rs.3.rs-3470346/v1

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published 20 Feb, 2024

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In this study, it is aimed to protect underwater vehicles against active sonar systems by anechoic metamaterial coating. A mixture of matrix material with close acoustic impedance to water, resistivity to hydrostatic pressure, suitability for the marine environment, and high material loss factor are selected. At low frequencies, the inclusions in different shapes and sizes are added to the matrix material. Since solid inclusions will increase the density considerably, air cavities are preferred as inclusions. More attention is paid to low frequency absorption, especially below 1 kHz, because of advancing sonar technology. The acoustic performance of the designed models is compared in three frequency range: low (0–3 kHz), middle (3–6 kHz), and high (6–10 kHz). The designed models are constructed by considering hydrostatic pressure; hence, volume of air cavities is tried to decrease while absorption performance is aimed to increase. Therefore, a conical air cavity is optimized by chancing its dimensions and location. Also, novel approaches, gong shape air cavity, and sandglass air cavities are introduced. The results show that, not only cavity shape, but also its location and dimensions are highly influential on absorption performance. High volume air cavities increase the absorption performance at the low frequency range, but they are not effective at high frequencies. The gong shape, and sandglass air cavities shows broadband absorption, also, gong shape air cavity volume is less than literature models. Thus, its usability increases at deep waters. The results of this study provide novel underwater meta surfaces for various applications.

Underwater

Acoustic

Meta-surface

Stealth

Low frequency

Metamaterials are novel artificial structures which show extraordinary features that not found in nature. The research about metamaterials began in optics and electrodynamics fields in the 1990s. The publications in the 2000s [1, 2] could be considered as first studies in the acoustic field. Acoustic metamaterials (AM) have been widely studying for a long time, and application areas are expanding. Acoustic absorption materials were improved to reduce mechanical sounds especially arising from aircrafts and cars up to the 20th century. On the other hand, acoustic science finds novel application areas such as underwater, structural acoustics, automotive, and aviation [3–7]. The first anechoic structures could be considered as German submarines rubber coatings during World War II [8].

Designing novel acoustic absorption structures accelerate with the technological advance in the field of sonar technology. Nowadays, acoustic absorption materials have been researched widely in many contents [9, 10]. Especially, studies in acoustic metamaterials are focused on underwater applications, most of them aim to obtain high acoustic absorption in wide frequency range. However, high absorption is shown only near zone of locally resonant frequencies in a narrowband. This problem could be solved by using layered structure. One of each layer has a unique resonant frequency. Hence, the complete material has different several resonant frequencies. By this way, acoustic absorption performance could be enhanced. Also, by adding air cavities and metal powders, acoustic performance could be improved.

On the other hand, the probability of a fiber-reinforced structure being visible to the sonar is very low. Therefore, engineers who want to turn gigantic submarines into ghosts prefer plastic materials, rubber-like materials, or other special surface coatings. Thus, they prevent the reflection of signals and ensures that they are dispersed in all directions. For underwater acoustic absorption, polymers have been a traditional material. Except its high damping properties and close acoustic impedance to water, they have high resistance to water, corrosion, and abrasion, also, high thermal and electrical insulation [11]. Polymers are effective absorption materials with a certain frequency level. Moreover, broadband acoustic absorption could not be achieved yet by these novel materials especially below 100 Hz [12]. To obtain high acoustic absorption at low frequencies, mostly used approaches contain air cavities [13], metal filler [14] and polymers [15].

