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Improving low-frequency sound absorption of micro-perforated panel absorbers by using mechanical impedance plate combined with Helmholtz resonators
Applied Acoustics 114 (2016) 92–98
Contents lists available at ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Improving low-frequency sound absorption of micro-perforated panel absorbers by using mechanical impedance plate combined with Helmholtz resonators Zhao Xiao-Dan ⇑, Yu Yong-Jie, Wu Yuan-Jun School of Automobile and Traffic Engineering, Jiangsu University, Zhenjiang 212013, China
a r t i c l e
i n f o
Article history: Received 8 June 2016 Received in revised form 14 July 2016 Accepted 19 July 2016 Available online 26 July 2016 Keywords: Micro-perforated panel Helmholtz resonator Mechanical impedance Low-frequency absorption
a b s t r a c t The traditional Micro-perforated plate (MPP) is a kind of clean and non-polluting absorption structure in the middle and high frequency and has been widely used in the field of noise control. However, the sound absorption performance is dissatisfied at low frequencies when the air-cavity depth is restricted. In this paper, a mechanical impedance plate (MIP) is introduced into the traditional MPP structure and a Helmholtz resonator is attached to the MIP. Mechanical impedance plate (MIP) provides a good absorption at low frequency by using mechanism of mechanical resonance and the acoustic energy is dissipated in the form of heat with viscoelastic material. Helmholtz resonator can fill in the defect of the poor absorption effect between the Micro-perforated plate (MPP) and the mechanical impedance plate (MIP). The acoustic impedance of the proposed sound absorber is investigated by using acoustic electric analogy method and impedance transfer method. The influence of the tube’s length of Helmholtz resonator and the number of Helmholtz resonator on the sound absorption is studied. The corresponding results are in agreement with the theoretical calculation and prove that the composite structure has the characteristics of improving the low frequency sound absorption property. Ó 2016 Published by Elsevier Ltd.
1. Introduction Micro-perforated panel (MPP) absorber which is regarded as a very promising sound absorbing structure has drawn much attention in recent years. It is clean and health friendly, inexpensive and easy to manufacture, reliable in hostile temperature and pressure environments [1,2]. The perforation diameters of MPP are submillimeter in size, which can provide acoustic resistance enabling improve sound attenuation [3], therefore the structure can keep a good sound absorption without using porous materials. In previous works [4], good sound absorbing property at mid- to high frequencies can be obtained by optimizing the MPP structure. But the sound absorption performance at low frequencies is inadequate with limited cavity depth, which prevents the MPP absorbers from wide application. In the past years, researchers have been looking for methods to enhance the sound absorbing property of MPP absorbers. Selamet and Dickey [5] studied resonators with small length-to diameter ratios in the cavity and found a reduction in the primary resonance frequency for low values of this ratio. Lv
⇑ Corresponding author. E-mail address: [email protected] (X.-D. Zhao). http://dx.doi.org/10.1016/j.apacoust.2016.07.013 0003-682X/Ó 2016 Published by Elsevier Ltd.
et al. [6] proposed a tube bundle type perforated plate resonance absorber model, which was filled with flexible tube bundles with different lengths into the orifices of perforated plate. But the structure is complex. Lin et al. [7] showed that putting sound absorbing materials into MPP absorbers can improve the sound absorption performance at low frequencies. However, it increases the thickness of the absorbing structure and pollution-free can’t be guaranteed. It is difficult to control the sound absorbing peak at low frequencies with limited cavity space. Xu et al. [8] penetrated copper fibers into the MPP’s apertures to extend the sound absorption bandwidth. But the absorption coefficient barely exceeded 0.2 from 200 Hz to 400 Hz. Park [9] introduced a micro-perforated panel absorber backed by Helmholtz resonators (MPPHRs) to improve the sound absorption at low frequency and a launcher fairing example indicated that MPPHRs can be an alternative acoustic protection system to mitigate the acoustic loading inside the fairing. In this paper, mechanical impedance plate and a Helmholtz resonator were introduced into the traditional MPP structure as a possible solution to improve low-frequency absorption. The sound absorption effect of the micro-perforated panel is mainly focused on the middle and high frequency when the cavity is restricted. In order to have a sound absorption effect, the micro-perforated
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X.-D. Zhao et al. / Applied Acoustics 114 (2016) 92–98
plate is needed to increase the cavity distance. Mechanical impedance plate is provided by sticking a layer of thin viscoelastic material along the rim of the micro-perforated panel. The resonance frequency of the MIP is designed near the low frequency. Based on the mechanism of mechanical resonance absorption, the sound energy at low frequency, which penetrates the prepositive MPP, can be effectively absorbed. Therefore, there is one absorption peak between 200 Hz and 400 Hz. Meanwhile, a Helmholtz resonator was fixed on the MIP to make full use of the cavity behind MIP. The resonance frequency of Helmholtz resonator is controlled by the length of the tube to the needed frequency. Through the experiment, the Helmholtz resonator, using its own cavity resonance mechanism, has a good sound absorption near 500 Hz. Additionally, that the number of Helmholtz resonators affects the absorbing performance was discussed. Following this introduction, absorption coefficient of this composite structure is calculated in Section 2. Experimental verification is showed in Section 3. The effects of the Helmholtz resonator’s parameters are exhibited in Section 4. Finally the conclusion is displayed in Section 5.
impedance type [12] is used to calculated acoustic impedance of the part A in Fig. 2. The sound is transmitted to the mechanical plate and the Helmholtz resonator. Because of the same speed of particle velocity, their acoustic impedance is parallel to each other. Their equivalent circuit of acoustic impedance is illustrated in Fig. 3. The acoustic impedance is
Z aMIP Z aHR 1 þ Z aMIP þ Z aHR jwC ak
Z aMH ¼
ð1Þ
where Z aMIP is the acoustic impedance of the MIP [12], Z aHR is the acoustic impedance of the Helmholtz resonator, C ak is the acoustic compliance of the cavity between the mechanical plate and the rigid wall.
K S2 R þ j wM w
Z aMIP ¼
ð2Þ
where R is the damping coefficient (N s/m) of the viscoelastic materials, j is the complex number, w ¼ 2pf is the angle frequency (rad/s), f is the sound frequency (Hz), M is the total mass (kg) of MIP and Helmholtz resonator, K is the stiffness coefficient (N/m) of the viscoelastic materials.
