# 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

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**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 |

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**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