# 3D Printing of Polymeric Multi-Layer Micro-Perforated Panels for Tunable Wideband Sound Absorption

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}laser beam to sinter thermoplastic polymer powders by using each layer. The cross sections of the parts are selectively sintered, while the un-sintered powders are served as supports and are highly recyclable [37]. A wide range of materials can be processed by SLS. One major advantage of SLS over other 3D printing techniques (e.g., Polyjet and SLA) is the exclusion of supporting structures to build complex objects such as hollow and overhang structures [39]. This support-free feature is ideal for fabricating complex hollow structures with multiple layers where conventional methods would require post-fabrication assembly to integrate individual components into multiple layers. The utilization of 3D printing techniques can facilitate the proof of concept of the designed acoustic structures by rapid manufacturing of prototypes [40]. It has great potential to expand for mass manufacturing in acoustic areas.

## 2. Materials and Methods

#### 2.1. Theoretical and Numerical Methods

_{0}and η are the density and viscosity of air, respectively, ω is the angular frequency, Δp is the sound pressure difference between the two ends of the tube, and l is the length of the tube’s unit element. The particle velocity v is obtained analytically and is equal to zero at the tube walls.

_{total}is defined as the ratio of the sound pressure difference to the average velocity.

_{total}is calculated by summing up the acoustic impedance of the panel layer and the air gap. The acoustic impedance of the air gap is calculated by using the equation below.

_{0}is the speed of sound in the air and f is the frequency. The acoustic impedance of the panel is derived by using a panel model that consists of an array of tubes and is expressed by the equation below [1].

^{th}series-connection MPP-cavity layer is given by the equation below.

_{M}(n) and Z

_{C}(n) are the acoustic impedance of the MPP and cavity of the n

^{th}layer, wherein the subscripts M and C represent the initials of the MPP and cavity, respectively. The acoustic impedance Z

_{C}(n) of the n

^{th}cavity is related to the acoustic impedance Z(n + 1) of the (n + 1)

^{th}layer, which is shown below.

^{th}layer Z

_{CS}(n) is the same as Z

_{D}in Equation (3). The calculation of the acoustic impedance of the MPP of the n

^{th}layer Z

_{M}(n) is identical to Z

_{M}in Equation (4).

#### 2.2. Experimental Method

_{1}, and h

_{2}(triple-layer) in Figure 2 could vary from 20 mm to 40 mm to quantify the effects of different h on the effective range of f and the absorption coefficient α. The geometric dimensions are shown in Table 1. All of the structures were manufactured in one batch by an SLS P395 machine (EOS, Krailling, Germany) with a CO

_{2}laser (wavelength: 10.6 µm, laser power: up to 50W). PA12 (PA2200 from EOS GmbH, Krailling, Germany), which is one of the commercial materials with advantages of a high melting flow rate, low melting temperature, low glass transition temperature, and a low degree of crystallization temperature [44], was used as the feedstock. The mechanical properties and viscosity of laser-sintered PA12 are shown in Table 2. The commercial printing parameters for PA12 from EOS P395 system including laser scanning speed of 4000 mm/s, laser power of 40 W, layer thickness of 0.12 mm, and hatching space of 0.3 mm were followed.

## 3. Results and Discussion

#### 3.1. Effect of the Number of Layers

_{0}in the air and the coefficient of the kinematic viscosity of air µ were assumed to be constant in the theory and FEM simulations but could have varied due to the temperature change in experiments. These previously mentioned causes of the discrepancies among the theory, FEM, and experiment results are also valid in the subsequent studies of tuning the absorption frequency ranges and optimizing the structural designs.

#### 3.2. Effect of the Air Gap Distance

#### 3.3. Effect of the Inter-Layer Distance

_{1}increases from 30 mm to 50 mm.

#### 3.4. Structural Optimization for Sound Absorption

_{1}and air gap distance at L = 190 mm is shown in Figure 10. The largest frequency coverage is achieved at h

_{1}= 28.5 mm and D = 19 mm.

_{1}= 28.5 mm, and D = 19 mm, the frequency coverage can reach up to 311.9 (shown in Figure 10), which is the largest among the single-layer and multi-layer structures with L varying from 10 mm to 200 mm.