2. Absorption coefficient calculation
Z aHR ¼ RaHR þ jwM aHR þ 1=ðjwC aHR Þ
2.1. Composite sound absorbing structure
where the intubation acoustic resistance RaHR [13] is calculated as
The basic structure of a MPP absorber consists of a microperforated panel, a rigid backing wall and the air cavity between them, as illustrated in Fig. 1. In this paper, a mechanical impedance plate (MIP) attached with a Helmholtz resonator is introduced into the air cavity. The proposed structure consists of a MPP, air cavity, a MIP and a Helmholtz resonator. The four parts constitute a composite sound absorber (CSA). The proposed structure is shown in Fig. 2.
RaHR ¼
l
pðd0 =2Þ3
As a result of the low frequency sound absorption effect is the combination effect of the mechanical impedance and the Helmholtz resonators, and the composite structure is more complex than the traditional micro-perforated plate structure, the traditional acoustic electric analogy method [4] or transfer matrix method [10] cannot calculate the acoustic impedance of the whole structure directly. The combination methods of acoustic electric analogy method and impedance transfer method [11] are proposed to predict the acoustic impedance and sound absorption coefficient of the whole structure. First, acoustic electric analogy method of
MIP
Rigid wall
Sound wave
Air cavity
ð4Þ
where l is the intubation length (m), d0 is the diameter (m) of intubation bore, g ¼ 1:83 105 kg=ðm sÞ is the shear viscosity coefficient. The intubation acoustic mass M aHR [13] is expressed as
MaHR ¼ 2.2. Absorption coefficient
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2gwq0
ð3Þ
q 0 l0
ð5Þ
S0
where l0 l þ 0:73d0 is the intubation effective length (m), S0 is the intubation sectional area ðm2 Þ. The resonator acoustic compliance C aHR and the cavity acoustic compliance C ak [13] are
C aHR ¼
V0
q0 c20
C ak ¼
V
q0 c20
ð6Þ
where V 0 is the resonator volume (m3 ), q0 is the air density (kg=m3 ), q0 ¼ 1:205 kg=m3 , c0 is the sound speed in the air (m/s), c0 ¼ 343 m=s V is cavity volume between mechanical plate and rigid wall. Then, impedance transfer method is used to calculate the acoustic impedance at the back of the micro perforated plate (MPP). The coordinate system is established as shown in Fig. 2. When the plane wave propagation in uniform rigid pipeline, instantaneous value of incident wave pressure and reflected wave pressure can be expressed
h xi pi ¼ pmi exp jx t c
ð7Þ
h xi pr ¼ pmr exp jx t þ c
ð8Þ
The relationship between vibration velocity and sound pressure can be expressed as
q0
@v @p ¼ @x @t
ð9Þ
The vibration velocity of the particle can be obtained by the above relationship. Fig. 1. Schematic diagram of traditional MPP structure.
v i ¼ v mi exp ½ jðxt kxÞ v r ¼ v mr exp ½ jðxt þ kxÞ
ð10Þ
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Rigid wall
MPP MIP Sound wave Intubation
Pi
Air cavity Pr
D
0
x Viscoelastic material
Resonator
Fig. 2. Schematic diagrams of composite sound absorber structure.
M aHR
R aHR
The acoustic impedance density can be known from Eqs. (15) and (16)
CaHR
Pn-1
Pn
Z s0 ¼ q0 c0
ZaMIP
Z sD þ jq0 c0 tanðklÞ q0 c0 þ jZ sD tanðklÞ
ð16Þ
So the acoustic impedance Z a0 at x = 0 is
Pn-1
Cak
Z a0 ¼
q c Z s0 q0 c0 Z MH þ j 0S 0 tanðkDÞ ¼ q0 c 0 S S þ jZ aHR tanðkDÞ S
ð17Þ
where D is the cavity thickness (m) Last, the total acoustic impedance of the CSA can be calculated from the impedance transfer method [14] Vn
Vn-1
Z aCSA ¼ Z aMPP þ Z a0
ð18Þ
where Z aMPP is the acoustic impedance of the MPP, as given by [15]
Z aMPP ¼ q0 c0 ðr þ jwmÞ=S
Fig. 3. Equivalent circuit model of the MIP and Helmholtz resonator.
ð19Þ
with where k ¼ w=c0 is wave number,
v mi ¼
pmi q0 c 0 ,
v mr ¼
qpmrc0 . 0
r¼
The total sound pressure at any point in the pipe is
pðxÞ ¼ pi þ pr p pr ¼ i q0 c0
m¼ ð12Þ
The acoustic impedance density at any point in the pipe is
Z sx ¼
pðxÞ
v ðxÞ
¼ q0 c 0
pmi expðjkxÞ þ pmr expðjkxÞ pmi expðjkxÞ pmr expðjkxÞ
ð13Þ
The acoustic impedance density Z sD at x ¼ D is
Z sD
p expðjklÞ þ pmr expðjklÞ ¼ Z aMH S ¼ q0 c0 mi pmi expðjklÞ pmr expðjklÞ
ð14Þ
The acoustic impedance density Z s0 at x ¼ 0 is
Z s0 ¼ q0 c0
rd2
kr
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi pffiffiffi x2 2 xd þ kr ¼ 1þ 32 8 t
ð11Þ
Particle vibration velocity is
v ðxÞ ¼ v i þ v r
0:147t
pmi þ pmr pmi pmr
ð15Þ
0:294 103 t
r
km
1=2 x2 d km ¼ 1 þ 9 þ þ 0:85 t 2
ð20Þ
ð21Þ
where t is the MPP thickness (mm), d is the perforation diameter (mm), r is the ratio of apertures area to the total area of MPP (%). The MPP’s constant is
qffiffiffiffiffiffiffiffiffiffiffi x ¼ d f =10
ð22Þ
The normal incident absorption coefficient is derived from the total acoustic impedance of the CSA as
4Re ZqaCSAc0S 0 a¼n o2 n o2 þ Im ZqaCSAc0S 1 þ Re ZqaCSAc0S 0
ð23Þ
0
where Re, Im are respectively the real part and imaginary part.
