# Effect of 3D-Printed PLA Structure on Sound Reflection Properties

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Characteristics of Samples

^{−3}, moisture absorption 0.3% at 28 °C and yield strength of the filament 57.4 MPa.

_{a}is the air volume in body cavities, and V

_{T}is the total body volume. The volume porosity of the specimens was regulated by the thickness of the strut in a lattice structure and by the cell size.

^{−3}), the porosity can be expressed by means of Equation (2)

_{A}is the apparent density and ρ is the density of PLA material (1.24 gcm

^{−3}).

^{−1}for the whole sample were applied to produce a preliminary sample. In this case, the 3D printer stringing effect appeared as seen in Figure 1.

^{−1}. A 1.7 mm diameter filament was used for 3D printing of the samples, which was applied in layer thickness of 0.254 mm using a 0.4 mm diameter nozzle. The samples were positioned so that their cylindrical axes were perpendicular to the building platform. They were built without supports because the lattice structures were self-supporting. The quality of the samples was checked visually, and no cracks or thin strands of plastic (as the result of 3D printer stringing) were observed.

#### 2.2. Measurement Methodology

#### 2.2.1. Sound Reflection Coefficient

_{I}is either reflected or absorbed by this material [38,39]. The sound reflection coefficient β is the measure of how much sound is reflected from a material [40]. It can be expressed as follows [41,42,43,44]:

_{R}is the reflected sound energy, E

_{A}is the absorbed sound energy, and α is the sound absorption coefficient.

#### 2.2.2. Sound Reflection Properties

^{3}and a large surface area (i.e., 10–12 m

^{2}) of investigated specimens.

_{1}and M

_{2}. This method defines the normal incidence sound reflection coefficient β as follows [53,54,55]:

_{12}is the pressure transfer function, H

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

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

_{0}is the complex wave number, and x

_{1}is the distance between the microphone M

_{1}and the tested material sample (see Figure 3b). The above transfer functions are expressed as:

_{1}and p

_{2}are the complex acoustic pressures measured by the microphones M

_{1}and M

_{2}, x

_{2}is the distance between the microphone M

_{2}and the studied material specimen, and s is the distance between the two microphones M

_{1}and M

_{2}.

## 3. Results and Discussion

#### 3.1. Influence of Structure Type

_{I}(see Figure 3b) into heat. These findings were observed mainly for low-frequency sound waves.

#### 3.2. Influence of Total Volume Porosity

#### 3.3. Influence of Specimen Thickness

#### 3.4. Influence of Air Gap Size

_{min}

_{1}(proportional to a quarter-wavelength, i.e., λ/4), the primary sound reflection maxima β

_{max}

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

_{min}

_{1}and f

_{max}

_{1}depending on the air gap size a of the most porous (i.e., P = 56%) PLA samples measuring 10 mm in thickness. It is obvious that the frequencies, which correspond to the primary sound reflection minima and maxima, generally shifted to lower values of the excitation frequencies with the increasing air gap size. However, the primary sound reflection minima and maxima generally increased with increasing air gap size. It can also be seen that the lowest values of the primary sound reflection minima and maxima and their corresponding excitation frequencies were found for the PLA samples produced with the starlit structure, which is in accordance with Figure 4. Similar results were found for the low porous (i.e., P = 30%) samples measuring 30 mm in thickness, as shown in Table 3. Here, the increasing air gap size led to an increase in the primary sound reflection minima and maxima and to a decrease in their corresponding excitation frequencies. However, it is also clear that the effect of the structure type of the thicker PLA samples on these excitation frequencies was practically negligible compared to the thin samples tested (see Table 2). Again, it was found that lower values of the sound reflection coefficient were observed for the specimens that were manufactured with the starlit structure. This was due to the more complex pore shapes of this 3D-printed structure than the other open-porous PLA structures, which led to multiple reflections during the propagation of sound waves through the starlit structure and consequently to greater conversion of sound energy into heat.

