Proceedings of the Institute of Acoustics

 

 

Development of ventilation and sound-absorbing materials using specimens generated by the multi-objective optimization method

 

Bach Lien Trieu¹, Shimane University, Matsue City, Shimane Prefecture, Japan
Keigo Kajitani², Shimane University, Matsue City, Shimane Prefecture, Japan
Kiichiro Sawada³, Shimane University, Matsue City, Shimane Prefecture, Japan
Thu Lan Nguyen⁴, Shimane University, Matsue City, Shimane Prefecture, Japan

 

ABSTRACT

 

In hot and humid tropical countries, the houses are designed to be naturally ventilated with vent louvers. However, these louvers play as direct paths for noise entering the house. It is necessary to create geometries that can maximize the noise transmission loss and the ventilation performance of the housing structure. This study aims to develop ventilation and sound-absorbing material that can be 3D printed and installed on the upper part of the buildings' windows. The multi-objective optimization method was applied to generate 3D model specimens based on fluid potential flow analysis. To examine the absorption coefficient of the cylindrical specimens made of ABS filament with different filling rates manufactured by the 3D printer, the experiments were conducted in an anechoic chamber using an impedance tube that can measure the absorption coefficient in a frequency range of 300 to 2000 Hz. It was found that the sound absorption coefficient was little affected by the filling rate of ABS filament and improved effectively at a high-frequency range when adopting the optimized spiral structure. The improvement of sound absorption coefficient at frequency of about 800 Hz and the performance of multiple-structural material will be further considered in the next study phase.

 

1. INTRODUCTION

 

Noise has been considered one of the most severe environmental pollutions that affect the quality of life and human health. Architectural solutions to minimize this impact by designing soundproof structures for houses have been targeted in many studies in the architectural field. Recently, many excellent sound-absorbing materials have been researched and proposed. However, performances other than sound absorption, especially ventilation performance, have not been studied much. Moreover, when the design is too focused on one specific function, it may not satisfy another aspect. For example, live houses have been equipped with thick iron doors and sound-absorbing materials but very few ventilation facilities. In this case, the soundproof function takes precedence over the ventilation function. As a result, many live houses were found not sufficiently ventilated, and indoor air was polluted by cigarette dust [1].

 

Ventilation and sound absorption performances are in a trade-off relationship [2]. Specifically, to improve ventilation performance, it is necessary to make innumerable holes through which air can pass. On the other hand, it is required to fill the gap to improve the sound absorption performance.

 

This conflict makes it challenging to achieve both aspects simultaneously. This study aims to develop new materials that allow air ventilation but prevent sound from passing through. These design can help control the sound propagation through the ventilation equipment and increase the overall ventilation capacity.

 

In this study, multi-objective optimization was performed to generate a model that satisfies both sound absorption and ventilation requirements in a cylindrical shape. Then, the impedance tube experiment was conducted in an anechoic chamber to investigate the sound absorption performance of all the specimens.

 

2. METHODS

 

2.1. The multi-objective Optimization and Formulations

 

The multi-objective optimization method to generate a cylindrical 3D model based on fluid potential flow analysis was applied to manufacture the test specimens by using a Python program. The program is written using the external libraries Platypus and NSGAⅡ. The model comprises 47x23x11 elements with 13536 nodes (Figure 1). It has a diameter of 105 mm, and a thickness of 20 mm. The red nodes in this model are "tangent points," and the area surrounded by the 8 points is called an "element." The objective function was set for clarifying whether the element pattern exists or not to satisfy the condition for all the elements.

 

 

Figure 1: The cylindrical 3D model

 

In this study, the following f1 and f2 were used as objective functions:

 

 

Here, Nm is the number of all the air elements and vMi is the velocity magnitude in i-th air element.

 

 

Here, Nb is the number of all the bottom air elements and vBi is velocity magnitude in i-th bottom air element.

 

The velocity magnitude in the above equations can be obtained from fluid potential flow analysis by finite element method (FEM) software LISA 8.0. In terms of Laplace's equation, a potential flow is an idealized fluid flow. Irrotational, incompressible, inviscid flow is required. The velocity potential, used in this analysis type, has one degree of freedom. Velocity is equivalent to a gradient in the velocity potential field that occurs when heat or electricity is flowing [6].

 

Function f1 was set based on the hypothesis that the larger magnitude of the overall flow velocity will allow a better sound absorption function. In other words, the more complicated the propagation path is created inside the specimens, the higher the sound absorption coefficient can be achieved. Function f2 is the flow velocity that exits from the bottom, indicating the ventilation performance magnitude.