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3. Experimental verification
4
3.1. Measurement of damping and stiffness coefficient
3.5 3
Amplitude (mv)
Two kinds experiments were carried out. One was vibrating experiment for determining the damping coefficient and stiffness coefficient of the MIP, the other was absorption coefficient test of the CSA on the standing wave tube.
2.5 2 1.5 1
According to Eq. (2), the damping coefficient, stiffness coefficient of the viscoelastic materials and the mass of the plate should be calculated before calculating the acoustic impedance of the MIP structure. The material of the plate is aluminum and the mass M is 25.67 103 kg measured by electronic balance. The damping and stiffness coefficient of the viscoelastic materials are determined by the half-power bandwidth method. Considering that the mass of the plate is small and the structure’s mass changes a lot after fixing the acceleration sensor on the plate, the contactless eddy current sensor is used to conduct the damping experiment. The testing arrangement is shown in Figs. 4 and 5. The curve of amplitude-frequency characteristic is drawn from the collected response signals, as shown in Fig. 6. The MIP natural
0.5 0 200
250
300
350
400
450
Frequency (Hz) Fig. 6. Vibration response curve.
frequency f n is 325 Hz and the half-power bandwidth Df is 32.5 Hz. Then the damping coefficient R and stiffness coefficient K is calculated as
K ¼ ð2pf n Þ M 2
R ¼ 2pM Df
ð24Þ
By substituting the above datum into Eq. (24), the stiffness coefficient K is 106,934 N/m and the damping coefficient R is 5.24 N s/m.
Hammer Eddy current sensor
3.2. Measurement of absorption coefficient Conditioner
UT3408-ICP
After the measurement of damping and stiffness coefficient, Helmholtz resonance is mounted on the back of MIP. The Helmholtz resonance is made of plastic, which weights 1:89 103 kg: The total mass of MIP and Helmholtz resonator
Viscoelastic material
Computer
Sleeve Experiment table
Fig. 4. Connection diagram of the damping test.
Fig. 5. Equipment of the damping test.
M ¼ 27:56 103 kg. The absorption coefficient of the CSA is tested on standing wave tube (SW002) as shown in Fig. 7. The MPP’s parameters are: the material is aluminum, the perforation diameter d = 0.8 mm, the sheet thickness t = 0.8 mm, the porosity r = 3%, the diameter of the MPP is 100 mm, the external diameter of the standing wave tube is 107 mm, the distance between MPP and MIP D is 40 mm, the distance between MIP and the rigid wall D0 is 50 mm. The resonator is made of plastic and its volume V 0 is 11,309 mm3 . The material of the intubation is plastic, its inside diameter d0 is 2.7 mm, length L is 4 mm. The absorption coefficient of the single-layer MPP with rigid wall was also calculated as comparison, which distance D1 is 40 mm between the MPP and the rigid wall. The results are given in Fig. 8. Two noticeable sound absorbing peaks are produced in low frequency by introducing mechanical impedance plate and Helmholtz resonance into the traditional single layer MPP structure, as shown in Fig. 8. The experimental results reflect the theoretical calculation of the CSA, demonstrating that using the combination methods to calculate the absorption coefficient of the CSA is rational. The results suggest a solution of improving sound absorption property in low frequencies. Resonant frequencies of the MIP and the Helmholtz resonator are set in low frequency. The sound wave arrives at the MIP and resonator through the MPP, causing the MIP or Helmholtz resonator to resonate as the sound frequency near to the natural frequency of the MIP or Helmholtz resonator and improving the sound absorption property effectively near the resonant frequencies. When the sound is in middle and high frequencies, the effects of the MIP and resonator are negligible and the MPP works. The first sound absorbing peak is emerged by the MIP, the second peak is created by the resonator and the third one is produced by the MPP.
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Computer Basw Audio Amplifier
Resonator
Signal Analyzer
Trolley Sensor
MPP
Sound source box
MIP
Standing wave tube
Intubation Sleeve
Fig. 7. The layout of sound absorption coefficient measurement.
1
1 Calculated (CSA) Measured (CSA) Calculated (single-layer MPP)
0.9
Measured (L=6mm) Measured (L=4mm)
0.8
Measured (L=2mm)
0.7
Absorption coefficient
Absorption coefficient
0.8
0.9
0.6 0.5 0.4 0.3 0.2
0.7 0.6 0.5 0.4 0.3 0.2
0.1 0 200
0.1 400
600
800
1000
1200
1400
1600
1800
2000
0 200
Frequency/Hz
400
600
800
1000
1200
1400
1600
1800
2000
Frequency/Hz Fig. 8. Absorption coefficients of the CSA and the single layer MPP. Fig. 9. Absorption coefficients of the CSA with different length of the intubation.
4. Effects of the Helmholtz resonator’s parameters 4.1. The length of the intubation Eq. (25) is the resonant frequency calculation of the Helmholtz resonator [14]. According to it, the resonant frequency moves to the low frequency when the length of the intubation increases.
f HR
c0 ¼ 2p
sffiffiffiffiffiffiffiffiffi S0 l0 V 0
ð25Þ
The sound absorbing peak of the resonator can be changed by modifying the length of the intubation, so a good sound absorption property can be obtained at one specific frequency. The tube’s length is changed from 2 mm to 4 mm then to 6 mm and the results are shown in Fig. 9. From Fig. 9, the sound absorption frequency can be changed with changing the Helmholtz tube’s length easily. However, the absorption coefficient also be changed. 4.2. The number of the resonator As shown in Figs. 8 and 9 the amplitude value and frequency bandwidth of the second sound absorbing peak which is caused
by combining the MIP with the resonator are not sufficient, so we attached more resonators to the MIP to investigate the effects of the number of the resonator on the sound absorbing peak. The Helmholtz resonators are parallel as illustrated in Fig. 10(a) and the equivalent circuit of Helmholtz resonators is illustrated in Fig. 10(b). When the parameters of the Helmholtz resonator are the same, the relative resistance of the Helmholtz resonators can be calculated as
Z aHR ¼
1 1 S RaHR þ jwMaHR þ n jwC aHR q0 c0
ð26Þ
where n is the number of the Helmholtz resonators. The absorption coefficient of the structure is
a¼
4r
ð27Þ
ð1 þ rÞ2 þ x2
where r, x are the relative acoustic resistance and reactance.
r ¼ ReðZ aHR Þ ¼
RaHR S nq0 c0
x ¼ ImðZ aHR Þ ¼ wM aHR
1 S wC aHR nq0 c0
ð28Þ
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X.-D. Zhao et al. / Applied Acoustics 114 (2016) 92–98
(a)
(b) Resonator
MaH
Pn-1
Ra
CaH
Pn
ZaMIP
Sound wave
Cak
Pn-1
Vn-1 Vn Fig. 10. (a) Schematic diagrams of Helmholtz resonators and (b) the equivalent circuit of Helmholtz resonators.
