# Design and Manufacturing of the Multi-Layered Metamaterial Plate with Interfacial Crack-like Voids and Experimental-Theoretical Study of the Guided Wave Propagation

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## Abstract

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## 1. Introduction

## 2. Design, Manufacturing and Experimental Setup

#### 2.1. Design

#### 2.2. AMM Manufacturing

#### 2.3. Experimental Setup

## 3. Simulation

## 4. Analysis

## 5. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Photographs of AMM specimens without voids (

**a**), with central voids (

**b**,

**c**) and with edge voids (

**d**,

**e**).

**Figure 4.**The real (

**a**) and imaginary parts (

**b**) of the wavenumbers of propagating symmetric and antisymmetric GWs propagating in AMM without voids.

**Figure 5.**The real (

**a**) and imaginary (

**b**) parts of the wavenumbers of propagating symmetric and antisymmetric GWs propagating in AMM with central voids.

**Figure 6.**The real (

**a**) and imaginary (

**b**) parts of the wavenumbers of propagating GWs propagating in AMM with edge voids.

**Figure 7.**Experimental (

**a**) and theoretical (

**b**) and transmission coefficients ${\eta}^{+}\left(f\right)$ and ${\gamma}^{+}\left(f\right)$, and the corresponding band-gaps for AMMs without voids.

**Figure 8.**Experimental (

**a**) and theoretical (

**b**) and transmission coefficients ${\eta}^{+}\left(f\right)$ and ${\gamma}^{+}\left(f\right)$, and the corresponding band-gaps for AMMs with central voids.

**Figure 9.**Experimental (

**a**) and theoretical (

**b**) and transmission coefficients ${\eta}^{+}\left(f\right)$ and ${\gamma}^{+}\left(f\right)$, and the corresponding band-gaps for AMMs with edge voids.

**Figure 10.**The measured signals $s\left(t\right)$ and its transmission spectra ${\eta}^{+}\left(f\right)$ for four specimens in the case of Hann-windowed input with ${f}_{0}=75$ kHz: bulk ABS, layered AMM without voids, layered AMM with central voids, layered AMM with edge voids.

Material | Elastic Constants | Piezoelectric Constants [${\mathbf{C}/\mathbf{m}}^{2}$] | Dielectric Constants ${10}^{-9}$ [$\mathbf{F}/\mathbf{m}$] | Density [${\mathbf{kg}/\mathbf{m}}^{3}$] |
---|---|---|---|---|

PLA | $E=4.4$ GPa | — | — | 1183 |

$\nu =0.3$ | ||||

ABS | $E=1.5$ GPa | — | — | 983 |

$\nu =0.4$ | ||||

PIC 155 | ${C}_{1111}=120$ GPa | ${e}_{211}=-7.24$ | ${\epsilon}_{11}=9.12$ | 7800 |

${C}_{1112}=67.3$ GPa | ${e}_{212}=13.77$ | ${\epsilon}_{22}=7.55$ | ||

${C}_{2222}=94.4$ GPa | ${e}_{112}=11.91$ | |||

${C}_{1212}=22.3$ GPa |

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## Share and Cite

**MDPI and ACS Style**

Golub, M.V.; Moroz, I.A.; Wang, Y.; Khanazaryan, A.D.; Kanishchev, K.K.; Okoneshnikova, E.A.; Shpak, A.N.; Mareev, S.A.; Zhang, C.
Design and Manufacturing of the Multi-Layered Metamaterial Plate with Interfacial Crack-like Voids and Experimental-Theoretical Study of the Guided Wave Propagation. *Acoustics* **2023**, *5*, 122-135.
https://doi.org/10.3390/acoustics5010008

**AMA Style**

Golub MV, Moroz IA, Wang Y, Khanazaryan AD, Kanishchev KK, Okoneshnikova EA, Shpak AN, Mareev SA, Zhang C.
Design and Manufacturing of the Multi-Layered Metamaterial Plate with Interfacial Crack-like Voids and Experimental-Theoretical Study of the Guided Wave Propagation. *Acoustics*. 2023; 5(1):122-135.
https://doi.org/10.3390/acoustics5010008

**Chicago/Turabian Style**

Golub, Mikhail V., Ilya A. Moroz, Yanzheng Wang, Artur D. Khanazaryan, Kirill K. Kanishchev, Evgenia A. Okoneshnikova, Alisa N. Shpak, Semyon A. Mareev, and Chuanzeng Zhang.
2023. "Design and Manufacturing of the Multi-Layered Metamaterial Plate with Interfacial Crack-like Voids and Experimental-Theoretical Study of the Guided Wave Propagation" *Acoustics* 5, no. 1: 122-135.
https://doi.org/10.3390/acoustics5010008