 

The topology pattern was represented with the following function:

 

 

t_e, r_e, h_e ： Element order in the rotation direction, radial direction, height direction

m_t ： Number of elements in the rotation direction (47 in this calculation example)

m_r ： Number of radial elements (23 in this calculation example)

m_h ： Number of elements in the height direction (11 in this example)

i : Imaginary unit

a_u,v,w, b_u,v,w ：Design variables (real values between -1 and 1)

f_t , f_r , f_h ： Fourier order in each direction (4 in this example)

 

The coordinate system in equation (1) is the Cartesian coordinate system X-Y-Z. The radial coordinate system t-r-h shown in Fig. 2 was proposed depending on the case. The coordinate origin O is the center of the bottom circle shown in Fig. 1.

 

 

Figure 2: The radial coordinate system t-r-h

 

The function Z in this expression indicates the presence or absence of an element. If it is 0 or more, it means the existence of the element, and if it is negative, it means a blank. By calculating Z for all elements, the topology pattern of the entire 3D model, that is, the optimized shape of the cylindrical 3D model, is shown. Consequently, the formulation is stated "Find a_u,v,w, b_u,v,w in Eq.(1), which maximize objective functions f1 and f2".

 

The optimization program used in this study allows the creation of more complex samples by varying the number of analyzes. Random numbers are also used to create structural forms. A reproducible random number appearance pattern can be generated by entering a random seed value into the program.

 

 

Figure 3: Used 3D printer and snapshot of the printing process

 

The specimens were printed from acrylonitrile butadiene styrene (ABS), classified as synthetic resin, using XYZ printing da Vinci 1.0 AiO 3D printer. Figure 3 shows the appearance of the printer and the image of the printing process. Moreover, cylindrical filling specimens in three different filling rates, i.e., 10%, 50%, and 90%, were also prepared for the comparison test. All the specimens have a cylindrical shape with the same diameter (105mm) and thickness (20mm).

 

2.2. Measurement Experiments

 

The impedance tube has been widely used to examine the acoustic performance of materials in the laboratory [3]. However, available merchandized tubes on the market are at a high cost. In this study, a low-cost impedance tube was designed and manufactured at Shimane University to measure the normal incident sound absorption coefficient according to standard ISO 10534-2:1998 [4]. The additional part of this tube will be developed and built in for transmission loss measurement shortly later.

 

 

Figure 4: The design of the impedance tube

 

The temperature in the anechoic chamber was kept stable at around 20⁰C for all experiments. The impedance tube has a total length of 1000mm, as shown in Figure 4. The opening end for placing the speaker was filled with oil clay. The insertion part of the test samples was covered with a 20mm steel backing plate. The operating frequency range is the lowest frequency allowed by the signal processing equipment to the highest operating frequency required to avoid non-plane wave mode propagation [4]. The impedance tube designed in this study has a size that allows testing the performance in the frequency range from 300 to 2000 Hz.

 

The impedance tube was connected with two BEHRINGER ECM8000 - Measurement Condenser Microphones, YAMAHA power Amplifier P1000S, and Behringer U-PHORIA UMC204HD. The experiment apparatus is shown in Figure 5. White noise was used as the sound source released by a speaker. The original signal in the form of WAV data files collected by two microphones was converted from the time domain to the frequency domain by Fast Fourier Transform (FFT) with the Python program. This procedure digitized the original signal from WAV files and was repeated three times for each test sample.

 

 

Figure 5: Experimental setup

 

A Python program was used to read the files and perform discrete Fourier transform to check the frequency component [5] was referred to and combined with the standard ISO 10534-2:1998 [4]. The sound absorption coefficient (𝛼𝑛) for half-octave bands was calculated according to the formulas below.

 

 

where 𝑟 is the sound reflection factor at normal incidence

𝐻₁₂ is the transfer function from microphone position one to two

𝑆₁₂ is cross spectrum determined from the complex sound pressures at two microphone positions

𝑆₁₁ is auto spectrum determined from the complex sound pressure at microphone position one

𝑘 = 2𝜋𝑓 / 𝑐 is the wave number with the frequency 𝑓

𝑐 = 331.5+0.6𝑇 (m/s) is the speed of sound at room temperature T

𝑠 = 0.05(𝑚) is the distance between two microphones

𝑥₁ = 0.2 − 𝑡₁ is the position of microphone 1 with the specimen's thickness 𝑡₁

 

3. RESULTS

 

3.1. Test Specimens

 

Figure 6 illustrates the results of a multi-objective optimization program and fluid potential flow method on FEM software LISA 8.0.