The resonance of the Helmholtz resonators occurs when the acoustic reactance is zero. The maximum absorption coefficient can be achieved at this frequency and it is
1 0.9
ð1 þ rÞ2
¼
4 r þ 1=r þ 2
ð29Þ
The maximum value of aHR is 1 with the r = 1 condition.
RaHR S r¼ ¼1 nq0 c0
ð30Þ
where RaHR is the resonant acoustic resistance of the Helmholtz resonators.
RaHR
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2gwHR q0 ¼ 3 pðd0 =2Þ l
RaHR S q0 c 0
0.6 0.5 0.4 0.3 0.2 0.1
ð31Þ
0
1
2
3
4
5
6
7
8
9
10
11
12
Number n
where wHR ¼ 2pf HR is the resonant angular frequency. When the resonant absorption coefficient is the maximum value, the number of the resonators n can be expressed as
n¼
0.7
Fig. 11. Resonant absorption coefficient trend with increasing the number of Helmholtz resonators.
ð32Þ
The relationship between the resonant absorption coefficient and the number of the resonators is shown in Fig. 11. When the number of the resonators is about three, four or five, the resonant absorption coefficient can reach above 0.9. Taking into account the experimental arrangement, five Helmholtz resonators with the same parameters were fixed on the MIP, which one sets in the center and the other four are evenly arranged in the center of a circle with radius of 30 mm. The testing results are given in Fig. 12. As shown in Fig. 12, the experimental results are in good agreement with the theoretical calculation results and the absorption peak value is increased when changing the number of Helmholtz resonators from one to five. 5. Conclusion
1 Calculated (five resonators) Measured (five resonators) Measured (one resonator)
0.9 0.8
Absorption Coefficient
4r
Absorption coefficient
0.8
aHR ¼
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 200
400
600
800
1000
1200
1400
1600
1800
2000
Frequency/Hz
The structure that introducing mechanical impedance plate and Helmholtz resonators into the traditional MPP is proposed to enhance sound absorption performance at low frequencies. The two methods of acoustic electric analogy and impedance transfer method are adopted to derive the acoustic impedance and the sound absorption coefficient of the whole composite structure is calculated. The sound absorption mechanism is the interaction result of mechanical resonance and cavity resonance. The
Fig. 12. Absorption coefficients of the modified CSA.
mechanical resonant frequency and Helmholtz resonant frequency are set in low frequencies. Low frequency sound penetrates the micro perforated plate and energy is absorbed effectively. The experimental results exhibit good agreement with the theoretical
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X.-D. Zhao et al. / Applied Acoustics 114 (2016) 92–98
calculation. In addition, it has revealed that the resonance frequency of the Helmholtz resonator moves to low frequency easily by changing the length of the intubation and increasing the number of Helmholtz resonator appropriately can enhance the low frequency sound absorption coefficient. It is proved that the combination of the cavity resonance and mechanical resonance absorption mechanism can broaden the sound absorption bandwidth effectively. The sound absorption coefficient can be moved to lower frequency by adjusting the other parameters of CSA almost without increasing the need length of the structure. Acknowledgments This work was supported by a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) and the High Level Talent Foundation of Jiangsu University (No. 11JDG096). References [1] Onen O, Caliskan M. Design of a single layer micro-perforated sound absorber by finite element analysis. Appl Acoust 2010;71(1):79–85. [2] Tayong R, Dupont T, Leclaire P. Experimental investigation of holes interaction effect on the sound absorption coefficient of micro-perforated panels under high and medium sound level. Appl Acoust 2011;72:777–84.
[3] Liu J, Herrin DW. Enhancing micro-perforated panel attenuation by partitioning the adjoining cavity. Appl Acoust 2010;71(2):120–7. [4] Zhao X-D, Zhang X-J, Jiang Z. Three layer micro-perforated panel optimal design and analysis of its characteristics. Acta Acust 2008;33(1):84–7. [5] Dicky NS, Selamet A. Helmhltz resonators: one-dimensional limit for small cavity length-to diameter ratios. J Sound Vib 1996;195:512–7. [6] Lv Y-D, Wei W, Li X-D. A brand new type sound absorbing structure -the perforated panel resonator with flexible tube bundles. In: The Acoustical Society of China 2002 the symposium of national acoustic academic conference, Gui Lin. p. 342–4. [7] Lin L, Wang Z-M, Jiang Z-X. Effect of sound-absorbing material on a microperforated absorbing construction. Acta Acust 2011;30(2):191–202. [8] Xu Y, Ren Y-F, Li C-X. Study on absorption performance of thin Microperforated panel penetrated with copper fiber. Noise Vib Control 2011;6 (3):136–9. [9] Park S-H. Acoustic properties of micro-perforated panel absorbers backed by Helmholtz resonators for the improvement of low-frequency sound absorption. J Sound Vib 2013;332:4895–911. [10] -Hu P, Mao G-P, Zhao X-D. Effect of structure parameters on the sound absorption of micro-perforated panel absorber. Piezoelectr Acoustooptics 2013;35(5):624–30. [11] Zhou J, Shen Y, Yang J-B. A note on the prediction method of reverberation absorption coefficient of double layer micro-perforated membrane. Appl Acoust 2006;67:106–11. [12] Du G-H, Zhu Z-M, Gong X-F. Acoustics basis. Nanjing, China: Nanjing University Press; 2001. p. 121–6. [13] Maa D-Y. Helmholtz resonator. Tech Acoust 2002;1(2):2–3. [14] Hu P, Zhao X-D. The experiments and calculation on the absorptivity of microperforated panel absorber with alterable air-cavity. Piezoelectr Acoustooptics 2013;35(1):38–42. [15] Maa D-Y. Theory and design of micro-perforated panel sound absorbing constructions. Sci Sinica 1975;18:55–71.
