Numerical investigation of microstructure effect on acoustic properties of underwater anechoic coatings

 Journal of Science and Technique - N.203 (11-2019) - Le Quy Don Technical University 
 NUMERICAL INVESTIGATION OF MICROSTRUCTURE 
 EFFECT ON ACOUSTIC PROPERTIES OF UNDERWATER 
 ANECHOIC COATINGS 
 Trinh Van Hai1*, Nguyen Van Tap2 
 1Le Quy Don Technical University 
 2Military Institute of Mechanical Engineering 
 Abstract 
 This paper presents a simulation-based model for predicting the acoustic properties of 
 underwater anechoic structures with its main layer made of viscoelastic sound absorbing 
 materials including air-filled cavities. Some preliminary numerical results are first 
 compared with the published analytical and experimental data to validate the proposed 
 modeling. Then, a developed design of anechoic using two arrays of air-filled bubbles is 
 considered. It is observed from the investigation results that the new coating shows an 
 interesting sound absorbing performance (i.e., absorbing > 80% incident energy in a large 
 frequency range 25 MHz) compared with the original one having a single air cavity array. 
 The developed structure allows broadening and tailoring their acoustic performance (peak 
 frequency and averaging level) by tuning some microstructural parameters of the air-filled 
 cavity (shape and size) and its distribution (location and fraction). 
 Keywords: Air-filled cavity; acoustic property; anechoic coating; resonant sound absorber. 
1. Introduction 
 The high-quality acoustic stealth coatings are a complicated multi-scale and multi-
component structure, by considering their microstructure, these anechoic structures can 
be categorized into three main types: air-filled cavity, multi-layer composite, pressure-
resisting [1]. In such layered configurations, there are two types of resonance 
mechanisms which are due to either the radial motion of the hole wall or the drum-like 
oscillations of the cover layer [2]. Additionally, the developed structure allows us to 
broaden and tailor its acoustic performance by tuning some geometrical parameters of 
the air bubble distribution. It can be stated that macroscopic acoustic properties are 
highly dependent on the local microstructural features of each individual layer as well 
as the layer configuration [3]. 
 Different approaches have been proposed in the literature to characterize the link 
between the microstructural parameter of anechoic structures and their macroscopic 
acoustic performance: analytical [4-7], numerical [8-11], and experimental methods 
* Email: hai.tv@lqdtu.edu.vn 
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Journal of Science and Technique - N.203 (11-2019) - Le Quy Don Technical University 
[6, 12, 13]. Various analytical studies addressing scattering from gratings and resonant 
sound absorbers exist: transfer matrix method [14], effective medium model [15, 16], 
and cavity resonances mode [17, 18]. However, these analytical models often make 
simplifications on the displacement field and geometry, thereby imposing limitations on 
the type of problem to be solved. On the contrary, the numerical approach such as the 
finite element method (FEM) is more flexible in dealing with complex structures which 
allows analyzing harmonic wave propagation in viscoelastic gratings with periodic or 
random distributions with single- or multi-layer structures. 
 As a survey introduced in [1], Russian designs enable to lower the noise level of 
Akula and Sierraz class submarines by 10~20 dB by anechoic coating using modified 
rubber. Britain technology has used polyurethane as anechoic material, lowering 
conventional submarine noise to 90 dB and meeting the qualifications of silent 
submarines. Furthermore, in US submarines, the double-layer anechoic structure 
composed of polyurethane and glass fibers can decrease noise by up to 40 dB and the 
radiated noise level of nuclear-powered submarines to less than 120 dB, approximately 
the ocean noise level (for more detailed about design and construction of US and Soviet 
submarines, see [19]). 
 The remaining part of the paper is organized as follows. In Sec. 2, we first briefly 
introduce the theoretical background of acoustic aspects of wave propagation and the 
definitions of several acoustic properties used for characterizing sound absorbing 
structures. Then, we present a numerical framework at a relevant scale to implement the 
acoustical model of a multi-layer anechoic coating. Sec. 3 provides an example 
validation together an extended investigation about acoustical behavior of air-filled 
cavity anechoic structure with a single-cavity array in order to demonstrate the 
verification of the proposed numerical framework. In Sec. 4, a developed anechoic 
configuration and an analysis on its acoustical potential performance are proposed. 
Finally, some concluding remarks are given. 
2. Theoretical formulation and numerical framework 
2.1. Governing equations for structure-acoustic analysis 
 The structure-acoustic problem is sketched sche ... sponding surfaces. It can be noted that each unknown 
coefficient requires one nodal pressure value. Thus, the anechoic performance of an 
acoustic sound absorbing medium is defined by the sound reflection (R), transmission 
(T) and absorption coefficients ( ) as [9, 23, 26]: 
 2 2 2 2
 RRTTRT mn,  mn , and 1 . (10) 
 2 2
 kmn 0 k mn 0
3. Verification and comments on single-cavity configuration 
3.1. Verification of the developed FEM procedure 
 Fig. 4. Comparison between the proposed numerical results and analytical model and 
 experimental data proposed in [12]: the reflectance (top, left), transmittance (top, right), and 
 absorption (bottom) coefficients. The results correspond to a case of Lx = 50 m. 