#### 3.5. Influence of Excitation Frequency

#### 3.6. Comparison of Sound Reflection Properties

_{m}that was determined as an arithmetical average of the sound reflection coefficients over the whole measured frequency range (i.e., from 200 to 6400 Hz). Some examples of the calculated values of the mean sound reflection coefficient are shown in Table 4. Regardless of the structure type of the tested porous PLA materials, it is obvious that the mean value of the sound reflection coefficient generally increased with increasing sample porosity and with decreasing specimen thickness and air gap size behind the tested sample inside the impedance tube. It was confirmed that the PLA specimens manufactured with the starlit structure exhibited the lowest sound reflection properties because of their complex shape structure compared to the other types of studied open-porous PLA structures. It can also be seen that the sound reflection behavior of the PLA samples, which were produced with the other types (i.e., cartesian, octagonal and rhomboid) of open-porous structures, was very similar. The highest value of the mean sound reflection coefficient (i.e., β

_{m,max}= 0.857), and thus the highest ability to reflect sound, was found for the PLA specimen that was produced with the cartesian structure, the highest total volume porosity (i.e., P = 56%), the smallest thickness (i.e., t = 10 mm) and which was placed on the solid wall SW (i.e., a = 0 mm).

## 4. Summary

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Examples of samples produced. (

**a**) samples of thickness t = 30 mm and volume porosity P = 43% with different types of structure, (

**b**) rhomboid samples with different volume porosities and (

**c**) a set of samples with octagonal structure. (Note: the numbers on the sample labels in the figure indicate the total volume porosity in %).

**Figure 3.**Circuit diagram of the experimental equipment for measuring the sound reflection coefficient (

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

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

_{A}—absorbed sound energy; E

_{I}—incident sound energy; E

_{R}—reflected sound energy; M

_{1}, M

_{2}—measuring microphones; MS—measured specimen; s—distance between microphones M

_{1}and M

_{2}; SS—sound source; SW—solid wall; t—sample thickness; x

_{1}, x

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

**Figure 4.**Influence of 3D-printed PLA structure type on the frequency dependencies of the sound reflection coefficient; (

**a**) porosity P = 30%, specimen thickness t = 10 mm, air gap size a = 70 mm, (

**b**) porosity P = 56%, specimen thickness t = 10 mm, air gap size a = 15 mm.

**Figure 5.**Effect of total volume porosity on the frequency dependencies of the sound reflection coefficient for the investigated PLA specimens: (

**a**) rhomboid structure, sample thickness t = 10 mm, air gap size a = 40 mm; (

**b**) cartesian structure, sample thickness t = 20 mm, air gap size a = 30 mm.

**Figure 6.**Effect of specimen thickness on the frequency dependencies of the sound reflection coefficient for the investigated PLA specimens: (

**a**) Starlit structure, porosity P = 30%, air gap size a = 0 mm; (

**b**) Octagonal structure, porosity P = 56%, air gap size a = 60 mm.

**Figure 7.**Influence of air gap size on the frequency dependencies of the sound reflection coefficient for the studied PLA specimens: (

**a**) Starlit structure, sample thickness t = 20 mm, porosity P = 43%; (

**b**) Cartesian structure, sample thickness t = 20 mm, porosity P = 56%.

**Table 1.**Basic characteristics of lattice structures designed to investigate the sound reflection properties.

Structure Type | Label | Volume Porosity (%) | Structure View | Strut Diameter (mm) | Cell Size x/y/z (mm) |
---|---|---|---|---|---|

Cartesian | 56 | 1 | 5/5/5 | ||

C | 43 | 1.4 | 5/5/5 | ||

30 | 1.8 | 5/5/5 | |||

Octagonal | 56 | 1 | 6/7/5 | ||

O | 43 | 1.4 | 6/7/5 | ||

30 | 1.7 | 5.5/7/5 | |||

Rhomboid | 56 | 1 | 5.5/7/7 | ||

R | 43 | 1.35 | 5/7/7 | ||

30 | 1.7 | 5/7/7 | |||

Starlit | 56 | 1 | 8/9/5 | ||

S | 43 | 1.4 | 7.5/9/5 | ||

30 | 1.8 | 8/9/5 |

**Table 2.**Primary sound reflection minima and maxima and their corresponding excitation frequencies depending on the air gap size for the studied 3D-printed open-porous PLA material structures of thickness t = 10 mm and porosity P = 56%.

