Absorption characteristics analysis of membrane sound absorber with magnet Junjuan Zhao 1 Yueyue Wang Liying Zhu Wenjiang Wang Xianhui Li Min Yang Institute Of Urban Safety And Environmental Science Beijing Academy Of Science And Technology No.55, Taoranting Road, Xicheng, Beijing, 100054, China

ABSTRACT This paper presents a membrane sound absorber (MSA) with tunable properties for low-frequency sound absorption. A series of experimental studies was conducted to obtain the acoustic characteristics of the MSA. The analysis indicate that the iron-platelet-magnet resonance mechanism introduced by the tuned magnetic field is the main factor leads to the appearance and shift of absorption peaks in low-frequency region, which are almost independent of the back cavity, and a strong magnetic field can help broaden the frequency tuning range of the MSA. This demonstrates that the structure has strong potential to achieve an extremely thin and low-frequency tunable-sound-absorption design which can be easily adapted to the noise source variation.

1. INTRODUCTION

For noise control in engineering, resonant structures such as membrane absorbers and micro- perforated panels are often used to gain better sound absorption performance in the low frequency region. However, their application is quite limited due to the need for large back cavities and the difficulty to tune their properties in practice especially at very low frequencies. Some researchers have proposed to resolve this problem by including a flexible back cavity or adding flexible structures within the absorbers [1-4]. Others have designed compound absorbers using multiple layers of microperforated panels or membranes to broaden the absorption bandwidth in the low frequencies [5,6]. However, these complex structures have only limited sound absorption capability in the deep subwavelength scale.

In recent years, acoustic metamaterials have received significant attention by researchers in physics and acoustical engineering due to their unusual properties [7-9]. Among them, membrane- type acoustic metamaterials MAMs are relatively simple and light-weight, and have the ability to actively tune the absorption characteristics. They are particularly important for noise control. Mei and Ma studied an acoustic metamaterial absorber which aims to absorb low-frequency airborne sound at selective resonance frequencies between 100 Hz and 1000 Hz [10]. Ma et al. reported on a novel acoustic metasurface with hybrid resonances that can achieve robust impedance matching and

1 tianqi 35@hotmail.com

perfect absorption [11]. Unfortunately, this type of metasurface naturally has a very narrow absorption bandwidth due to the causality constraint on the minimal structural thickness [12,13].

This paper presents a membrane sound absorber which employs a different resonance mechanism induced by a centralized magnetic field to make the design thinner and to allow the dynamic properties to be adjusted conveniently. A series of experimental studies and analysis were conducted here, these analyses are focused on the low-frequency absorption region to demonstrate the controllable functionality.

2. EXPERIMENT STRUCTURE

The structure of an MSA consists of three parts, one is a membrane with a centralized rigid iron platelet, one is a magnet to generate nonlinear magnetic field, and one is a cylindrical cavity formed between the solid stainless-steel support frame and the membrane, shown in Fig. 1. The iron platelet has radius r = 7.5 mm and mass m = 350 mg. The membrane parameters are density ρ = 1.33×10 -3

g/mm 3 , radius R = 50 mm, and thickness t = 0.1 mm. Its boundary is fixed on the edges of a support frame, forming a sealed cavity, and pre-stress is applied to the membrane. The solid support frame has an outer diameter of 100 mm, an internal diameter of 98 mm, a thick back wall of 5 mm with a centralized magnet at its bottom and the cavity depth is d . The magnet is cylindrical with height h = 10 mm and radius r 0 = 5 mm. The distance between the original position of the membrane and the top of the magnet is b .

Iron platelet

Membrane l

d h Magnet

Cavity

Support frame

Figure 1: Schematic and experiment structure of the MSA; 3. EXPERIMENTS AND ANALYSIS

Experimental studies were carried out in an impedance tube to obtain the sound absorption characteristics of the MSA, shown in Fig 2. The experiment structures are for three different cavity depths, d = 50 mm, 30 mm and 20 mm.

Figure 2: The impedance tube testing system

The MSA is installed in an impedance tube and tested according to ISO-10534-2 (1998). The absorption peak for the membrane absorber without magnet is about 800 Hz for d = 50 mm. This increases to around 1100 Hz for d = 30 mm, and 1200 Hz for d = 20 mm. The test results are also shown for the MSA using a magnet with top magnetic field of 4800 Gs at different relative distances l between the top of the magnet and the iron platelet. There are now two regions of high absorption, one at low frequency and one at higher frequency, as shown in Fig. 3. The relative distance l was adjusted by turning a screw attached to the magnet to bring it closer to the iron platelet. As this distance l is reduced, the absorption coefficient of the absorber gradually decreases

in the high frequency region and the peak moves to higher frequencies, while in the low frequency region the absorption peak is gradually raised and also moves to higher frequencies. When the magnet was adjusted to a point where it was very close to the iron platelet, the absorption peak in the high frequency region almost disappears, while the absorption peak in the low frequency region reaches its maximum value and its frequency increases to about 450 Hz for d = 50 mm (at l = 2.2 mm), 530 Hz for d = 30 mm ( l =1.9 mm), and 600 Hz for d = 20 mm ( l = 1.6 mm).

This shows that the absorber has two distinct absorbing regions. The lower one results mainly from the introduction of the magnet and can be identified with the iron-platelet-magnet resonance, while the higher one is related to the membrane-cavity resonance. By adjusting the relative distance l between the top of the magnet and the iron platelet, the absorption peaks in different cavities have a same large frequency shift from approximately 200 Hz to 600 Hz in the low-frequency region and are almost independent of the size of the back cavity, which demonstrates that the structure has a good potential to achieve an extremely thin and low-frequency tunable sound absorption structure.