 In this validation step, the obtained numerical results are compared with the 
available data proposed somewhere in the literature. Here, to verify our FEM work, the 
analytical models and measurement data proposed by V. Leroy et al. in [12] are used. 
The acoustical model of anechoic tile are structured with a soft elastic layer within an 
air cavity array and backing by a steel layer. A detailed configuration of the absorbing 
layer is drawn in Fig. 3a. In this sample, the elastic material layer has a thickness of 
Lz 230 m and cylindrical cavities of diameter D 24 µm and height H 12 µm. 
The Young’s modulus, density, and Poisson’s ratio of the steel plate are 2.16 1011 Pa, 
7800 kg/m3, and 0.3, respectively. As shown in Fig. 4, the comparison between the 
proposed numerical results and analytical model and experimental gives a good 
agreement which validates the finite element modeling procedure. 
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3.2. Tuning the fraction of air cavity 
 Fig. 5. Acoustic performance of anechoic tiles with tuning air fraction. The results from top to 
 bottom are respectively for the reflectance, transmittance and absorption coefficients 
 In this section, we present how the distribution density of air cavity affects the 
acoustical behavior of the single air array anechoic. As demonstrated in [12], for the 
steel block alone, 88% of the energy is reflected and the remaining energy fraction 
(12%) is transmitted. Fig. 5 presents the energy proportions that are reflected (top), 
transmitted (middle) and absorbed (bottom) for various configurations of Lx (50 µm, 
75 µm, 100 µm, 125 µm, and 150 µm). As expected, when the block is covered by the 
Lx = 120 µm meta-screen, the reflectance is drastically reduced (line with markers in 
Fig. 6 (top)), especially between 1.3 and 2.8 MHz where less than 6% of the incident 
energy is reflected, with the measured reflectance dropping nearly to zero at 1.3 MHz 
and 2.8 MHz. In terms of absorption (Fig. 6 (bottom)), all anechoic configurations 
manage to dissipate a significant part of the energy over a broad frequency range. 
Interestingly, the configuration with Lx = 100 µm (markers in Fig. 5 (bottom)) provides 
a very high absorption over the entire 1.32.8 MHz range, throughout which more than 
91% of the incoming energy is dissipated, with a maximum absorbance of nearly 100% 
at 1.3 MHz and 2.8 MHz. The obtained trends here are in very good agreement with the 
suggested results illustrated in [12] for cases of Lx = 50 µm and Lx = 120 µm. 
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Journal of Science and Technique - N.203 (11-2019) - Le Quy Don Technical University 
4. Results and discussion on double-cavity configuration 
4.1. Design configuration 
 Fig. 6. Configuration of viscoelastic absorbing layer with double void array. 
 In this section, acoustical properties of anechoic tile with an absorbing panel of 
two lattice layers of air cylindrical cavities is investigated (Fig. 7). Compared to the 
original one, the geometric properties of the additional layer of voids are also introduced 
by the d h cylindrical cavities with their distances Lx and Ly in the x and y-direction, 
respectively, at the location l within the elastic layer. 
 The potential acoustical performance of this developed coating structure is 
demonstrated in the following part by tuning several structural parameters. Here, we 
focus only on the reflection and absorption property, for simplicity, the added air cavity 
is identical with the original one in terms of shape (d = D, h = H) and distributions 
(Lx and Ly). The effect of the configuration difference between two air layers on its 
acoustical properties will be characterized in the forthcoming works. 
4.2. Cylindrical cavity size effect (D) 
 Fig. 7 shows the performance of anechoic tile based on air cavity having 
H = 13 m, Lx = Ly = 100 m, l = Lx/4, and varying its diameter D from 10 m to 25 m. 
It is observed that by the acoustical behavior of the double air array coating depends 
strongly on the air-filled cavity diameter. The anechoic within small void seems to have 
good acoustical behavior at low frequencies nearly 1.6 MHz (see the shape peak in 
Fig. 7 with more than 96% of the incoming energy is absorbed while remaining less 
than 3% reflected energy). Interestingly, compared with the results demonstrated in 
Fig. 5 with 24-diameter air cavities, the double array configuration (with D = 15 m and 
D = 20 m representing respectively by thin dashed and thick solid line) can provide a 
good acoustical functional factors ( 94.5%) at high frequency range (4  5 MHz). 