Gao et al. [14] designed a metamaterial which consist of conical air cavity, metal filler, and backing steel. They aimed to obtain high acoustic absorption at low frequencies. They selected the matrix material as viscoelastic rubber because of its high damping properties. Moreover, metal filler enhances the longitudinal to shear wave transformations. The conical air cavity increases the acoustic absorption performance of metamaterial, especially, at low frequencies. They done the analysis as 2D and 3D. Also, to verify the FEA model, the transfer matrix method is applied to the metamaterial. Wang et al. [16] proposed an underwater metamaterial layer which consist of several steel scatters and rubber as soft matrix material. The dimensions of scatters are set as parameters and several parametric studies are done to reach high acoustic absorption performance. Also, effect of adding a metal backing to the metamaterial is investigated. Their results show that increasing number of scatters enhances the sound absorption in several frequency ranges. Yang et al. [17] proposed a novel hybrid metastructure design for underwater acoustic absorption which consist of air cavities and locally resonant metastrucure. They proposed that the absorption performance of air embedded rubber with steel backing could be improved by the locally resonant metastrucure. Their results show that locally resonant scatterers cause wave attenuation, inertial loss, and impedance matching with water. The combination of air cavities which are efficient at high frequencies, and locally resonant scatters which efficient at low frequencies, provide broadband absorption performance. Jin et al. [18] proposed a novel underwater acoustic metamaterial which consist of air cavities and periodic multi-resonator which embedded in sound insulation and absorption layer, respectively. To optimize acoustic performance of slab, interior geometries of layers are arranged, finite element method is utilized to obtain the absorption performance of slab. Firstly, they introduced two different combinations. The difference between of these is location of flat steel plate both models consist of epoxy, steel, and soft rubber. The cylindrical form steel plates which surrounded by soft rubber behave as different resonators. Therefore, it is expected to behave like a multi-resonator. Meng et al. [19] designed an anechoic slab based upon layers of locally resonant acoustic metamaterial (LRAM). They applied genetic algorithm to optimize underwater acoustic absorption of LRAM. They determined that, layers of slab oscillate independently depending own resonant frequency. They determined that, each layer of anechoic slab oscillate depending on resonant frequency, hence, proposed that independent oscillate modes occurs. Their experimental and theoretical results indicates that various type of scatterers with different resonances enhance acoustic absorption characteristics in wide frequency range. They determined that some parameters such as thickness of layers, lattice constants, and shape of scatterers are vital to optimization process of underwater anechoic layers. Wang et al. [20] designed a metastructure which consist of one and double microperforated panels with backing cavities (MPPB). They suggest that it provide high underwater acoustic absorption in wide frequency range, especially, at low frequencies. Adding one more MPPB to the structure increases the number of absorption peaks at higher frequencies. However, at low frequencies, while the number of MPPB are increasing, absorption performance of the structure is nearly unchanged.

In this study, to pretend underwater vehicles against active sonar systems, an acoustic metamaterial is designed. Firstly, a matrix material is chosen that host the internal geometry. After, several air cavities with different shape, size, and location are added the matrix material. The significant factors are determined to be done parametric studies and optimization process. The finite element analyses are done as 3D via COMSOL Multiphysics 6.1 acoustic module.

Acoustic coatings could be fitted different parts of submarine hull such as bridge fin, pressure hull, and bridge casing according to needs. Also, there are several non-acoustic needs in naval architecture while fitting acoustic coating. They could be listed as, limited coating thickness (generally a few centimeters), density, and static compressibility, convenient thermal conductivity, resistance to environmental conditions, availability for gluing process, and fire resistance. Designed structure must be responds these requirements.

2.1 Underwater Acoustic Absorption Mechanism

Polymers show high acoustic absorption performance due to their damping properties, and close acoustic impedance to water. Characteristic specific impedances of some materials are shown in Table 1. Moreover, to enhance the acoustic performance of polymers, matrix materials, air cavities are quite helpful, especially at low frequencies. In polymers, incident wave acoustic energy is converted to heat, and vibration, hence, the energy is dissipated.

