# Study of the Sound Absorption Properties of 3D-Printed Open-Porous ABS Material Structures

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Samples Production

_{r}”. This parameter expresses how much cell space is filled with material, and is described by the Equation (1) [23]:

_{S}is the volume of the solid phase and V

_{T}is the total body volume. In this study, three types of lattice structures (Cartesian, Starlit, and Octagonal) were modelled and produced from the plastic material ABSplus-P430 Ivory using the FDM technique. All the samples had a cylindrical shape with an outer diameter of φ29 mm (based on the testing device requirements) and three different lengths (thicknesses), i.e., 10, 20, and 30 mm. The core of every sample was filled with a lattice structure with a volume ratio V

_{r}= 57%, while the thickness of the outside cylindrical shell (fully filled by the material) was 2 mm. All basic cell types were modelled with the outer horizontal, outer vertical, and inner angular beams/struts. The z axis is the building axis, normal to the building platform (plane xy). The volume ratio was controlled by using a strut diameter of 1.4 mm. The structure types and their characteristics are presented in Table 1, while the produced samples are shown in Figure 2.

#### 2.3. Measurement Methodology

#### 2.3.1. Sound Absorption Coefficient

_{I}is propagated from a noise source to a material surface, some of this incident energy is reflected from the surface. The remainder of the incident acoustic energy is absorbed by the tested acoustical material. The material’s ability to damp noise is expressed by the sound absorption coefficient α, which is defined by the following equation [24]:

_{A}represents the absorbed acoustic energy and E

_{R}is the reflected acoustic energy (see Figure 3b). The basic function of sound-absorbing materials is to transform the incident acoustic energy into heat. There are two mechanisms by which the acoustic energy is dissipated: viscous-flow losses and internal friction [25].

#### 2.3.2. Noise Reduction Coefficient

#### 2.3.3. Sound Absorption Properties

_{r}and r

_{i}are the real and imaginary components of the factor r, which is given by

_{12}is the complex acoustic transfer function, H

_{I}is the transfer function for the incident wave, H

_{R}is the transfer function for the reflection wave, k

_{0}is the wave number, and x

_{1}is the distance between the investigated material sample and the microphone M

_{1}(see Figure 3b). The transfer functions are expressed as follows:

_{1}and p

_{2}are the complex sound pressures at the two microphone positions, and x

_{2}is the distance between the investigated material sample and the microphone M

_{2}(see Figure 3b).

## 3. Results and Discussion

#### 3.1. Frequency Dependencies of the Sound Absorption Coefficient

#### 3.1.1. Effect of Structure Type

#### 3.1.2. Effect of Material Thickness

#### 3.1.3. Effect of the Air Gap Size

_{max}

_{1}(corresponding to a quarter-wavelength, i.e., λ/4), the primary sound absorption minima α

_{min}

_{1}(corresponding to a half-wavelength, i.e., λ/2), and the corresponding excitation frequencies f

_{max}

_{1}and f

_{min}

_{1}of the ABS samples whose frequency dependencies of the sound absorption coefficient are depicted in Figure 6.

_{max}

_{1}and f

_{min}

_{1}generally decrease with an increase in the air gap size a. Therefore, it can be concluded that open-porous structures with air gaps are effective for improving sound absorption properties at low excitation frequencies instead of increasing the thickness of the sound absorber, which requires more materials [37].

#### 3.1.4. Effect of Excitation Frequency

_{max}= 0.81 was observed at the frequency f = 5328 Hz (see Figure 6b) for a sample thickness t = 10 mm. The same sample type (with a thickness t = 20 mm) that was directly mounted on the solid wall had the best sound absorption properties (α

_{max}= 0.88) at the frequency f = 2760 Hz (see Figure 4a). Similarly, the sample with a thickness t = 10 mm and the Starlit structure placed at a distance of 50 mm from the solid wall had the greatest ability to absorb sound (α

_{max}= 0.84) at the frequency f = 3648 Hz (see Figure 6b).