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 Journal of Science and Technique - N.203 (11-2019) - Le Quy Don Technical University 
 Fig. 7. Effects of the cylindrical cavity size on acoustical performance of anechoic tiles: 
 reflection (left) and absorption (right). 
4.3. Air cavity density effect (Lx) 
 Fig. 8. Effects of the air cavity distribution on acoustical performance of anechoic tiles: 
 reflection (left) and absorption (right). 
 In order to show the effect of the air-filled cavity density, this section investigates 
anechoic tile based on air cavity having H = 13 m, D = 24 m, l = 100 m, and 
varying cavity distance from 50 m to 125 m. It can be seen from the results from 
Fig. 8 that the length Lx affects both in the level of reflected and absorbed energy and 
the frequency occurring the second shape peak. In detail, the absorption property 
increases monotonically when Lx increases for Lx < 100 m and then decreases 
monotonically when Lx continues to increase above the critical value Lx = 100 m. 
Generally, the air cavity with length around 100 m shows good acoustical performance 
(see the thick solid line). 
4.4. Cavity array distance effect (l) 
 The third parameter of anechoic tile is the distance between two cavity layers 
l (50 m, 100 m, 150 m and 250 m). Here, the remaining parameters are kept as: 
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Journal of Science and Technique - N.203 (11-2019) - Le Quy Don Technical University 
D = 24 m, H = 13 m, and Lx = Ly = 100 m. From the Fig. 9, it is seen that both 
fluctuations of reflection and absorption property are related fully to the air cavity 
distance. Within the distance l ranging from 50 m to 250 m, we enable to tailor the 
number of shape peaks and the fluctuated amplitude of acoustic performance. It should 
finally be noticed that the configuration with l = 150 m provides a good absorption 
(>80% of the incident energy, see the thick solid line) in the frequency range 25 MHz. 
 Fig. 9. Effects of the cavity distance on acoustical performance of anechoic tiles: 
 reflection (left) and absorption (right). 
5. Conclusions 
 In this paper, the simulation-based approach is presented to investigate the link 
between microstructure and acoustic properties of an anechoic structure with periodic 
air cavities. To this regard, the multi-layer anechoic coating is reconstructed, and the 
acoustic-structure model is generated including a cover layer, a viscoelastic absorbing 
panel and the steel layer as the backing. From this, the reflection, absorption, and 
transmission properties of the anechoic coating backing a steel plate are calculated 
numerically. Very good agreements are observed between the present numerical results 
of and an anechoic layer within a single cavity array with the analytical model, 
numerical results, and experimental data from the literature, which validates the 
suggested simulation-based procedure. From investigated results of the developed 
configuration, it is seen that all tuning geometrical parameters of the added air cavity 
affect strongly the acoustical properties. The air cavity size and its density have an 
effect on the level of reflected and absorbed energy, whereas the air cavity distance has 
only effect on the fluctuating behavior. This interesting point shows a good opportunity 
to achieve a desired reflection or absorption properties in an entire frequency range by 
tuning together all three parameters mentioned here and also others fixed (e.g., 
thickness layer L, ratios d/D, h/H). 
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 KHẢO SÁT ẢNH HƯỞNG CỦA CẤU TRÚC VI MÔ ĐẾN ĐẶC TÍNH 
 ÂM CỦA LỚP KHÔNG PHẢN XẠ DƯỚI NƯỚC 
 Tóm tắt: Bài báo này trình bày mô hình dựa trên mô phỏng số để dự đoán tính chất âm 
học của cấu trúc không phản xạ dưới nước với lớp chính được làm bằng vật liệu hấp thụ âm 
có cấu tạo gồm các khoang khí. Một số kết quả số trước tiên được so sánh với kết quả giải 
tích và dữ liệu thực nghiệm đã công bố để kiểm chứng mô hình đề xuất. Sau đó, tiến hành xem 
xét thiết kế mới cấu trúc ngói sử dụng hai lớp khoang khí. Theo kết quả khảo sát nhận được, 
lớp ngói không phản xạ mới cho hiệu quả hấp thụ âm thanh tốt hơn (chẳng hạn hấp thụ hơn 
80% năng lượng sóng tới trên dải tần rộng từ 2 đến 5 MHz) so với cấu hình gốc chỉ có một 
lớp khoang khí duy nhất. Ngoài ra, cấu trúc phát triển cho phép mở rộng và điều chỉnh hiệu 
quả âm (tần số đạt khả năng hấp thụ cao cũng như mức độ hấp thụ trung bình) bằng cách 
điều chỉnh một số thông số hình học (hình dáng và kích thước) và phân bố (vị trí và mật độ) 
của khoang khí. 
 Từ khóa: Khoang khí; đặc tính âm; lớp không phản xạ; hấp thụ âm cộng hưởng. 
 Received: 02/4/2019; Revised: 18/11/2019; Accepted for publication: 22/11/2019 
  
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