Table 1

Some materials with characteristic specific acoustic impedances [21]
Materials	Speed of sound (m/s)	Density (kg/m³)	Impedance (Rayl)
Air	340	1.23	418
Water	1490	1053	1.56 x 10⁶
Aluminum	6420	2690	1.73 x 10⁷
PDMS	1119	969	1.08 x 10⁶
Steel	5950	7860	4.64 x 10⁷
Epoxy	2490	1180	2.95 x 10⁶
PU	1040	1528	1.59 x 10⁶
Ecoflex	989	1070	1.06 x 10⁶

The loss factor is defined as the ratio of imaginary part of phase angle to real part of phase angle [22]. Increases loss factor result of high acoustic sound absorption in water domain. Table 2 shows the loss factors comparison with some materials which using underwater acoustic applications and other materials. Adding inclusions to underwater metamaterial, introduces additional mechanisms for underwater acoustic absorption such as friction, resonance, and wave mode conversion. Inclusions which embedded to matrix material have own natural frequencies, hence, as incident waves get closer to their natural frequency, metamaterial tend to resonance. Therefore, absorption peaks are shown with resonances.

Table 2

Loss factors of some materials [23–25]
Materials	Loss factor
PDMS	\(\approx\) 0.15
Epoxy	\(\approx\)0.039
Steel	0.2\(\sim\) 3 x 10⁻⁴
Aluminum	0.3 \(\sim\)10 x 10⁻⁵
PU	\(\approx\)0.05–0.15

While designing the anechoic coating, studies in literature are based on [14, 26] and marine requests are considered such as density, and water resistivity. Also, several dimensional concerns are examined in terms of submarine sailing. After that, the matrix material which hosts the internal air cavity are chosen as polyurethane, a kind of polymer due to its high damping features [27]. Frequently used coating materials are shown in Table 3.

Table 3

Materials classes of country-based submarines [28, 29]
Country	Acoustic Coating Substrates
Germany	Composite rubber
United States	Polyurethane, glass fiber, butyl rubber
Russia	Styrene-butadiene rubber, polybutadiene rubber, rubber ceramics
France	Polyurethane, polysulfide rubber
United Kingdom	Polyurethane
Japan	Neoprene
China	Styrene-butadiene rubber, polyurethane

The coating consists of unit cells. The external shape of the acoustic coating unit cell is designed as hexagon, and it shown in Fig. 2(a). The hexagonal unit cells could be united without interior gaps. The bottom hexagon and the top hexagons represent the backing steel and water domain, respectively. The mid hexagon is the matrix material PU. The backing steel, and water domain thickness are set as 10 mm. The air cavities are placed in the PU (mid hexagon). The width of the one side of hexagon is set as 20 mm. Therefore, width of one unit cell is 40 mm. Technical drawing of one of the designed models is shown in Fig. 2(b). The dimensions are used as same representation in other models. The analyzes is done by using the Bloch period boundary to three symmetric boundaries of hexagonal unit cell [14]. By this way, the computational time is reduced.

The distance between upper surface of first cavity and lower surface of water domain is represented as h2, and the distance from upper surface of second cavity and lower surface of water domain is represented as h3. The top and bottom radius of conical cavity are represented as r1, and r2, respectively, and h1 represent the length of conical cavity. The thickness of water domain and backing steel are represented as h_water, and h_steel, respectively. Both are set as 10 mm in all models. The width of one unit cell is 40 mm, a represents the half of the width of 20 mm. The thickness of matrix material is represented as h_matrix, and it is set as 30 mm in all models. The gong shape air cavity is obtained from the literature [30] and all dimensions are shown in Table 4.

Table 4

Dimensions of the gong
Variable	H₁ (m)	H₂ (m)	D₁ (m)	D₂ (m)	t (m)	\(\varvec{\theta }\)
Value	0.03	0.0145	0.0615	0.1125	0.002	15.87^o

There are several parameters which affect the absorption performance of coating such as thickness of matrix material, form, dimensions, and location of air cavity. Firstly, in optimization section each parameter is examined separately. After determined the optimum value of each parameter, all parameters are examined together. So, the effect of each parameter on each other could be seen. Recently, absorber structure design met two concepts: soft coating and gradient medium [4]. The reflection coefficient of absorber tends to decrease with these two conditions. Soft coating is fulfilled by using PU and gradient mediums are used in the matrix material. After the material selection of matrix material is done, geometric conditions of cavity are examined. Air cavity could be in the cylindrical form; thus, absorption performance of pure PU could be enhanced. However, gradient condition is not satisfied with this form, and the absorption performance is limited. To obtain high absorption, cylindrical form is transformed into conical cavity form. The effect of the dimensions of conical air cavity (top and bottom radius and thickness) and location of it, are analyzed. Firstly, the model which consist of pure PU with 30 mm thickness as matrix material and backing steel is analyzed. Figure 2(a) shows the model and acoustic performance of this model.