 

 

Figure 6: Design solution on Pareto front by multi-objective optimization regarding the objective functions f1 and f2

 

The estimation was applied with a population size of 50, the seed values of 0, 1, or 2. The number of function evaluations was 50, 100, 500, 2500, 5000, or 7500. The execution of the program resulted in a large number of design solutions on the Pareto front, but not all of them were tested. This paper only presents experiments examining the absorption coefficient of the specimens manufactured by 2500 executed analysis times. For each case (each random seed number), select three samples with the maximized f1 value, the maximized f2 value, and f1 and f2 both have average values, respectively, to print out in 3D with ABS materials. The top surface of each specimen manufactured by a 3D printer with a 10% filling rate is shown in Table 1.

 

Table 1: The topology optimization specimens with 10% filling rate

 

^* Random seed number used to initialize a pseudorandom number generator in Python program

 

3.2. Sound Absorption Coefficient

 

The average sound absorption coefficient in the frequency range from 300 to 2000 Hz of each sample was presented in Figure 7. The measurement results of the cylindrical filling specimens made with three different filling rates (r) at the first experiment in Figure 7(a) show that all three samples have the peak observed at around 1350 Hz and 1700 Hz. However, the sample r=10 absorbs sound more effectively than two other samples in the wide frequency range (from 800 to 1300Hz). Therefore, only specimens with r = 10% were examined in the second and later experiments.

 

Figures 7(b)-(d) illustrate the sound absorption coefficient of three spiral structure materials designed by the optimization method at each random seed. With n_seed = 0, the sound absorption coefficient of the three materials is quite similar, except in the frequency range from 1000 to 1400 Hz, the 00 is more effective than the two others (Figure 7(b)). In addition, the percentage of sound absorbed by 01 is higher than two others at high frequencies (from 1700 Hz). When n_seed = 1, the 10 and 11 have only one peak (80%) at around 1250 Hz, while the 113 has two peaks (about 75%) at 1150 Hz and 1675 Hz (Figure 7(c)). All three materials which have n_seed = 2 reach an 80% absorption ratio around 1200 Hz, however, from 1270 Hz, the ratio of 20% decreases sharply while the ratio of 21A keeps increasing to 88% (Figure 7(d)).

 

 

Figure 7: The sound absorption coefficient of each sample

 

4. CONCLUSIONS

 

In this research, to create a new material that achieves both sound absorption and ventilation performance by a structural approach, we set objective functions f1 and f2 that are oriented to each performance and executed a multi-objective optimization program based on them. We confirmed the trade-off relationship between f1 and f2 of the design solution.

 

This study examined the noise reduction coefficient experiments of the 3D-printed ABS specimens manufactured by topology optimization. All the specimens absorbed the sound more effectively at high frequencies (above 1000 Hz) than at low frequencies, and in general, their sound absorption ability had the same tendency. The application of algorithms to research and manufacture materials will continue to be implemented to improve the sound absorption quality and the ventilation capacity of the materials at a broader range of frequencies. The test specimens will be further qualified by conducting the field measurement with an installation in the resident context in the next step of this study. At the same time, the revision of further formulation using acoustic cavity modes will be conducted to improve the performance.

 

5. ACKNOWLEDGEMENTS

 

We gratefully acknowledge Mr. Pham Van Quan, a bachelor of the Department of Architectural Design at Shimane University since 2018, for his cooperation in designing and manufacturing the impedance tube used in this study.

 

6. REFERENCES

 

1. Kaito Shoda. Actual Survey of the Air Environment in Live Music Club. Graduation thesis at Shibaura Institute of Technology, 2015 (Japanese)
2. Yang WeiDong, Li Yan. Sound absorption performance of natural fibers and their composites. Science China Technological Sciences, 55, 2278–2283 (2012)
3. Martin Vasina, Katarina Monkova, Peter Pavol Monka, Drazan Kozak and Jozef Tkac. Study of the Sound Absorption Properties of 3D-Printed Open-Porous ABS Material Structure. Polymers, 12, 1062 (2020)
4. ISO 10534-2:1998 Acoustics - Determination of sound absorption coefficient and impedance in impedance tubes – Part 2: Transfer-function method
5. http://nalab.mind.meiji.ac.jp/~mk/lecture/fourier-2017/python-sound/node5.html
6. LISA 8.0 Manual https://lisafea.com/

 

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¹ trieulien0903@gmail.com

² kajikei.rto@gmail.com

³ kich@riko.shimane-u.ac.jp

⁴ lan@riko.shimane-u.ac.jp