Sound absorption performance of a conch-imitating cavity structure

Abstract

At present, in order to solve noise pollution, many experts are studying methods to improve the noise reduction performance of sound barriers and acoustic devices. However，the development of sound-absorbing structures under external noise environments with multiple frequencies has not made significant progress.To improve the sound absorption performance (SAP) and sound insulation performance (SIP) of structures, a novel cavity-imitating sound-absorbing structure model was established based on the multi-cavity resonance structure of conches. By performing experiments with an impedance tube and finite element simulation, the internal design of, and experimental results from a conch-imitating cavity structure (CICS) were analysed. In addition, a variety of structural parameters were investigated and the application of the sound absorber was analyzed. The analytical results showed that the CICS exhibits excellent SAP at low and intermediate frequencies. The peak frequency and sound absorption bandwidth can be changed and optimised by adjusting the structural parameters. The results show that the structure can effectively improve the sound absorption and insulation performance of the sound barrier to achieve the purpose of improving the acoustic performance, and proposes a new solution for the realisation of sound absorption and noise reduction in a multi-noise environment.

Introduction

The construction industry and transportation industry have developed apace during the current period of modern urbanisation, which results in increasingly severe noise pollution. Since the last century, novel materials and structures available for sound absorption have abounded in order to abate this increasingly severe noise pollution.^1–3 Traditional sound insulation materials conform to the mass law of sound insulation: the larger the surface density of a structure, the better the sound insulation effect; when the material density remains the same, it is necessary to increase the mass and thickness of a vehicle body structure to increase global sound insulation, which militates against the weight limits on such vehicle body structures.^4,5 Porous materials with favourable sound absorption performance (SAP) and low density show favourable sound absorption at high frequencies but offer poor sound absorption at intermediate and low frequencies. Moreover, they are mostly soft materials and do not have sufficient mechanical strength and stiffness to serve as bearing parts.^6–8 Besides, porous and fibre-based materials generate particulate emissions when used and subject to wear and tear, therefore, they should not be used in crowded spaces such as hospitals and food-processing areas where onerous environmental tolerances rightly prevail. Some experts including Gao ⁹ and Qingbo ¹⁰ developed various materials (e.g. metal porous materials and hybrid composites) for improving and expanding the range of available porous sound-absorbing structures; these are commonly used in the construction industry. Research results showed that this can reduce noise along railways and inside trains by use of such materials as paving in railway lines and train bodies.^11–13 Thus, how to develop high-performance sound absorption materials meeting the complex conditions pertaining to use along railway lines is of theoretical and practical significance for further reducing track noise pollution inside and outside trains.

To attain excellent mechanical and acoustic properties simultaneously, many scholars proposed increasing the SAP of materials by utilising composite structures.^14–16 Composite structures allow significant improvements to the SAP by strengthening multiple reflections and micro-vibrations of sound waves, which are also characterised by advantages, including high specific strength, vibration reduction, and favourable impact resistance. ¹⁷ For example, Li et al. ¹⁸ proposed a type of lightweight multilayer honeycomb membrane-type acoustic metamaterial. They suggested that lightweight honeycomb sandwich panel AMs can break the mass law of insulation and a high sound transmission loss is attained using just a light weight of material.

Additionally, micro-perforated panels can also act as a sound-absorption device, with their simple structures, they are easy to manufacture and are readily optimised; however, a single-layer micro-perforated panel has drawbacks such as a narrow absorption frequency band and a single peak.^19,20 Researchers found that the absorption frequency band can be increased by superimposing structures in multiple layers. To solve these drawbacks, scholars have designed novel micro-perforated panels, which can be divided into cavity-parallel micro-perforated panels and multi-layer superposed micro-perforated panels. Xie et al. ²¹ designed a polyester fibre filled Nomex honeycomb to form a new composite structure to improve its acoustic properties by increasing the absorption of additional sound waves. Gao et al. ²² designed a teaching-learning-based optimisation algorithm to model an ultra-broadband parallel sound absorber. With the aid of the algorithm, the average sound absorption coefficient (SAC) of the ultra-broadband parallel sound absorber ranging from 0 to 2000 Hz can be optimised, with the average SAC of 0.9255. Research on superposition of multi-layer micro-perforated panels is more abundant. Wang et al. ²³ proposed a novel ultralight micro-perforated sandwich structure, with a face-centred cubic (FCC) core as the sound absorber, resulting in excellent mechanical and acoustic properties.