Contents lists available at ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Improving low-frequency sound absorption of micro-perforated panel absorbers by using mechanical impedance plate combined with Helmholtz resonators Zhao Xiao-Dan ⇑, Yu Yong-Jie, Wu Yuan-Jun School of Automobile and Traffic Engineering, Jiangsu University, Zhenjiang 212013, China
a r t i c l e
i n f o
Article history: Received 8 June 2016 Received in revised form 14 July 2016 Accepted 19 July 2016 Available online 26 July 2016 Keywords: Micro-perforated panel Helmholtz resonator Mechanical impedance Low-frequency absorption
a b s t r a c t The traditional Micro-perforated plate (MPP) is a kind of clean and non-polluting absorption structure in the middle and high frequency and has been widely used in the field of noise control. However, the sound absorption performance is dissatisfied at low frequencies when the air-cavity depth is restricted. In this paper, a mechanical impedance plate (MIP) is introduced into the traditional MPP structure and a Helmholtz resonator is attached to the MIP. Mechanical impedance plate (MIP) provides a good absorption at low frequency by using mechanism of mechanical resonance and the acoustic energy is dissipated in the form of heat with viscoelastic material. Helmholtz resonator can fill in the defect of the poor absorption effect between the Micro-perforated plate (MPP) and the mechanical impedance plate (MIP). The acoustic impedance of the proposed sound absorber is investigated by using acoustic electric analogy method and impedance transfer method. The influence of the tube’s length of Helmholtz resonator and the number of Helmholtz resonator on the sound absorption is studied. The corresponding results are in agreement with the theoretical calculation and prove that the composite structure has the characteristics of improving the low frequency sound absorption property. Ó 2016 Published by Elsevier Ltd.
1. Introduction Micro-perforated panel (MPP) absorber which is regarded as a very promising sound absorbing structure has drawn much attention in recent years. It is clean and health friendly, inexpensive and easy to manufacture, reliable in hostile temperature and pressure environments [1,2]. The perforation diameters of MPP are submillimeter in size, which can provide acoustic resistance enabling improve sound attenuation [3], therefore the structure can keep a good sound absorption without using porous materials. In previous works [4], good sound absorbing property at mid- to high frequencies can be obtained by optimizing the MPP structure. But the sound absorption performance at low frequencies is inadequate with limited cavity depth, which prevents the MPP absorbers from wide application. In the past years, researchers have been looking for methods to enhance the sound absorbing property of MPP absorbers. Selamet and Dickey [5] studied resonators with small length-to diameter ratios in the cavity and found a reduction in the primary resonance frequency for low values of this ratio. Lv
⇑ Corresponding author. E-mail address: [email protected] (X.-D. Zhao). http://dx.doi.org/10.1016/j.apacoust.2016.07.013 0003-682X/Ó 2016 Published by Elsevier Ltd.
et al. [6] proposed a tube bundle type perforated plate resonance absorber model, which was filled with flexible tube bundles with different lengths into the orifices of perforated plate. But the structure is complex. Lin et al. [7] showed that putting sound absorbing materials into MPP absorbers can improve the sound absorption performance at low frequencies. However, it increases the thickness of the absorbing structure and pollution-free can’t be guaranteed. It is difficult to control the sound absorbing peak at low frequencies with limited cavity space. Xu et al. [8] penetrated copper fibers into the MPP’s apertures to extend the sound absorption bandwidth. But the absorption coefficient barely exceeded 0.2 from 200 Hz to 400 Hz. Park [9] introduced a micro-perforated panel absorber backed by Helmholtz resonators (MPPHRs) to improve the sound absorption at low frequency and a launcher fairing example indicated that MPPHRs can be an alternative acoustic protection system to mitigate the acoustic loading inside the fairing. In this paper, mechanical impedance plate and a Helmholtz resonator were introduced into the traditional MPP structure as a possible solution to improve low-frequency absorption. The sound absorption effect of the micro-perforated panel is mainly focused on the middle and high frequency when the cavity is restricted. In order to have a sound absorption effect, the micro-perforated
93
X.-D. Zhao et al. / Applied Acoustics 114 (2016) 92–98
plate is needed to increase the cavity distance. Mechanical impedance plate is provided by sticking a layer of thin viscoelastic material along the rim of the micro-perforated panel. The resonance frequency of the MIP is designed near the low frequency. Based on the mechanism of mechanical resonance absorption, the sound energy at low frequency, which penetrates the prepositive MPP, can be effectively absorbed. Therefore, there is one absorption peak between 200 Hz and 400 Hz. Meanwhile, a Helmholtz resonator was fixed on the MIP to make full use of the cavity behind MIP. The resonance frequency of Helmholtz resonator is controlled by the length of the tube to the needed frequency. Through the experiment, the Helmholtz resonator, using its own cavity resonance mechanism, has a good sound absorption near 500 Hz. Additionally, that the number of Helmholtz resonators affects the absorbing performance was discussed. Following this introduction, absorption coefficient of this composite structure is calculated in Section 2. Experimental verification is showed in Section 3. The effects of the Helmholtz resonator’s parameters are exhibited in Section 4. Finally the conclusion is displayed in Section 5.
impedance type [12] is used to calculated acoustic impedance of the part A in Fig. 2. The sound is transmitted to the mechanical plate and the Helmholtz resonator. Because of the same speed of particle velocity, their acoustic impedance is parallel to each other. Their equivalent circuit of acoustic impedance is illustrated in Fig. 3. The acoustic impedance is
Z aMIP Z aHR 1 þ Z aMIP þ Z aHR jwC ak
Z aMH ¼
ð1Þ
where Z aMIP is the acoustic impedance of the MIP [12], Z aHR is the acoustic impedance of the Helmholtz resonator, C ak is the acoustic compliance of the cavity between the mechanical plate and the rigid wall.
K S2 R þ j wM w
Z aMIP ¼
ð2Þ
where R is the damping coefficient (N s/m) of the viscoelastic materials, j is the complex number, w ¼ 2pf is the angle frequency (rad/s), f is the sound frequency (Hz), M is the total mass (kg) of MIP and Helmholtz resonator, K is the stiffness coefficient (N/m) of the viscoelastic materials.
