# Investigation of Alberich Coating to Optimise Acoustic Stealth of Submarines

^{*}

## Abstract

**:**

## 1. Introduction

^{−1}[6], the mesh sizing, corresponding to the appropriate criteria, is relatively large and requires little computational power.

## 2. Computation Methodology

#### 2.1. Computer Model Setup

^{−1}was used in this model so the element size applied to the anechoic layer was $\frac{325}{3500\times 12}=0.00774\mathrm{m}$, where 3500 Hz is the maximum value of frequency used in the harmonic analysis. In order to decrease the CPU time the element size on the steel backplate was set to the same value. The speed of sound in steel is 5960 ms

^{−1}. Therefore, satisfying a $\frac{\lambda}{12}$ criterion using this wave speed produced elements with length greater than that of the geometry. Therefore, using the same value as the anechoic layer was more applicable while still meeting the criteria.

#### 2.2. Computational Methodology

#### 2.2.1. Cylindrical Cavity Diameter

#### 2.2.2. Anechoic Layer

#### 2.2.3. Steel Backplate

#### 2.2.4. Cavity Length

#### 2.2.5. Spherical Cavity

#### 2.2.6. Optimised Model

## 3. Results

#### 3.1. Cylindrical Cavity Diameter

#### 3.2. Anechoic Layer

#### 3.3. Steel Backplate

#### 3.4. Cavity Length

#### 3.5. Spherical Cavity

#### 3.6. Optimised Model

## 4. Discussion

#### 4.1. Resonance of the Cavity

#### 4.2. Resonance of Anechoic Layer

#### 4.3. Impedance Mismatch

#### 4.4. Stiffness

#### 4.5. Volume Fraction of Air

#### 4.6. Velocity and Pressure

^{−1}, respectively. It is reasonable to suggest that the first absorption peak was due, at least partly, to this increase in velocity.

#### 4.7. Rubber Absorption

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Eggler, D.; Kessissoglou, N. Active acoustic illusions for stealth and subterfuge. Sci. Rep.
**2019**, 9, 13596. [Google Scholar] [CrossRef] [PubMed] - Li, B.; Peng, Z.; Wen, H.; Fan, J.; Song, H. Research on the Optimization Design of Acoustic Stealth Shape of the Underwater Vehicle Head. Acoust. Aust.
**2020**, 48, 39–47. [Google Scholar] [CrossRef] - Tang, J.H. Acoustic propagation characteristics of heteromorphic metamaterials. AIP Adv.
**2018**, 8, 105305. [Google Scholar] - Méresse, P.; Audoly, C.; Croënne, C.; Hladky-Hennion, A.C. Acoustic coatings for maritime systems applications using resonant phenomena. Comptes Rendus Mec.
**2015**, 343, 645–655. [Google Scholar] [CrossRef] - Hladky Hennion, A.-C.; Decarpigny, J.N.A. Analysis of the scattering of a plane acoustic wave by a doubly periodic structure using the finite element method: Application to Alberich anechoic coatings. J. Acoust. Soc. Am.
**1991**, 90, 3356–3367. [Google Scholar] [CrossRef] - Fu, X.; Jin, Z.; Yin, Y.; Liu, B. Sound absorption of a rib-stiffened plate covered by anechoic coatings. J. Acoust. Soc. Am.
**2015**, 137, 1551–1556. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Meng, H.; Wen, J.; Zhao, H.; Lv, L.; Wen, X. Analysis of absorption performances of anechoic layers with steel. J. Acoust. Soc. Am.
**2012**, 132, 69–75. [Google Scholar] [CrossRef] [PubMed] - Easwaran, V.; Munjal, M.L. Analysis of reflection characteristics of a normal incidence plane. J. Acoust. Soc. Am.
**1993**, 93, 1308–1318. [Google Scholar] [CrossRef] - Panigrahi, S.N.; Jog, C.S.; Munjal, M.L. Multi-focus design of underwater noise control linings based on finite element analysis. Appl. Acoust.
**2008**, 69, 1141–1153. [Google Scholar] [CrossRef] - Zhong, J.; Zhao, H.; Yang, H.; Wang, Y.; Yin, J.; Wen, J. Theoretical requirements and inverse design for broadband perfect absorption of low-frequency waterborne sound by ultrathin metasurface. Sci. Rep.
**2019**, 9, 1181. [Google Scholar] [CrossRef] [PubMed] - ANSYS, Inc. Harmonic Acoustic Analysis. 14 December 2020. Available online: https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/v202/en/wb_sim/ds_harmonic_acoustics.html (accessed on 6 September 2021).
- Zhou, F.; Fan, J.; Wang, B.; Peng, Z. Absorption Performance of an Anechoic Layer with a Steel Plate Backing at Oblique Incidence. Acoust. Aust.
**2018**, 46, 217–327. [Google Scholar] [CrossRef] - Britannica. Impedance. 23 January 2021. Available online: https://www.britannica.com/science/sound-physics/Impedance (accessed on 20 October 2021).
- Ketabdari, S.H. Numerical simulation of a viscoelastic sound absorbent coating with a doubly periodic array of cavities. Cogent Eng.
**2018**, 5, 1529721. [Google Scholar]

**Figure 16.**Absorption vs frequency for the optimised model and 26 mm diameter cylindrical cavity model.

**Figure 18.**Total acoustic velocity of Alberich coating with 8 mm diameter cavity before (

**a**) and after (

**b**) 790 Hz, and 26 mm diameter cavity before (

**c**) and after (

**d**) 790 Hz.

**Figure 20.**Alberich structure side by side to mass-spring oscillator. Arrows represent direction of applied planar wave (force).

**Table 1.**Material properties used in impedance calculations [6].

Material Property | Anechoic Layer | Steel Layer |
---|---|---|

Density ($\rho $)/kgm^{−3} | 1100 | 7800 |

Length ($l$)/mm | 50 | 12 |

Wave speed ($c$)/ms^{−1} | 325 | - |

Loss factor ($\eta $). | 0.23 | - |

**Table 2.**Controlled variables for all simulations [10].

Controlled Variable | Anechoic Layer | Steel Layer |
---|---|---|

Young’s Modulus ($E$)/Pa | $3\times {10}^{7}$ | $2.16\times {10}^{11}$ |

Bulk Modulus ($B$)/Pa | $7.78\times {10}^{9}$ | $1.8\times {10}^{11}$ |

Shear Modulus ($G$)/Pa | $4.68\times {10}^{7}$ | $8.31\times {10}^{10}$ |

Poisson’s Ratio ($\nu $) | $0.497$ | $0.3$ |

Parameter | Value |
---|---|

Length_{A}/mm | $40$ |

Length_{S}/mm | 25 |

Cavity Diameter/mm | 26 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Daniels, C.; Perera, N.
Investigation of Alberich Coating to Optimise Acoustic Stealth of Submarines. *Acoustics* **2022**, *4*, 362-381.
https://doi.org/10.3390/acoustics4020022

**AMA Style**

Daniels C, Perera N.
Investigation of Alberich Coating to Optimise Acoustic Stealth of Submarines. *Acoustics*. 2022; 4(2):362-381.
https://doi.org/10.3390/acoustics4020022

**Chicago/Turabian Style**

Daniels, Callum, and Noel Perera.
2022. "Investigation of Alberich Coating to Optimise Acoustic Stealth of Submarines" *Acoustics* 4, no. 2: 362-381.
https://doi.org/10.3390/acoustics4020022