According to the coupled mode theory, to achieve greater radiation loss, the total thickness will increase. So now many experts and scholars have designed and invented many acoustic structures with applications for spiral structures, which have great scientific and engineering significance for suppressing broadband and low-frequency sounds.^24,25 When sound waves enter the spiral structure, they will be reflected multiple times in the internal cavity, and the sound energy will be converted into heat and other forms of energy. Prasetiyo et al. ²⁶ studied a sub-wavelength absorber structure. In that paper, the coiled space method was introduced into the tube resonator system to realise the sub-wavelength absorber structure, up to 1/32 wavelength of the sound absorption peak. Long et al. ²⁷ designed a multi-type coiled spatial resonator integrated with porous materials, which can broaden the frequency range of sound absorption. The absorption efficiency is greatly improved and the absorption bandwidth is expanded. These studies use the spiral structure to reduce the thickness of the sound absorbers so that their thickness is still sub-wavelength. This has enlightening significance for reducing the thickness of low-frequency sound absorbers.

Conches have a spiral structure in their interior, probably leading to resonance.^28,29 Resonance is a phenomenon that an object vibrates more at a specific frequency than at the other frequencies. A conch itself is considered a favourable physical system which probably triggers resonance owing to its zigzag internal structure, which is full of air. The conch resonates once sound without enters therein.^30–32

In the present study, a conch-imitating cavity structure (CICS) was designed according to the structural characteristics of conches. Figure 1 shows a cylindrical structure with the diameter of 100 mm, consisting of micro-perforated panels and partitions with holes. After being incident upon the micro-perforated panel at the top surface, air propagates, and energy is absorbed layer-by-layer through holes on the partitions, thus realising sound absorption. The influences of different cavity thicknesses, the numbers of divisions, dividing angle and panel aperture on SAC were investigated by conducting impedance tube tests. Moreover, the sound absorption effect of the proposed filling structure was verified. In addition, the pressure acoustic and visco-thermal acoustics modules in COMSOL are used to simulate the SAC of the impedance tube test material, and the reliability of the test is verified.

Figure 1.

(A) conch-like arc structure; (B) conch-like straight structure; (C) the tested specimen; (D) cross-sectional view of a conch.

Methods and materials

Test method

Test theory

A Helmholtz resonator formed by connecting short tubes with cavities is a classical acoustic model. As for the sound absorption mechanism of the Helmholtz resonator, scholars have conducted numerous detailed studies.^33,34 Micro-perforated panels, as a resonant sound-absorbing structure, are characterised by a low acoustic mass and a high acoustic resistance. The SAC and frequency bandwidth for reflecting the SAP of micro-perforated panels are mainly dependent on the acoustic mass m and acoustic resistance r. The acoustic mass is influenced by distribution and areal density of perforations while the acoustic resistance is inversely proportional to the panel aperture. Therefore, the acoustic resistance and acoustic mass can be controlled independently. Ma verified that the micro-perforated panels themselves exhibit enough acoustic resistance and a low enough mass reactance when the panel aperture is of the order of tenths of a millimetre. Without the need to add porous sound absorbing materials, micro-perforated panels can be used as favourable broadband sound-absorbing structures.