2. Absorption coefficient calculation
Z aHR ¼ RaHR þ jwM aHR þ 1=ðjwC aHR Þ
2.1. Composite sound absorbing structure
where the intubation acoustic resistance RaHR [13] is calculated as
The basic structure of a MPP absorber consists of a microperforated panel, a rigid backing wall and the air cavity between them, as illustrated in Fig. 1. In this paper, a mechanical impedance plate (MIP) attached with a Helmholtz resonator is introduced into the air cavity. The proposed structure consists of a MPP, air cavity, a MIP and a Helmholtz resonator. The four parts constitute a composite sound absorber (CSA). The proposed structure is shown in Fig. 2.
RaHR ¼
l
pðd0 =2Þ3
As a result of the low frequency sound absorption effect is the combination effect of the mechanical impedance and the Helmholtz resonators, and the composite structure is more complex than the traditional micro-perforated plate structure, the traditional acoustic electric analogy method [4] or transfer matrix method [10] cannot calculate the acoustic impedance of the whole structure directly. The combination methods of acoustic electric analogy method and impedance transfer method [11] are proposed to predict the acoustic impedance and sound absorption coefficient of the whole structure. First, acoustic electric analogy method of
MIP
Rigid wall
Sound wave
Air cavity
ð4Þ
where l is the intubation length (m), d0 is the diameter (m) of intubation bore, g ¼ 1:83 105 kg=ðm sÞ is the shear viscosity coefficient. The intubation acoustic mass M aHR [13] is expressed as
MaHR ¼ 2.2. Absorption coefficient
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2gwq0
ð3Þ
q 0 l0
ð5Þ
S0
where l0 l þ 0:73d0 is the intubation effective length (m), S0 is the intubation sectional area ðm2 Þ. The resonator acoustic compliance C aHR and the cavity acoustic compliance C ak [13] are
C aHR ¼
V0
q0 c20
C ak ¼
V
q0 c20
ð6Þ
where V 0 is the resonator volume (m3 ), q0 is the air density (kg=m3 ), q0 ¼ 1:205 kg=m3 , c0 is the sound speed in the air (m/s), c0 ¼ 343 m=s V is cavity volume between mechanical plate and rigid wall. Then, impedance transfer method is used to calculate the acoustic impedance at the back of the micro perforated plate (MPP). The coordinate system is established as shown in Fig. 2. When the plane wave propagation in uniform rigid pipeline, instantaneous value of incident wave pressure and reflected wave pressure can be expressed
h xi pi ¼ pmi exp jx t c
ð7Þ
h xi pr ¼ pmr exp jx t þ c
ð8Þ
The relationship between vibration velocity and sound pressure can be expressed as
q0
@v @p ¼ @x @t
ð9Þ
The vibration velocity of the particle can be obtained by the above relationship. Fig. 1. Schematic diagram of traditional MPP structure.
v i ¼ v mi exp ½ jðxt kxÞ v r ¼ v mr exp ½ jðxt þ kxÞ
ð10Þ
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Rigid wall
MPP MIP Sound wave Intubation
Pi
Air cavity Pr
D
0
x Viscoelastic material
Resonator
Fig. 2. Schematic diagrams of composite sound absorber structure.
M aHR
R aHR
The acoustic impedance density can be known from Eqs. (15) and (16)
CaHR
Pn-1
Pn
Z s0 ¼ q0 c0
ZaMIP
Z sD þ jq0 c0 tanðklÞ q0 c0 þ jZ sD tanðklÞ
ð16Þ
So the acoustic impedance Z a0 at x = 0 is
Pn-1
Cak
Z a0 ¼
q c Z s0 q0 c0 Z MH þ j 0S 0 tanðkDÞ ¼ q0 c 0 S S þ jZ aHR tanðkDÞ S
ð17Þ
where D is the cavity thickness (m) Last, the total acoustic impedance of the CSA can be calculated from the impedance transfer method [14] Vn
Vn-1
Z aCSA ¼ Z aMPP þ Z a0
ð18Þ
where Z aMPP is the acoustic impedance of the MPP, as given by [15]
Z aMPP ¼ q0 c0 ðr þ jwmÞ=S
Fig. 3. Equivalent circuit model of the MIP and Helmholtz resonator.
ð19Þ
with where k ¼ w=c0 is wave number,
v mi ¼
pmi q0 c 0 ,
v mr ¼
qpmrc0 . 0
r¼
The total sound pressure at any point in the pipe is
pðxÞ ¼ pi þ pr p pr ¼ i q0 c0
m¼ ð12Þ
The acoustic impedance density at any point in the pipe is
Z sx ¼
pðxÞ
v ðxÞ
¼ q0 c 0
pmi expðjkxÞ þ pmr expðjkxÞ pmi expðjkxÞ pmr expðjkxÞ
ð13Þ
The acoustic impedance density Z sD at x ¼ D is
Z sD
p expðjklÞ þ pmr expðjklÞ ¼ Z aMH S ¼ q0 c0 mi pmi expðjklÞ pmr expðjklÞ
ð14Þ
The acoustic impedance density Z s0 at x ¼ 0 is
Z s0 ¼ q0 c0
rd2
kr
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi pffiffiffi x2 2 xd þ kr ¼ 1þ 32 8 t
ð11Þ
Particle vibration velocity is
v ðxÞ ¼ v i þ v r
0:147t
pmi þ pmr pmi pmr
ð15Þ
0:294 103 t
r
km
1=2 x2 d km ¼ 1 þ 9 þ þ 0:85 t 2
ð20Þ
ð21Þ
where t is the MPP thickness (mm), d is the perforation diameter (mm), r is the ratio of apertures area to the total area of MPP (%). The MPP’s constant is
qffiffiffiffiffiffiffiffiffiffiffi x ¼ d f =10
ð22Þ
The normal incident absorption coefficient is derived from the total acoustic impedance of the CSA as
4Re ZqaCSAc0S 0 a¼n o2 n o2 þ Im ZqaCSAc0S 1 þ Re ZqaCSAc0S 0
ð23Þ
0
where Re, Im are respectively the real part and imaginary part.
