3D Printed Nature Pattern Metastructure for The Sound Absorption Coefficient

This research investigates the influence of the shape of 3D printed metastructures on sound absorption performance, focusing on three distinct configurations inspired by nature: honeycomb, spiderweb, and gyroid. The objectives involve designing and producing sound-absorbing structures using the 3D printing Fused Deposition Modelling (FDM) method. Simultaneously, the study analyzes and compares their sound absorption performance by considering the sound absorption coefficient and the noise reduction coefficient (NRC) for each pore shape. Using computer-aided software, the three different pore shapes were designed and produced using Polylactic Acid (PLA) material through FDM 3D printing. Each design was replicated at three different thicknesses: 10mm, 20mm, and 30mm, all with a diameter of 94mm. The sound absorption coefficient of the samples was evaluated through impedance tube experiments, collecting data for alpha (α) from 250 Hz to 2000 Hz. Subsequently, NRC values were calculated for four different frequencies: 250Hz, 500Hz, 1000Hz, and 2000Hz, ensuring a comprehensive analysis. Results indicate that the gyroid structure exhibited the highest overall sound absorption coefficient across the tested frequency range, followed by the spider-web and honeycomb structures. Additionally, the 30mm thickness demonstrated greater sound-absorbing performance than the 20mm and 10mm thicknesses. These outcomes provide valuable insights into the sound absorption capabilities of 3D printed metastructures, highlighting the superior performance of the gyroid structure. Understanding the impact of pore shape and thickness on sound absorption performance contributes to the development of acoustically optimized materials for various applications


Introduction
The noise pollution brings negative effects on public health.It originates from uncontrolled levels of noise.Noise is unpleasant sound, commonly produced by machines, causing disturbance to the surrounding.In urban areas, among the main contributors to the increase in noise pollution are primarily from cars, airplanes, trains, and factories operating around those areas [1].A study conducted by Jariwala et al. [2] showed that noise pollution can have various adverse effects on an individual's health.
Noise disturbances can also occur within residences, originating from electronic devices at home such as vacuum cleaners, amplifiers, kids toys, and others.This not only causes discomfort in the peaceful environment at home but can also result in serious effects on the health of family members.Toys that produce high and impulsive noise levels carry a significant risk of permanent hearing loss and tinnitus if exposed for prolonged periods [3].
Hence, numerous structures and materials designed for sound absorption have emerged as solutions for noise reduction.Conventional sound-absorbing structures possess distinctive attributes like irregular surfaces, voids, fibers, and convolutions.The application of 3D printing techniques has empowered researchers to fabricate intricate sound-absorbing structures, including metastructures.The research conducted by Johnston & Sharma [4] suggests that utilizing 3D printing to create lattice-based fibrous sound-absorbing structures results in a notably elevated level of sound absorption.
Moreover, there has been considerable interest in sound-absorbing structures that draw inspiration from natural configurations like beehives and spiderwebs.In 1999, Davis devised an acoustic panel design resembling a beehive to mitigate noise in aircraft.Naify et al. [5] delved into the efficacy of honeycomb-mimicking acoustic sandwich panels in augmenting sound insulation while minimally impacting the weight of the original material.Toyoda et al. [6] examined the influence of beehiveshaped structures on the sound absorption traits of panel-type sound absorbers.Miniaci et al. [7] discovered that metastructures inspired by spiderweb patterns effectively establish band gaps for low frequencies.Furthermore, Rafique et al. [8] explored the potential of spiderweb-like structures as rear cavities for micro-perforated non-homogeneous panels, assessing their sound-absorbing efficiency.The increasingly prevalent adoption of 3D printing across industries has presented significant avenues for producing and advancing sound-absorbing materials, particularly acoustic metastructures.However, to achieve optimal sound-absorbing configurations tailored to specific applications, comprehensive comparisons become imperative.This is owing to multiple variables that impact the extent of sound absorption in a material-namely, density, material thickness, and the depth of the air gap behind the sound-absorbing material, as discussed by Everest & Pohlmann [9].This study aims to establish a comparative analysis of sound absorption levels and transmission losses by investigating the potential of employing natural structures such as beehives, spiderwebs, and honeycomb patterns as sound-absorbing materials fabricated through 3D printing.

Materials
The material chosen for the study to produce sound-absorbing structures is Polylactic Acid (PLA).This material functions as the plastic filament essential for the 3D printing apparatus that will be employed.Additionally, PLA ranks among the widely utilized thermoplastic polymers in the realm of 3D printing technology.Moreover, the accessibility and ease of management of this PLA material for 3D printing applications are noteworthy, as highlighted by Stansbury & Idacavage [10].Notably, PLA is characterized by its recyclability and possesses a smooth surface, as pointed out by Vasina et al. [11].This attribute renders PLA well-suited for constructing cost-effective prototypes in engineering and research pursuits, as emphasized by Bourell et al. [12].