The SAC is defined as dividing the acoustic energy (such as acoustic resistances of short tubes and cavities) absorbed by micro-perforated panels by the acoustic energy at normal incidence, which is (after simplification) expressed as follows:

$$E_i=E_r+E_{\alpha }+E_t$$ (1)

$$\alpha =E_a/E_i=(E_{\dot{i}}-E_r)/E_i$$ (2)

where, $E_i$ , $E_r$ , $E_{\alpha }$ , and $E_t$ indicate the total energy of incident sound waves, the reflected sound energy, the absorbed sound energy and the transmitted sound energy.

The sound-absorbing structure based on micro-perforated panels involves four parameters: panel thickness t (mm), panel aperture d (mm), depth D (mm) of cavities at the back of such panels, and the percentage P of the area of the perforations in total area of the panel. The main SAP of micro-perforated panels depends on a combination of the four parameters. The internal wall of each micro-perforation shows strong viscosity, forming a certain acoustic resistance, thus increasing the SAC of micro-perforated panels.

Figure 2(a) compares the SAC of the CICS with those of the ordinary vertically tandem structure with six cavities and the parallel structure with six cavities, showing the same rate of perforation of the panel on which sound waves are incident. By comparing SACs of CICS (red dashed line), a tandem structure (green short dashed line), and a parallel structure (blue dash-dot line) in the figure, both the CICS and the tandem structure are found to exhibit six peaks; by contrast, only a single peak appears in the parallel structure: the SAC of the CICS is greater than those of the other two structures with a single connection mode within quite a large range; moreover, the sound absorption bandwidth of the CICS also increases in relative terms.

Figure 2.

Transmitted, reflected, and absorbed waves at an infinite sandwich panel.

Test materials

The CICS specimens were prepared by applying three-dimensional (3-d) printing (DSM Company) through stereolithography (SLA), with a printing accuracy of ± 0.1 mm. The Wenext 8100 resins were taken as test materials, showing a series of advantages such as a low density, high strength, flame-retardancy, and heat-insulation characteristics. At a cavity depth of 40 mm, the influences of different shapes of partitions, numbers of divisions, areas of the panel receiving incident waves, apertures of micro-perforated panels, perforation rates, and thicknesses of micro-perforated panels on the SAC of the sound-absorbing structure CICS were investigated. Table 1 lists all test parameters pertaining to the CICS specimens used in impedance tube tests. The test samples were prepared with a diameter (d) of 100 mm and a thickness of 40 mm, as shown in Figure 1(c).

Table 1.

Parameters of ICCS for experiment.

Specimens	Shape of partition	Number of divisions	Incident cavity angle/°	Panel aperture/mm	Dividing plate aperture/mm	Plate thickness /mm
Exp1	Straight board	6	90	1	1	1
Exp2	Curved board	6	90	1	1	1
Exp3	Curved board	5	90	1	1	1

Test equipment

According to ASTM E1050-08, the SAC of the samples was measured based on a two-microphone impedance tube, as shown in Figure 3(a). The impedance tube (model ZT13, SKC Acoustics Technology Co., Ltd, China) can be used at the frequency of 63 to 6300 Hz. During the impedance tube test, the samples were tightly and flexibly sealed because the gaps around the edges of the samples significantly affected the measured SAC. Here, the samples were fixed in an appropriate position with the aid of Teflon tape to avoid sound leakage through the surrounding fractures or gaps.

Figure 3.

(A) The impedance tube, (B) schematic of the experimental system.

Tests were conducted at room temperature (22 ± 1 °C) and a relative humidity of 65 ± 2%. The sample was placed in the other end of the sound source. As shown in Figure 3(b), the plane waves were generated from the sound source, passed through the sample, and then reflected by the rigid walls. The energies of incident and reflected waves were detected and collected by using two microphones distributed at different positions in the impedance tube. The signals from two microphones were resolved by the test system based on the transfer matrix method to attain the incident and reflected sound waves. Furthermore, the SAC of the sample was derived by use of Equations (1) and (2).