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3. Experimental verification
4
3.1. Measurement of damping and stiffness coefficient
3.5 3
Amplitude (mv)
Two kinds experiments were carried out. One was vibrating experiment for determining the damping coefficient and stiffness coefficient of the MIP, the other was absorption coefficient test of the CSA on the standing wave tube.
2.5 2 1.5 1
According to Eq. (2), the damping coefficient, stiffness coefficient of the viscoelastic materials and the mass of the plate should be calculated before calculating the acoustic impedance of the MIP structure. The material of the plate is aluminum and the mass M is 25.67 103 kg measured by electronic balance. The damping and stiffness coefficient of the viscoelastic materials are determined by the half-power bandwidth method. Considering that the mass of the plate is small and the structure’s mass changes a lot after fixing the acceleration sensor on the plate, the contactless eddy current sensor is used to conduct the damping experiment. The testing arrangement is shown in Figs. 4 and 5. The curve of amplitude-frequency characteristic is drawn from the collected response signals, as shown in Fig. 6. The MIP natural
0.5 0 200
250
300
350
400
450
Frequency (Hz) Fig. 6. Vibration response curve.
frequency f n is 325 Hz and the half-power bandwidth Df is 32.5 Hz. Then the damping coefficient R and stiffness coefficient K is calculated as
K ¼ ð2pf n Þ M 2
R ¼ 2pM Df
ð24Þ
By substituting the above datum into Eq. (24), the stiffness coefficient K is 106,934 N/m and the damping coefficient R is 5.24 N s/m.
Hammer Eddy current sensor
3.2. Measurement of absorption coefficient Conditioner
UT3408-ICP
After the measurement of damping and stiffness coefficient, Helmholtz resonance is mounted on the back of MIP. The Helmholtz resonance is made of plastic, which weights 1:89 103 kg: The total mass of MIP and Helmholtz resonator
Viscoelastic material
Computer
Sleeve Experiment table
Fig. 4. Connection diagram of the damping test.
Fig. 5. Equipment of the damping test.
M ¼ 27:56 103 kg. The absorption coefficient of the CSA is tested on standing wave tube (SW002) as shown in Fig. 7. The MPP’s parameters are: the material is aluminum, the perforation diameter d = 0.8 mm, the sheet thickness t = 0.8 mm, the porosity r = 3%, the diameter of the MPP is 100 mm, the external diameter of the standing wave tube is 107 mm, the distance between MPP and MIP D is 40 mm, the distance between MIP and the rigid wall D0 is 50 mm. The resonator is made of plastic and its volume V 0 is 11,309 mm3 . The material of the intubation is plastic, its inside diameter d0 is 2.7 mm, length L is 4 mm. The absorption coefficient of the single-layer MPP with rigid wall was also calculated as comparison, which distance D1 is 40 mm between the MPP and the rigid wall. The results are given in Fig. 8. Two noticeable sound absorbing peaks are produced in low frequency by introducing mechanical impedance plate and Helmholtz resonance into the traditional single layer MPP structure, as shown in Fig. 8. The experimental results reflect the theoretical calculation of the CSA, demonstrating that using the combination methods to calculate the absorption coefficient of the CSA is rational. The results suggest a solution of improving sound absorption property in low frequencies. Resonant frequencies of the MIP and the Helmholtz resonator are set in low frequency. The sound wave arrives at the MIP and resonator through the MPP, causing the MIP or Helmholtz resonator to resonate as the sound frequency near to the natural frequency of the MIP or Helmholtz resonator and improving the sound absorption property effectively near the resonant frequencies. When the sound is in middle and high frequencies, the effects of the MIP and resonator are negligible and the MPP works. The first sound absorbing peak is emerged by the MIP, the second peak is created by the resonator and the third one is produced by the MPP.
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Computer Basw Audio Amplifier
Resonator
Signal Analyzer
Trolley Sensor
MPP
Sound source box
MIP
Standing wave tube
Intubation Sleeve
Fig. 7. The layout of sound absorption coefficient measurement.
1
1 Calculated (CSA) Measured (CSA) Calculated (single-layer MPP)
0.9
Measured (L=6mm) Measured (L=4mm)
0.8
Measured (L=2mm)
0.7
Absorption coefficient
Absorption coefficient
0.8
0.9
0.6 0.5 0.4 0.3 0.2
0.7 0.6 0.5 0.4 0.3 0.2
0.1 0 200
0.1 400
600
800
1000
1200
1400
1600
1800
2000
0 200
Frequency/Hz
400
600
800
1000
1200
1400
1600
1800
2000
Frequency/Hz Fig. 8. Absorption coefficients of the CSA and the single layer MPP. Fig. 9. Absorption coefficients of the CSA with different length of the intubation.
4. Effects of the Helmholtz resonator’s parameters 4.1. The length of the intubation Eq. (25) is the resonant frequency calculation of the Helmholtz resonator [14]. According to it, the resonant frequency moves to the low frequency when the length of the intubation increases.
f HR
c0 ¼ 2p
sffiffiffiffiffiffiffiffiffi S0 l0 V 0
ð25Þ
The sound absorbing peak of the resonator can be changed by modifying the length of the intubation, so a good sound absorption property can be obtained at one specific frequency. The tube’s length is changed from 2 mm to 4 mm then to 6 mm and the results are shown in Fig. 9. From Fig. 9, the sound absorption frequency can be changed with changing the Helmholtz tube’s length easily. However, the absorption coefficient also be changed. 4.2. The number of the resonator As shown in Figs. 8 and 9 the amplitude value and frequency bandwidth of the second sound absorbing peak which is caused
by combining the MIP with the resonator are not sufficient, so we attached more resonators to the MIP to investigate the effects of the number of the resonator on the sound absorbing peak. The Helmholtz resonators are parallel as illustrated in Fig. 10(a) and the equivalent circuit of Helmholtz resonators is illustrated in Fig. 10(b). When the parameters of the Helmholtz resonator are the same, the relative resistance of the Helmholtz resonators can be calculated as
Z aHR ¼
1 1 S RaHR þ jwMaHR þ n jwC aHR q0 c0
ð26Þ
where n is the number of the Helmholtz resonators. The absorption coefficient of the structure is
a¼
4r
ð27Þ
ð1 þ rÞ2 þ x2
where r, x are the relative acoustic resistance and reactance.
r ¼ ReðZ aHR Þ ¼
RaHR S nq0 c0
x ¼ ImðZ aHR Þ ¼ wM aHR
1 S wC aHR nq0 c0
ð28Þ
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(a)
(b) Resonator
MaH
Pn-1
Ra
CaH
Pn
ZaMIP
Sound wave
Cak
Pn-1
Vn-1 Vn Fig. 10. (a) Schematic diagrams of Helmholtz resonators and (b) the equivalent circuit of Helmholtz resonators.