Moreover, a conical air cavity with 14 mm long with 1- and 15-mm top and bottom radius, respectively are added to matrix material. The length and bottom radius of the cone kept constant, and the top radius of cone is set as 1, 4, 7, and 10 mm. The location of the top of cone is below 1 mm the water domain. The air domains are shown as blue. The acoustic performance of these parameters is shown in Fig. 2(b). Also, the bottom radius of conical air cavity is considered as a significant parameter in terms of acoustic performance. Therefore, a parametric study are done which based on the bottom radius. The lengt, location and top radius of the cone are kept constant, and bottom radius is set as 5, 10, 15, and 18 mm. The results of parametric study is shown in Fig. 2(c). After, the the top and bottom radius of conical air cavity kept constant, and length of cavity is set as 6,10, 14, and 18 mm. The results of parametric study are shown in Fig. 2(d).

The location of air cavity is significant in terms of impedance matcing between the coating and water domain. Therefore, a parametric study based on the location of air cavity are done. The top and bottom radius of conical cavity is 1 and 15 mm, respectively in this analysis. The length of the cavity is 14 mm. The distance between surface of coating and the top of conical cavity is set as 1, 5, 9, and 13 mm. The result are shown in Fig. 3(a). After, each parameter is examined separately, top, and bottom radius of conical air cavity are examined together. The results are shown in Fig. 3(b). Optimization studies are also carried out by reducing the dimensions of conical air cavity. Firstly, all the dimensions of the cavity reduced by 20%. So, top, and bottom radius are set as 0.2 and 3 mm, respectively. The length of the cavity is set as 2.8 mm, and the location of the cavity is kept constanst, 1mm below from the upper surface of coating. The results are shown as Fig. 3(c). Also, the optimization of reduced conical cavity are done with parametric study. The reduced model are set as 20%, 50%, 80% and 100% of top and bottom radius 1 and 15 mm, respectively. The length of cavity is set as 2.8 mm. The results are shown in Fig. 3(d) The location of cavity is kept constanst, 1 mm below the upper surface of the coating.

Also, an array designed is arranged as array with 1mm gap horizontally and vertically. To obtain conical array, the model arranged conically in both interior and exterior geometry. The result is shown in Fig. 4(a). A novel approach, which proposed in this study is adding a tradational gong geometry as air cavity to matrix material. The model dimensions is taken from the literature [30]. It is expected that the incident sound wave energy transform into vibration, and heat energy thanks to gong air cavity. The technical drawing of the gong is shown in Fig. 1. In this study, width of the coating is 40mm, hence, the tradational gong model not directly applicable to matrix material. Therefore, all of the dimensions of gong are offset according to width of the model which proposed in this study (40 mm).

Consequently, the literature model with 112.5 mm width reduced to 15 mm with dimension of reduction ratio of 0.133, at the same time, all other dimensions are reduced according to the certain ratio. Also, a parametric study which examine the location of the gong air cavity is done. In this analysis the distance between upper surface of gong and upper surface of coating is set as a parameter. Figure 4(b) shows the model and parametric study results of gong air cavity. Moreover, the length of the gong must be reduced because of the model width is 40 mm. However, the thickness of gong could be increased. So, the thickness of gong is set as 2 mm, and distance between the upper surface of gong and upper surface of coating is set as a parameter (h3). Figure 4(c) shows the model and results of parametric study. Effect of conical air cavity on acoustic performance is observed. Therefore, it is aimed to enhance its performance by designing novel gradient cavity. Sandglass model is firstly introduced. The model is arranged as arrays no gap in vertically, and 1mm gap horizontally. Moreover, a parametric study is done to determine effect of number of sandglasses. Firstly, 25 sandglasses which designed as shown in Fig. 10.13(b). After, 25, 22, 18, 13 sandglasses models are analyzed. The acoustic performance of the models is shown in Fig. 4(d).