Test result

Considering the influence of the sealing condition of samples on the test, two samples were separately prepared for each type of specimen to perform a repeat test to guarantee the accuracy and repeatability of the test results. Additionally, to verify the efficacy of the adopted sealing measures, triplicate tests were conducted on each specimen (giving a total of six tests).

The results of the repeated tests on specimens Exp₁ and Exp₂ are shown in Figures 4(a) and (b). The results reveal that the SACs measured during multiple tests were consistent in terms of trend and peak frequencies. This implies that the specimens and the impedance tube were adequately sealed; moreover, the test was repeatable and the results reliable, enabling validation of the effectiveness and accuracy of the finite element simulation and the impedance tube test used to measure sound absorption. There are some differences between the experimental results and the simulation results: this was attributed to various factors, including the application of Teflon tape on the contact surface between the specimens and the impedance tube, thus deviating from the ideal boundary condition set during simulation, the influence of environmental noise during the test, and errors in the dimensions of the specimens.

Figure 4.

(A) The reliability test of Exp₁; (B) the reliability test of Exp_2.

Simulation analysis

Simulation model

Based on the method for measuring the SAC by using the transfer function method in a two-microphone impedance tube, an acoustic simulation model for the specimen structure is established by employing COMSOL, as shown in Figure 5(a). A portion belongs to the air domain while the other corresponds to the domain containing sound-absorbing materials. The components are composed of materials following pressure acoustics and visco-thermal acoustics, both of which are solid elements. Air in cavities in the impedance tube and CICS is thought to be non-viscous and therefore the impedance tube and CICS are set as in the pressure acoustics model; the micro-perforated panels are set in the visco-thermal acoustics model to consider the viscosity and heat loss therein. The connection between the micro-perforated panels and the cavities at the back is set as a sound-visco-thermal acoustic boundary. The specific material properties are defined in Table 2.

Figure 5.

(A) geometric model of the CICS; (B) meshing of the CICS model.

Table 2.

Definition of material properties.

Attributes	Variable	value	Unit	Attribute group
Bulk viscosity	muB	muB(T)	Pa·s	Basic
Dynamic viscosity	mu	eta(T)	Pa·s	Basic
Density	rho	rho(pA,T)	kg/m3	Basic
Thermal Conductivity	k_iso	k(T)	W/(m·K)	Basic
Speed of sound	c	cs(T)	m/s	Basic
Constant pressure Heat capacity	Cp	Cp(T)	J/(kg·K)	Ideal gas
Specific heat rate	gamma	1.4	1	Ideal gas

The left-most boundary of the geometric model is determined as the incident pressure field, on which plane waves are radiated; as shown in Figure 5(a), the incident pressure field exerts pressure p (Pa), and the other boundaries form hard boundaries to the sound field. When determining the element size parameters in the user-defined window, the globally maximum element size is set as one-eighth of the minimum wavelength, that is, ${\lambda }_{\min }/8=c_0/f_{\max }/8$ , in which $f_{max}=$ 6300 Hz and $c_0$ denotes the speed of sound. Mesh generation is performed using free tetrahedra (Figure 5(b)).

Model validation

The specific geometric parameters used in these simulations are listed in Table 3. The frequency domain from 0 to 6300 Hz was selected. The SACs of the sound-absorbing structure CICS were separately calculated based on different models. By making comparisons with specimens Exp₁, Exp₂ and Exp₃ for the impedance tube in Table 1, and with the sound-absorbing structure CICS using the same 3-d geometric model, the effectiveness of the simulation model and the test reliability were verified. Figure 6 indicates that the change in the measured SAC of the CICS is similar to that obtained through simulation. The difference is mainly ascribed to the sample size used for the tests, especially regarding that induced by manufacturing tolerances in the panel aperture. The test values are larger than the simulated values, especially at frequencies above 3500 Hz. This is because the non-rigid and rough structural surface of samples during the tests possibly results in the growth of the heat loss and viscosity loss.