#### 3.2. Noise Reduction Coefficient

## 4. Conclusions

_{max}

_{1}≅ 〈2.0; 6.1〉 kHz for the ABS samples mounted directly (without an air gap) on the solid wall of the impedance tube to f

_{max}

_{1}= 〈416; 656〉 Hz for the ABS samples placed at a distance of 100 mm from the wall.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Tested samples: (

**a**) Cartesian structure, (

**b**) Starlit structure, and (

**c**) Octagonal structure.

**Figure 3.**Schematic diagram of the apparatus for measuring the sound absorption coefficient (

**a**) and a schematic of the impedance tube equipment (

**b**). Legend of the abbreviations: a—air gap size; E

_{A}—absorbed acoustic energy; E

_{I}—incident acoustic energy; E

_{R}—reflected acoustic energy; M

_{1}, M

_{2}—measuring microphones; t—sample thickness; W—solid wall; x

_{1}, x

_{2}—microphone distances from the tested ABS sample.

**Figure 4.**Effect of the 3D-printed ABS material structure on the frequency dependencies of the sound absorption coefficient; (

**a**) sample thickness t = 20 mm, air gap size a = 0 mm, (

**b**) sample thickness t = 10 mm, air gap size a = 30 mm.

**Figure 5.**Effect of the sample thickness on the frequency dependencies of the sound absorption coefficient for the investigated ABS samples with a (

**a**) Cartesian and (

**b**) Octagonal structures.

**Figure 6.**Effect of the air gap size on the frequency dependencies of the sound absorption coefficient for the investigated ABS samples with a (

**a**) Cartesian and (

**b**) Starlit structure.

**Figure 7.**Effect of material structure on the noise reduction coefficient vs. air gap size dependencies for the investigated ABS samples with the following thicknesses: (

**a**) 10 mm and (

**b**) 20 mm.

**Figure 8.**Noise reduction coefficient vs. air gap size dependencies for the investigated ABS samples with (

**a**) Cartesian and (

**b**) Octagonal structures. Inset legend: sample thickness.

**Figure 9.**Effect of the material structure on the noise reduction coefficient vs. the material thickness dependencies for the investigated ABS samples placed at a distance from the wall inside the impedance tube: (

**a**) 30 mm and (

**b**) 75 mm.

**Figure 10.**Noise reduction coefficient vs. material thickness dependencies for the investigated ABS samples with (

**a**) Cartesian and (

**b**) Octagonal structures. Inset legend: air gap size.

Structure Type | Volume ratio (%) | Label | Front View | Strut Diameter | Cell Sizes (mm) |
---|---|---|---|---|---|

Cartesian | 57 | C_57 | 1.4 | x = 5 | |

y = 5 | |||||

z = 5 | |||||

Starlit | 57 | S_57 | 1.4 | x = 9 | |

y = 9 | |||||

z = 5 | |||||

Octagonal | 57 | O_57 | 1.4 | x = 7 | |

y = 7 | |||||

z = 5 |

**Table 2.**Primary sound absorption maxima and minima and their corresponding frequencies depending on the air gap size for the investigated ABS samples with Cartesian and Starlit structures.

Structure Type | t (mm) | a (mm) | f_{max}_{1} (Hz) | α_{max}_{1} (−) | f_{min}_{1} (Hz) | α_{min}_{1} (−) |
---|---|---|---|---|---|---|

Cartesian | 30 | 0 | 2096 | 0.76 | 4184 | 0.25 |

10 | 1304 | 0.73 | 3000 | 0.23 | ||

50 | 656 | 0.63 | 1864 | 0.22 | ||

100 | 432 | 0.55 | 1136 | 0.17 | ||

Starlit | 10 | 0 | 5328 | 0.81 | - | - |

10 | 2064 | 0.71 | 5912 | 0.15 | ||

50 | 904 | 0.55 | 2992 | 0.08 | ||

100 | 552 | 0.48 | 1312 | 0.09 |

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**MDPI and ACS Style**

Vasina, M.; Monkova, K.; Monka, P.P.; Kozak, D.; Tkac, J. Study of the Sound Absorption Properties of 3D-Printed Open-Porous ABS Material Structures. *Polymers* **2020**, *12*, 1062.
https://doi.org/10.3390/polym12051062

**AMA Style**

Vasina M, Monkova K, Monka PP, Kozak D, Tkac J. Study of the Sound Absorption Properties of 3D-Printed Open-Porous ABS Material Structures. *Polymers*. 2020; 12(5):1062.
https://doi.org/10.3390/polym12051062

**Chicago/Turabian Style**

Vasina, Martin, Katarina Monkova, Peter Pavol Monka, Drazan Kozak, and Jozef Tkac. 2020. "Study of the Sound Absorption Properties of 3D-Printed Open-Porous ABS Material Structures" *Polymers* 12, no. 5: 1062.
https://doi.org/10.3390/polym12051062