_{1}= 28.5 mm, h

_{2}= 142.5 mm, and D = 19 mm. With the designed parameters, the sound absorption of the structures for the frequency range of 800–1200 Hz is optimized by the maximization of the frequency coverage, which is the area under the absorption curve. Figure 12 shows the absorption coefficients of the optimized structures by Maa’s theory, FE simulations, and experiments. The frequency coverage of the optimized double-layer MPP by experiment is 308.9, which is 8.3% larger than the theoretical prediction. The frequency coverage of the optimized triple-layer MPP by experiment is 319.3, which is 2.4% larger than the theoretical prediction. In this case, the absorption curve of the double-layer MPP only has one peak, while the absorption curve of the triple-layer MPP has three peaks with large absorption coefficients that indicate effective acoustic absorptions at multiple frequency ranges by the optimized structural design.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The schematic diagram of an MPP, which consists of a thin panel, an air gap, and a rigid wall.

**Figure 4.**The schematic demonstration of the multi-layer MPPs: (

**a**) a double-layer MPP and (

**b**) a triple-layer MPP in the impedance tube.

**Figure 5.**Comparison of the absorption coefficients of the single-layer, double-layer, and triple-layer MPPs obtained by the theoretical predictions, numerical simulations, and experiments.

**Figure 6.**The microscope images of a printed panel: (

**a**) two perforations in imperfect circular shapes and (

**b**) a part of the unsmooth rim with grains.

**Figure 7.**Comparison of absorption coefficients of MPPs with varying air gap distances obtained by the theoretical predictions, numerical simulations, and experiments.

**Figure 8.**Comparison of absorption coefficients of the MPPs with varying inter-layer distances obtained by the theoretical predictions, numerical simulations, and experiments.

**Figure 9.**The frequency coverages of the single-layer and double-layer MPPs at each L varying from 10 mm to 200 mm.

**Figure 11.**The maximum frequency coverage of single-layer, double-layer, and triple-layer MPPs at a different L.

**Figure 12.**Absorption coefficients of optimized MPPs obtained by theoretical predictions, numerical simulations, and experiments: (

**top**) double-layer MPP and (

**bottom**) triple-layer MPP.

Sample Number | Number of Layers | Inter-Layer Distances |
---|---|---|

MPP_1 | 1 | NA |

MPP_2 | 2 | h = 30 mm |

MPP_3 | 2 | h = 40 mm |

MPP_4 | 2 | h = 50 mm |

MPP_5 | 3 | h_{1} = 30 mm, h_{2} = 40 mm |

MPP_6 | 3 | h_{1} = 40 mm, h_{2} = 40 mm |

MPP_7 | 3 | h_{1} = 50 mm, h_{2} = 40 mm |

Tensile Modulus (MPa) | Tensile Strength (MPa) | Toughness (J/mm^{3}) | Elongation at Break (%) | Viscosity (Pa·s) at 200 °C |
---|---|---|---|---|

1291 (±12.1) | 44 (±1.3) | 10.18 (±0.9) | 24 (±0.8) | 2616 (±99) |

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**MDPI and ACS Style**

Yang, W.; Bai, X.; Zhu, W.; Kiran, R.; An, J.; Chua, C.K.; Zhou, K.
3D Printing of Polymeric Multi-Layer Micro-Perforated Panels for Tunable Wideband Sound Absorption. *Polymers* **2020**, *12*, 360.
https://doi.org/10.3390/polym12020360

**AMA Style**

Yang W, Bai X, Zhu W, Kiran R, An J, Chua CK, Zhou K.
3D Printing of Polymeric Multi-Layer Micro-Perforated Panels for Tunable Wideband Sound Absorption. *Polymers*. 2020; 12(2):360.
https://doi.org/10.3390/polym12020360

**Chicago/Turabian Style**

Yang, Wenjing, Xueyu Bai, Wei Zhu, Raj Kiran, Jia An, Chee Kai Chua, and Kun Zhou.
2020. "3D Printing of Polymeric Multi-Layer Micro-Perforated Panels for Tunable Wideband Sound Absorption" *Polymers* 12, no. 2: 360.
https://doi.org/10.3390/polym12020360