Low-frequency region High-frequency region

1

Absorption coefficient

l = 2.2 mm

l = 3.2 mm

l = 3.8 mm l = 6.4 mm

0.5

without magnet

0 200 400 600 800 1000 1200 1400 1600 0

(a)

Frequency (Hz)

Low-frequency region High-frequency region

1

Absorption coefficient

l = 1.9 mm

l = 2.6 mm

l = 2.9 mm l = 5.0 mm

0.5

without magnet

0 200 400 600 800 1000 1200 1400 1600 0

(b)

Frequency (Hz)

Low-frequency region High-frequency region

1

Absorption coefficient

l = 1.6 mm

l = 2.1 mm

l = 2.8 mm l = 5.2 mm

0.5

without magnet

0 200 400 600 800 1000 1200 1400 1600 0

(c) Figure 3: Absorption coefficients of the MSA for different relative distances l , at magnetic field

Frequency (Hz)

intensity of 4800 Gs, and cavity depth (a) d = 50 mm, (b) d = 30 mm, (c) d = 20 mm.

To investigate the effect of magnetic fields on absorption coefficient of the MSA, experiments were conducted using two more different magnets in the MSA with same d = 30 mm. The results

are shown in Fig. 4, which illustrates that the tuned frequency region become larger as the magnetic field strength increases.

Low-frequency region High-frequency region

1

l = 0.9 mm l = 1.1 mm l = 1.3 mm l = 2.4 mm without magnet

Absorption coefficient

0.8

0.6

0.4

0.2

0 200 400 600 800 1000 1200 1400 1600 0

Frequency (Hz)

(a)

Low-frequency region High-frequency region

1

l = 2.5 mm l = 4.6 mm l = 7.2 mm l = 10.6 mm without magnet

Absorption coefficient

0.8

0.6

0.4

0.2

0 200 400 600 800 1000 1200 1400 1600 0

(b) Figure 4: Absorption coefficients of the MSA for different l , at cavity depth d = 30 mm, and

Frequency (Hz)

magnetic field intensity (a) 2400 Gs, (b) 5800 Gs. 4. CONCLUSIONS

In summary, this paper presents a compact and feasible design of MSA, which has a good potential to achieve an extremely thin and low-frequency tunable sound absorption structure. A series of experimental studies was conducted to obtain the acoustic characteristics of the MSA. Analytical investigations indicate that adjusting the magnetic force exerted on the central platelet leads to the increase in level and shift in frequency of the MSA’s absorption peaks in the low-frequency region while not being significantly affected by the back cavity. This concept has good application prospect for low-frequency noise absorption where is space limited and there is a need to adjust the tuned frequency according to the spectrum of the noise source. 5. ACKNOWLEDGEMENTS

This work is supported by the Beijing Natural Science Foundation (No. 1202008); BJAST Young Scholar Programs (B) (No. YS202101); BJAST Scholar Programs(B) (No. BS201901); BJAST Budding Talent Program (No. BGS202109), BJAST Innovation Cultivation Programes (No. 11000022T000000468161).

6. REFERENCES

1. Liu, J. and Herrin, D.W. Enhancing micro-perforated panel attenuation by partitioning the

adjoining cavity. Appl Acoust, 71(2) , 20-127 (2010). 2. Wang, C. and Huang, L. On the acoustic properties of parallel arrangement of multiple micro-

perforated panel absorbers with different cavity depths. J Acoust Soc Am , 130(1) , 208-218 (2011). 3. Wang, C., Cheng, L., Pan, J., et al. Sound absorption of a microperforated panel backed by an

irregular-shaped cavity. J Acoust Soc Am, 127(1) , 238-246 (2010). 4. Tao, J., Jing, R. and Qiu, X. Sound absorption of a finite micro-perforated panel backed by a

shunted loudspeaker. J Acoust Soc Am, 135(1) , 231-238 (2014). 5. Sakagami, K., Fukutani, Y., Yairi, M., et al. Sound absorption characteristics of a double-leaf

structure with an MPP and a permeable membrane. Appl Acoust, 76 : 28-34 (2014). 6. Zhang, Z.M. and Gu, X.T. The theoretical and application study on a double layer

microperforated sound absorption structure. J Sound Vib, 215(3) : 399-405 (1998). 7. Yang, Z., Mei, J., Yang, M., et al. Membrane-type acoustic metamaterial with negative dynamic

mass. Phys Rev Lett, 101 : 204301 (2008). 8. Li, Y. and Assouar, B.M. Acoustic metasurface-based perfect absorber with deep

subwavelength thickness. Appl Phys Lett, 108 : 063502 (2016). 9. Liang, Z. and Li, J. Extreme acoustic metamaterial by coiling up space. Phys Rev Lett, 108 :

114301 (2012). 10. Mei, J. and Ma, G. Dark acoustic metamaterials as super absorbers for low-frequency sound.

Nat Commun, 3(27) : 7561-7567 (2012). 11. Ma, G., Yang, M., Xiao, S., et al. Acoustic metasurface with hybrid resonances. Nat Mater,

13(9) : 873-878 (2014). 12. Yang, M. and Sheng, P. Sound absorption structures: From porous media to acoustic

metamaterials. Ann Rev Mater Res, 47 : 83-114 (2017). 13. Li, X., Xing, T., Zhao, J., et al. Broadband low frequency sound absorption using a monostable

acoustic metamaterial. J Acoust Soc Am, 147 (2) : 113-118 (2020).