Cavity Designs
Using computer-aided design (CAD) software including Solidworks and Cura 5, three distinct cavity designs for sound-absorbing structures were conceived prior to initiating the 3D printing procedure.Ensuring accurate design of the sound-absorbing structure is imperative to minimize any inaccuracies during acoustic experiments.The initial design embodies a honeycomb pattern, the second takes inspiration from the natural origins of phononic crystals, specifically spiderwebs, while the third is fashioned after the gyroid configuration.
All three cavities uphold an identical volume ratio of 30%, with variations in sample thickness set at 10mm, 20mm, and 30mm.The adoption of the 30% volume ratio aims to attain efficacious sound absorption performance without entirely dampening the sound.The material volume contained within the voids of the sound-absorbing structure sample is denoted by the volume ratio, VVrr, as formulated in the subsequent equation: Where VVss refers to the volume of the material used to produce the sample structure and VVtt is the total volume of the sample [13].Furthermore, all three samples are designed in the form of cylinders with an outer diameter of 94 mm, following the inner diameter of the impedance tube used.The three types of designs for the sound-absorbing cavity structures that were printed, along with their characteristics, are formulated in Table 1

Experimental work
The impedance tube method is a frequently employed technique in acoustic experiments, especially for determining the sound absorption coefficient, α, of a material.This sound absorption coefficient serves as a measure of the amount of sound energy absorbed by the material as sound waves pass through it.Therefore, the higher the sound absorption coefficient, the greater the level of sound absorption for a given material.Figure 1 outlines the process for obtaining sound absorption coefficient values for honeycomb structures, spider webs, and cavities.
All three of these cavities have the same volume ratio of 30%, with three different sample thicknesses of 10mm, 20mm, and 30mm.The 30% volume ratio is employed to achieve effective sound absorption performance without densification.An impedance tube with a diameter of 94mm and two microphones were utilized to measure the Sound Pressure Level (SPL).Bruel & Kjaer microphones were connected to the data acquisition device, National Instrument CDAQ-9171, to undergo calibration procedures before the experiment was conducted.Subsequently, the impedance value of the empty impedance tube (without a sample) was measured as the reference impedance.This was used to calculate the sound absorption coefficient for the sample.Next, the sample was inserted into the impedance tube, and its impedance value was measured.This was accomplished by introducing sound, reaching a maximum frequency of 2000 Hz within the tube, delivered through a loudspeaker, and the sound pressure level was measured using a microphone.Finally, the readings of the sound absorption coefficient values were recorded in Matlab software, and this process was repeated 3 times to obtain the average sound absorption coefficient value and ensure accuracy of measurements.For a sample thickness of 30mm, a significant increase in the sound absorption coefficient can be observed overall compared to the thicknesses of 10mm and 20mm.The highest sound absorption coefficient value is recorded at a frequency around 2000Hz, reaching 0.34.Consequently, until about frequency of 1500Hz, the sound absorption coefficient increases as the sample thickness increases for the honeycomb cavity design, before showing irregular pattern between 1500Hz to 2000 Hz.

Spiderweb design
Figure 4 presents an overall depiction of the sound absorption levels generated by the spider web cavity design across different sample thicknesses.At a thickness of 10mm, the spider web cavity design records a low sound absorption coefficient, ranging from approximately 0 to 0.13 in the frequency range of 350 Hz to 2000 Hz.However, at the lower frequency of 250 Hz, the sound absorption level produced by the spider web cavity design is around 0.45-0.47.The maximum sound absorption coefficient value for the 10mm thickness is recorded in the frequency of 1630 Hz, reaching a value of 0.13, which is lower than the sound absorption coefficient value for the 20mm thickness in the same frequency range.However, samples with a thickness of 20mm show higher sound absorption coefficient values compared to the 10mm thickness overall.Meanwhile, for the 10mm and 20mm thicknesses, the sound absorption coefficient values produced in the same frequency range 0.0 and 0.34 respectively.A significant increase in sound absorption coefficient is also evident in the 30mm thickness from the frequency range of 650Hz to 2000Hz.At a frequency of 2000 Hz, the highest sound absorption coefficient value is from the 30mm sample thickness, at around 0.44.