Table 3.

Parameters of ICCS for simulation.

Specimens	Shape of partition	Number of divisions	Incident cavity angle/°	Panel aperture/mm	Panel porosity	Plate thickness /mm
A1	Straight board	6	90	1	9%	1
A2	Curved board	6	90	1	9%	1
B1	Curved board	5	90	1	9%	1
B2	Curved board	6	90	1	9%	1
B3	Curved board	7	90	1	9%	1
C1	Curved board	6	90	1	9%	1
C2	Curved board	6	105	1	9%	1
C3	Curved board	6	120	1	9%	1
D1	Curved board	6	90	1	9%	1
D2	Curved board	6	90	0.8	9%	1
D3	Curved board	6	90	0.6	9%	1
E1	Curved board	6	90	1	9%	1
E2	Curved board	6	90	0.8	5.06%	1
E3	Curved board	6	90	0.6	3.24%	1
F1	Curved board	6	90	1	9%	1
F2	Curved board	6	90	1	9%	1.5
F3	Curved board	6	90	1	9%	2

Figure 6.

(A) test and simulation results: Exp₁ and A₁; (B) test and simulation results: Exp₂ and A_2.

As shown in Figure 6, according to the measured SAC (blue dash-dot line) in the impedance tube, the CICS can absorb more than 98% of incident acoustic energy at the first peak at around 1000 Hz. The simulation result is similar to the test result. During the impedance tube test in the laboratory, the vertically incident sound waves reciprocate in the tube due to the sealing of air in the tube, which increases the consumption of the acoustic energy, especially at the resonance frequency of the structure. A perfectly matched layer (PML) is established in the simulation model which assumes that the sound waves are entirely reflected only by panels, so multiple reflections of sound waves are ignored. Therefore, the test value of the sound absorption peak is greater than the simulated value.

Analysis on influencing factors

Influence of the shape of the partitions

Partitions between cavities can be divided into those with a straight board and those with a curved board the better to represent the actual characteristics of conches, as shown in Figure 7(a). The resonant frequency $f_0$ of the resonant cavity can be expressed as $f_0=\frac{c}{2\pi }\sqrt{\frac{S}{V(t+\delta )}}$ , in which c, S, V, t, and δ refer to the speed of sound (340 m/s), the area of the perforations, the cavity volume, the thickness of the micro-perforated panels, and a correction factor ( $\delta =0.85d$ for a circular hole of aperture d). ³⁵ According to the equation of $f_0$ , the resonant frequency is related only to the cavity volume while it is unrelated to the shape of the cavity when keeping other variables unchanged. The shape of the partitions between cavities does not influence the resonant frequency or SAC. ³⁶ As shown in Figure 7(b), curves A₁ and A₂ are similar and also exhibit the same resonant frequency owing to them having the same cavity volume. Both the SACs of the two groups of CICS specimens approximate to 1.0 at around 850 Hz, showing a sound absorption of more than 98% and an SAP reaching a peak. There are six divided cavities, and the other five sound absorption peaks separately appear at around 1700, 2700, 3300, 4050, and 5500 Hz. These tend to stabilise at 5800 Hz. The nephogram of the sound pressure for specimen A₁ is shown in Figure 7(c). However, the SAC of the structure with the partition appearing as the curved board is slightly larger than that appearing as the straight board within the full frequency band. This is because the sound waves are reflected more often within the irregular space enclosed by the cavity walls, thus consuming more acoustic energy. Therefore, the CICSs in latter section all refer to those with a curved board.

Figure 7.

(A) Top view of A₁ and A₂; (B) simulation results of A₁ and A₂, (C) The cloud map of sound pressure of A_1.