The parametric studies which based on conical air cavity dimensions and location is examined with/without gong shape air cavity. To observe effect of gong, conical air cavity with r1 = 1 mm, and r2 = 15 mm, are examined with/without gong shape air cavity (h3 = 22 mm) and shown in Fig. 6(a). For bottom radius, r2 = 5 mm is selected, and results are shown in Fig. 6(b) For cavity length, h1 = 6 mm is selected, and results are shown in Fig. 6(c). For combined parametric study based on top-bottom radius the critical values are selected as r1 = 7 mm, and r2 = 15 mm, and results are shown in Fig. 6(d).

Acoustic metamaterials have been researched for a few decades, but most of these studies are related to air borne acoustic. Underwater acoustic metamaterials are not common as much as air borne. Nevertheless, with progressing naval technologies and their critical role in military, water borne acoustic gains a great importance. While the underwater acoustic studies tend to military field, sonar technology has advanced. To take precautions against advanced sonar systems, underwater acoustic metamaterial would be the first choice. However, there are still several issues that must be overcome for totally protecting from sonar systems. Firstly, absorption at low frequencies is a significant problem. Furthermore, metamaterial coating must be light, short, and resistant to hydrostatic pressure, and compatible with the marine environment. Also, its absorption performance should not be limited for specific frequencies, it should provide broadband acoustic absorption.

In this study, firstly, the literature is examined and with obtained data, a default model which consist of a matrix material (PU), steel backing (HY-80), and conical air cavity, is constructed. After, each dimension data is set as a parameter, and several parametric studies have been done. The results shows that, each dimension of conical air cavity is a significant parameter (r1,r2,h1,h2). Also, the different combinations of these parameters affect the absorption performance significantly. Generally, at low frequency range, acoustic performance is strongly related to air volume, increasing air volume, improves the absorption performance. Nevertheless, at middle, and high frequency ranges, the situation is exactly the opposite. The location of air cavity is other significant parameter, and it is seen that, increasing distance between upper surface of cavity, and lower surface of water (h2), improves absorption performances at middle, and high frequency ranges. But in low frequency range, these are opposite to each other.

Moreover, two novel approaches which proposed in this study, are introduced to the matrix material. The gong shape is known with its strong vibration feature. By changing its material from copper to air, and reducing its dimensions by a reduction coefficient, a gong shape air cavity is constructed. Its location is set as a parameter, and effect of location is examined. It is seen that, while the distance between upper surface of gong and lower surface of water medium (h3) increases, absorption performance of gong increases at middle and high frequency ranges. However, at low frequency range, the distance must be decreased to obtain high absorption performance. Also, effect of adding gong shape air cavity on other models is examined, and the results shows that, it increases the absorption performance of low volume air cavities. Nevertheless, when the air cavity volume is large enough, its effect is slight. Since anechoic coatings must be used in deep waters, hydrostatic pressure is a significant factor. Hence, air volume must be reduced as much as possible, the gong shape air cavity volume is less than other shapes. This situation is increasing its usability.

The authors have no relevant financial or non-financial interests to disclose.

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Journal Publication

published 20 Feb, 2024

Read the published version in Journal of the Brazilian Society of Mechanical Sciences and Engineering →

Reviewers agreed at journal
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28 Oct, 2023
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You are reading this latest preprint version

Design of Acoustic Meta-surfaces for Underwater Stealth in Low Frequency Ranges

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Journal Publication

Version 1

Abstract

Figures

1. Introduction

2. Materials and Method

2.1 Underwater Acoustic Absorption Mechanism

2. Design and Optimization

3. Results and Discussion

4. Conclusion

Declarations

References

Status:

Journal Publication

Version 1