Gyroid Cavity Design
The effect of different thicknesses on the sound absorption coefficient for the gyroid cavity design is formulated in Figure 5.At frequencies around 750 Hz to 2000 Hz, there is a noticeable difference in the sound absorption coefficient values among the three thicknesses (10mm, 20mm, and 30mm).For a sample thickness of 10mm, the majority of the sound absorption coefficient values are very low, ranging between 0 to 0.1 in the frequency range of 500 Hz to 2000 Hz.However, absorption peak was observed at frequency of 1985 Hz with values of 0.71.These absorption peaks can occur when there is significant sound energy loss and resonant frequencies within the cavity space of the gyroid structure.Frequency, Hz Gyroid Spiderweb Honeycomb The impact of cavity design on the sound absorption coefficient for the 10mm sample thickness is shown in Figure 6.At the frequency of 1690 Hz, the highest sound absorption coefficient value is recorded by the spiderweb-shaped cavity, reaching 0.12, followed by the gyroid-shaped and honeycomb-shaped cavities, with values of 0.05 and 0.04 respectively.

Sample Thickness: 20mm
Figure 7 below illustrates the lowest sound absorption coefficient values for the honeycomb-shaped cavity, around 0 to 0.1 in the frequency range of 500 Hz to 1900 Hz.Meanwhile, for the spider webshaped cavity, the recorded sound absorption coefficient values are around 0.1 to 0.2 in the same frequency range.This is because the spider web cavity design possesses a convoluted maze-like structure that allows sound energy to be scattered, leading to energy loss [13].The sound absorption coefficient for the spiderweb-shaped cavity demonstrates a higher increase compared to the other designs in the frequency range of 1250 Hz to 1600 Hz and 1816 Hz to 2000 Hz For the honeycomb structure, as the thickness increases from 10mm to 20mm and then to 30mm, there is a noticeable improvement in sound absorption.The NRC values progressively increase from 0.048 at a thickness of 10mm to 0.100 at a thickness of 20mm, and further to 0.148 at a thickness of 30mm.As for the spider web design, the NRC values increase from 0.105 at a thickness of 10mm to 0.142 at a thickness of 20mm, and then to 0.171 at a thickness of 30mm.The spider web cavity design, with its maze-like structure, exhibits an encouraging response to thicker configurations, resulting in improved sound absorption characteristics.
The most significant results are observed in the gyroid structure.The NRC values demonstrate a substantial increase with thicker configurations, showcasing a clear advantage over other cavity designs.The gyroid cavity design records impressive noise reduction coefficient values of 0.052 at a thickness of 10mm, 0.058 at a thickness of 20mm, and 0.231 at a thickness of 30mm.This indicates that the unique and complex geometry of this design contributes to more efficient sound energy absorption, making it highly effective in absorbing sound across varying thicknesses.

Conclusion
In conclusion, the configuration of the cavity design in sound-absorbing materials significantly influences sound absorption performance.The gyroid cavity design exhibits higher overall sound absorption coefficients across the studied frequency range, followed by the spider web-shaped and honeycomb designs.Furthermore, the sound absorption coefficient for each cavity design based on its thickness was also analyzed.A thickness of 30mm demonstrates better sound absorption performance compared to 20mm and 10mm.Sound absorption peaks typically form toward the end of concerned frequency range for all evaluated samples.Additionally, there are also abrupt drops in the sound absorption coefficient detected within the frequency range of 1750 Hz to 2000 Hz.Focusing on the optimization of thickness and cavity design in 3D-printed sound-absorbing materials can result in effective sound-absorbing materials.
Noise Reduction Coefficient (NRC) according to design and sample thickness

FIGURE 1 .
FIGURE 1.The flow chart for sound absorption coefficient measurement

3 .FIGURE 3 .
FIGURE 3. The Effect of Sample Thickness on the Sound Absorption Coefficient, α, for the Honeycomb Cavity Design.

FIGURE 4 .
FIGURE 4. The Effect of Sample Thickness on the Sound Absorption Coefficient, α, for the Spiderweb Cavity Design

FIGURE 5 .Figure 6 FIGURE 6 .
FIGURE 5.The Effect of Sample Thickness on the Sound Absorption Coefficient, α, for the Gyroid Cavity Design

Table 1 .
below The design of structures for sound absorption and their dimensions 7th International Conference on Noise, Vibration and Comfort(NVC 2023) Comparison of Sound Absorption Coefficient, α, againstFrequency, Hz for the Gyroid pattern design α 7th International Conference on Noise, Vibration and Comfort (NVC 2023) The comparison of Sound Absorption Coefficient, α, against Frequency, Hz for a Thickness of 10mm