However, it can be seen from the curve that the CICS sound absorption coefficient of the curved plate is slightly higher than that of the straight plate in the whole frequency range. Many studies have discussed the influence of square cavity and triangular cavity on the sound absorption performance of the perforated plate. In addition, some scholars have also discussed the influence of variable cross-section cavities on the acoustic performance. According to the thermoviscous acoustic theory of irregular cavities, sound propagation in the air is related to the displacement and movement speed of small particles. When the shape of the sound-absorbing cavity is more complex, that is to say, the more reflective surfaces, the smaller particles need to travel more distance. Therefore, part of the reason is that the sound waves are reflected more frequently in the irregular space of the cavity wall, which consumes more sound energy and improves the sound absorption capacity of the middle and low frequencies.

Influence of the number of divisions

The dividing angle $\theta$ of the CICS is determined according to the arithmetic progression formulae: $a_n=a_1+(n-1)d$ and $S_n=n{a}_1+\frac{n(n-1)}{2}d,n\in N^{*}$ . When the dividing angle (90°) of the micro-perforated panel receiving incident waves remains the same, the tolerances d of specimens B₁, B₂, and B₃ are −18°, −12°, and −8.5° (Figure 8(a)). According to the change of SACs in Figure 8(b), increasing the number of divisions influences the number and frequency of peaks when keeping the area of the panel receiving incident waves and rate of perforation unchanged. According to the test result of SAC obtained at n = 5 through the simulation by COMSOL, it is proposed that the panel can absorb 99% of the incident acoustic energy at 678 Hz and the subsequent four sound absorption peaks gradually decrease in amplitude. According to the result at n = 6, about 98% of the incident acoustic energy can be absorbed by the panel at the first resonant frequency of 844 Hz. At n = 7, the SAC reaches 0.98 at 951 Hz and the corresponding curve follows that at n = 5. With the growth in number of divided cavities, the low-frequency bandwidth remains unchanged and the peak gradually shifts to a higher frequency, which ran counter to expectation.

Figure 8.

(A) Top views of B₁ and B₂; (B) simulated results for B₁ and B_2.

Influence of the area of the panel receiving incident waves

Keeping the porosity the same, the area of the micro-perforated panel receiving incident waves is changed, as shown in Figure 9(a). In addition, θ was set to 90°, 105°, and 120°, respectively. It can be seen from the curves in Figure 9(b) that all peak frequencies decrease slightly when increasing the area of the micro-perforated panel receiving incident waves; moreover, the sound can always be perfectly absorbed at the first peak, with absorption of over 99% of the incident acoustic energy. The left-shift of the peak frequency is induced by the increase in the volume of the cavity. Additionally, it is possible to attain more high-order peaks within the target range of frequencies by changing the area of the micro-perforated panel receiving incident waves. For example, at θ = 120°, four high-absorption peaks were obtained for the structure at frequencies below 2500 Hz; moreover, the first peak frequency is found at a frequency of as low as 500 Hz, which is conducive to realising low-frequency broadband absorption.

Figure 9.

(A) Top views of C₁, C₂, and C₃; (B) simulated results for C₁, C₂, and C_3.

Influence of the panel aperture of micro-perforated panels

Figure 10(a) and (b) separately display the top views and SAC curves with the panel apertures d of 1, 0.8, and 0.6 mm on micro-perforated panels, respectively. The change of the panel aperture d can synchronously alter the equivalent resistance r_p and acoustic mass m_p of the structure. Thus, the ratio of the number of perforations in specimens D₁, D₂, and D₃ was set to 9:16:25 to ensure consistency with respect to the perforation rate. When keeping the resistance r_p constant, the reduction in panel aperture d leads to the decrease of the mass m_p. It can be seen from Figure 10(b) that the SAP gradually increases in high-frequency bands and the SAC peak of the CICS gradually shifts to a lower frequency as the panel aperture diameter d decreases and the frequency increases. In addition, by comparing the frequency bandwidths of various sound absorption curves, the sound absorption bandwidth increases with increasing diameter of panel aperture. As a result, appropriately shrinking the aperture in micro-perforated panels can improve the SAP of the CICS within the range of frequencies tested (and especially at f > 3000 Hz); however, as the aperture diameter is decreased, various peaks also gradually shift to higher frequencies.