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

Cartesian | 25 | 2272 | 0.73 | 5904 | 0.91 |

50 | 1392 | 0.75 | 2984 | 0.94 | |

70 | 1192 | 0.78 | 2296 | 0.95 | |

100 | 784 | 0.81 | 1424 | 0.97 | |

Octagonal | 25 | 1936 | 0.70 | 5032 | 0.91 |

50 | 1336 | 0.74 | 2920 | 0.93 | |

70 | 1040 | 0.76 | 2256 | 0.93 | |

100 | 728 | 0.81 | 1360 | 0.97 | |

Rhomboid | 25 | 2024 | 0.71 | 5536 | 0.90 |

50 | 1384 | 0.72 | 2960 | 0.91 | |

70 | 1080 | 0.77 | 2272 | 0.93 | |

100 | 760 | 0.81 | 1392 | 0.98 | |

Starlit | 25 | 1928 | 0.60 | 5024 | 0.89 |

50 | 1320 | 0.64 | 2872 | 0.92 | |

70 | 960 | 0.70 | 2224 | 0.92 | |

100 | 680 | 0.75 | 1248 | 0.92 |

**Table 3.**Primary sound reflection minima and maxima and their corresponding excitation frequencies depending on the air gap size for the studied 3D-printed open-porous PLA material structures of thickness t = 30 mm and porosity P = 30%.

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

Cartesian | 0 | 1728 | 0.00 | 3608 | 0.79 |

25 | 704 | 0.09 | 2056 | 0.86 | |

50 | 488 | 0.14 | 1760 | 0.87 | |

100 | 336 | 0.18 | 1288 | 0.91 | |

Octagonal | 0 | 1776 | 0.01 | 3672 | 0.79 |

25 | 712 | 0.10 | 2152 | 0.85 | |

50 | 488 | 0.16 | 1808 | 0.86 | |

100 | 336 | 0.20 | 1312 | 0.91 | |

Rhomboid | 0 | 1864 | 0.02 | 3696 | 0.79 |

25 | 728 | 0.14 | 2176 | 0.86 | |

50 | 512 | 0.19 | 1824 | 0.86 | |

100 | 360 | 0.24 | 1344 | 0.88 | |

Starlit | 0 | 1824 | 0.02 | 3640 | 0.80 |

25 | 696 | 0.08 | 2120 | 0.84 | |

50 | 504 | 0.13 | 1792 | 0.84 | |

100 | 344 | 0.20 | 1296 | 0.86 |

**Table 4.**Mean values of the sound reflection coefficient of selected 3D-printed open-porous PLA materials.

Structure Type | t (mm) | P (%) | a (mm) | β_{m}(-) |
---|---|---|---|---|

Cartesian | 10 | 56 | 0 | 0.857 |

20 | 43 | 50 | 0.702 | |

30 | 30 | 100 | 0.598 | |

Octagonal | 10 | 56 | 0 | 0.844 |

20 | 43 | 50 | 0.699 | |

30 | 30 | 100 | 0.601 | |

Rhomboid | 10 | 56 | 0 | 0.842 |

20 | 43 | 50 | 0.692 | |

30 | 30 | 100 | 0.610 | |

Starlit | 10 | 56 | 0 | 0.820 |

20 | 43 | 50 | 0.679 | |

30 | 30 | 100 | 0.589 |

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**MDPI and ACS Style**

Monkova, K.; Vasina, M.; Monka, P.P.; Vanca, J.; Kozak, D.
Effect of 3D-Printed PLA Structure on Sound Reflection Properties. *Polymers* **2022**, *14*, 413.
https://doi.org/10.3390/polym14030413

**AMA Style**

Monkova K, Vasina M, Monka PP, Vanca J, Kozak D.
Effect of 3D-Printed PLA Structure on Sound Reflection Properties. *Polymers*. 2022; 14(3):413.
https://doi.org/10.3390/polym14030413

**Chicago/Turabian Style**

Monkova, Katarina, Martin Vasina, Peter Pavol Monka, Jan Vanca, and Dražan Kozak.
2022. "Effect of 3D-Printed PLA Structure on Sound Reflection Properties" *Polymers* 14, no. 3: 413.
https://doi.org/10.3390/polym14030413