The resonance of the Helmholtz resonators occurs when the acoustic reactance is zero. The maximum absorption coefficient can be achieved at this frequency and it is
1 0.9
ð1 þ rÞ2
¼
4 r þ 1=r þ 2
ð29Þ
The maximum value of aHR is 1 with the r = 1 condition.
RaHR S r¼ ¼1 nq0 c0
ð30Þ
where RaHR is the resonant acoustic resistance of the Helmholtz resonators.
RaHR
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2gwHR q0 ¼ 3 pðd0 =2Þ l
RaHR S q0 c 0
0.6 0.5 0.4 0.3 0.2 0.1
ð31Þ
0
1
2
3
4
5
6
7
8
9
10
11
12
Number n
where wHR ¼ 2pf HR is the resonant angular frequency. When the resonant absorption coefficient is the maximum value, the number of the resonators n can be expressed as
n¼
0.7
Fig. 11. Resonant absorption coefficient trend with increasing the number of Helmholtz resonators.
ð32Þ
The relationship between the resonant absorption coefficient and the number of the resonators is shown in Fig. 11. When the number of the resonators is about three, four or five, the resonant absorption coefficient can reach above 0.9. Taking into account the experimental arrangement, five Helmholtz resonators with the same parameters were fixed on the MIP, which one sets in the center and the other four are evenly arranged in the center of a circle with radius of 30 mm. The testing results are given in Fig. 12. As shown in Fig. 12, the experimental results are in good agreement with the theoretical calculation results and the absorption peak value is increased when changing the number of Helmholtz resonators from one to five. 5. Conclusion
1 Calculated (five resonators) Measured (five resonators) Measured (one resonator)
0.9 0.8
Absorption Coefficient
4r
Absorption coefficient
0.8
aHR ¼
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 200
400
600
800
1000
1200
1400
1600
1800
2000
Frequency/Hz
The structure that introducing mechanical impedance plate and Helmholtz resonators into the traditional MPP is proposed to enhance sound absorption performance at low frequencies. The two methods of acoustic electric analogy and impedance transfer method are adopted to derive the acoustic impedance and the sound absorption coefficient of the whole composite structure is calculated. The sound absorption mechanism is the interaction result of mechanical resonance and cavity resonance. The
Fig. 12. Absorption coefficients of the modified CSA.
mechanical resonant frequency and Helmholtz resonant frequency are set in low frequencies. Low frequency sound penetrates the micro perforated plate and energy is absorbed effectively. The experimental results exhibit good agreement with the theoretical
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X.-D. Zhao et al. / Applied Acoustics 114 (2016) 92–98
calculation. In addition, it has revealed that the resonance frequency of the Helmholtz resonator moves to low frequency easily by changing the length of the intubation and increasing the number of Helmholtz resonator appropriately can enhance the low frequency sound absorption coefficient. It is proved that the combination of the cavity resonance and mechanical resonance absorption mechanism can broaden the sound absorption bandwidth effectively. The sound absorption coefficient can be moved to lower frequency by adjusting the other parameters of CSA almost without increasing the need length of the structure. Acknowledgments This work was supported by a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) and the High Level Talent Foundation of Jiangsu University (No. 11JDG096). References [1] Onen O, Caliskan M. Design of a single layer micro-perforated sound absorber by finite element analysis. Appl Acoust 2010;71(1):79–85. [2] Tayong R, Dupont T, Leclaire P. Experimental investigation of holes interaction effect on the sound absorption coefficient of micro-perforated panels under high and medium sound level. Appl Acoust 2011;72:777–84.
[3] Liu J, Herrin DW. Enhancing micro-perforated panel attenuation by partitioning the adjoining cavity. Appl Acoust 2010;71(2):120–7. [4] Zhao X-D, Zhang X-J, Jiang Z. Three layer micro-perforated panel optimal design and analysis of its characteristics. Acta Acust 2008;33(1):84–7. [5] Dicky NS, Selamet A. Helmhltz resonators: one-dimensional limit for small cavity length-to diameter ratios. J Sound Vib 1996;195:512–7. [6] Lv Y-D, Wei W, Li X-D. A brand new type sound absorbing structure -the perforated panel resonator with flexible tube bundles. In: The Acoustical Society of China 2002 the symposium of national acoustic academic conference, Gui Lin. p. 342–4. [7] Lin L, Wang Z-M, Jiang Z-X. Effect of sound-absorbing material on a microperforated absorbing construction. Acta Acust 2011;30(2):191–202. [8] Xu Y, Ren Y-F, Li C-X. Study on absorption performance of thin Microperforated panel penetrated with copper fiber. Noise Vib Control 2011;6 (3):136–9. [9] Park S-H. Acoustic properties of micro-perforated panel absorbers backed by Helmholtz resonators for the improvement of low-frequency sound absorption. J Sound Vib 2013;332:4895–911. [10] -Hu P, Mao G-P, Zhao X-D. Effect of structure parameters on the sound absorption of micro-perforated panel absorber. Piezoelectr Acoustooptics 2013;35(5):624–30. [11] Zhou J, Shen Y, Yang J-B. A note on the prediction method of reverberation absorption coefficient of double layer micro-perforated membrane. Appl Acoust 2006;67:106–11. [12] Du G-H, Zhu Z-M, Gong X-F. Acoustics basis. Nanjing, China: Nanjing University Press; 2001. p. 121–6. [13] Maa D-Y. Helmholtz resonator. Tech Acoust 2002;1(2):2–3. [14] Hu P, Zhao X-D. The experiments and calculation on the absorptivity of microperforated panel absorber with alterable air-cavity. Piezoelectr Acoustooptics 2013;35(1):38–42. [15] Maa D-Y. Theory and design of micro-perforated panel sound absorbing constructions. Sci Sinica 1975;18:55–71.