Figure 10.

(A) Top views of D₁, D₂, and D₃; (B) Simulated results for D₁, D₂, and D_3.

Qian et al. ³⁷ reported that an efficient way to obtain high sound absorption over a wide frequency band is to reduce the diameter of the perforation and appropriately increase the density of the perforation. Figure 11(a) shows top views of specimens when changing only the panel aperture while keeping the number of perforations constant. The reduction in size of the panel aperture leads to the decreased rate of perforation of panels for a fixed number of perforations per micro-perforated panels. From the global perspective of the panels as an entity, the perforation rates are separately taken as η = 9%, 5.06%, and 3.24%. In this case, the peak bandwidth is narrower, and all peak frequencies experience a right-shift, running counter to expectation. Although the perforation rate has a qualitative effect on the sound absorption performance of the perforated plate material, the analysis of the influence of the geometric parameters of the perforated plate on the area of high sound absorption performance of the sound absorber also needs to consider the influence factors of the limit of the Ma Dayou theory.

Figure 11.

(A) Top view of E₁, E₂ and E₃, (B) Simulation results of E₁, E₂ and E_3.

When the number of holes is constant, the influence of the aperture is mainly concentrated at the peak of the resonance domain. The size of the aperture will affect the acoustic resistance and acoustic reactance of the structure. The calculation formula for the acoustic impedance ratio of MPP is:

$$Z_1={\displaystyle \frac{32\mu t}{\sigma d^2}\left(\sqrt{1+{\displaystyle \frac{k^2}{32}}}+{\displaystyle \frac{\sqrt{2}}{8}k{\displaystyle \frac{d}{t}}}\right)+{\displaystyle \frac{j\rho \omega t}{\sigma }\left(1+{\displaystyle \frac{1}{\sqrt{9+{\displaystyle \frac{k^2}{2}+0.85{\displaystyle \frac{d}{t}}}}}}\right)}}$$ (3)

d is the diameter of the hole, D is the depth of the cavity behind the plate, ρc is the characteristic impedance of the air, b is the hole spacing, t is the plate thickness, ρ is the air density, and c is the sound wave propagation velocity in the air. Z_D is the acoustic impedance rate of the cavity behind the board, and its value is:

$$Z_D=-j\rho ccot\left({\displaystyle \frac{\omega D}{c}}\right)$$ (4)

If the aperture is too small, the acoustic resistance will be too large, and the sound absorption coefficient will be greatly reduced. If the aperture is too large, when the perforation rate limit of the perforated plate is exceeded, the acoustic resistance will be very small, and there will be multiple low sound absorption coefficient troughs. Therefore, appropriate consideration should be given to the reasonable aperture and number of holes to improve the sound absorption performance of CICS.

Influence of the panel thickness

Figure 12 shows the SAC curves at different thicknesses (1, 1.5, and 2 mm) of micro-perforated panels: the trend in the SAC curves is similar to that when only changing the panel aperture (Figure 11(b)), that is, the first-order peak does not change to any significant extent, with a sound absorption efficiency of 98% or more; the second-order peak starts to vary remarkably. The comparison of the three groups of curves shows that, when increasing the thickness of the micro-perforated panels, the peak shifts to the left and the SAC increases; the global sound absorption effect is thereby enhanced. It can be seen from ① that the first-order peak also tends to show that the SAC increases while the peak frequency decreases as the panel thickness is increased.

Figure 12.

(A) Simulated results for F₁, F₂, and F₃, (B) the instantaneous local velocity of F₁ and F_3.

In order to clearly reveal the influence of the panel thickness on the sound absorption coefficient of the conch-like cavity sound absorber, the instantaneous local velocity field is shown in Figure 12 (b). It can be seen from the instantaneous local velocity field diagram that a large velocity field exists at the position of the perforated plate, and resonance is excited to cause the formation of a velocity boundary layer along the inner wall of the perforation. It can be seen that the energy dissipation in the incident panel mainly comes from the viscous loss of the perforated plate, which corresponds to the velocity boundary layer in the instantaneous local velocity field diagram. This indicates that a certain increase in the thickness of the panel is beneficial to enhance the energy dissipation of the incident sound wave.

In addition, comparing the 1.0 mm and 2.0 mm thickness plates in (b), it can be found that the dissipation is concentrated in the entrance area of the incident panel, so the increase in thickness cannot increase the viscosity loss once and for all.

Application of sound barrier with built-in conch-imitating cavity structure

Setup of noise source test model for high-speed railway

When CICS will be applied to railway sound barriers, before designing and optimising specific structural parameters, it is first necessary to analyze the sound source spectrum characteristics of the noise generated by the railway. The traditional single sound source prediction method is not suitable for high-speed railway noise prediction. The sound source layout refers to Measured value of vertical distribution characteristics of noise source of 368 km/h high-speed train. The simulation of noise sources in the current research includes single-point noise source, double-point noise source and multi-point noise source. Taking into account the vertical distribution characteristics of each noise source and the noise generation mechanism, as shown in Figure 13(a), the noise source is simplified to a three-equivalent sound source. The heights of the designed sound sources are 0.1 m, 2 m and 5 m above the track surface respectively, and the positions are shown as the blue marked points in Figure 14. The air is set as an ideal gas, and the track, car body and ground are assumed to be rigid bodies, and the background noise is ignored in the simulation calculation. The simulation results of the three-point sound source Figure 13(b) are compared with the noise source identification results of the Chinese standard EMU in Figure13(a). The errors are both less than 0.1%, which is considered reliable.

Figure 13.

(A) Three-equivalent sound source, (B) Sound source simulation.

Figure 14.

Sound source and measuring point location distribution.

Arrange the measuring points (7.5, 1.2), (7.5, 3.5), (25,3.5) according to the Measurement positions in ISO03095-2013, as shown in the red marked points in Figure 14.

In order to verify the correctness of the model, the test and simulation spectrum characteristics of three standard field points under the sound barrier working condition are compared. It can be seen from the figure that the simulation results are in good agreement with the measured results. The trend of the spectrum change law is consistent. The difference between the test and simulation results is within 3.5 dB, and the relative error rate does not exceed 4% Figure 15.

Figure 15.

Comparison of simulation results of measuring points.

Sound barrier model setting and application effect

The sound barrier with built-in conch type sound absorber is composed of double-layer aluminum plate and resin structure CICS, as shown in Figure 16. The CICS in the simulation is set to D1 above. A unit cell is 30cm*30 cm, and 1∼4 sound absorbers are installed respectively. The structural material parameters are set in Table 4.

Figure 16.

Sound barrier panel with built-in CICS.

Table 4.

Material parameter table.

Aluminum 3003	Young's modulus	E	6.8e9	Pa
	Poisson's ratio	nu	0.36	1
	Density	rho	2750	kg/m3
	Isotropic structure loss factor	eta_s	0.002	1
Resin 8200	Young's modulus	E	2.58e9-2.69e9	Pa
	Poisson's ratio	nu	0.4-0.44	1
	Density	rho	1120-1180	kg/m3
	Isotropic structure loss factor	eta_s	0.008	1

Studying sound-absorbing and insulating sound barriers is an important method to improve its noise reduction performance. When sound-absorbing materials are used in engineering applications, their specific effects are related to factors such as the structure of the sound-absorbing material, the installation position, and the incident angle of the sound source. The sound insulation effect of the rigid structure is unstable. When the sound barrier has sound absorption characteristics, it can effectively reduce the multiple sound wave reflections between the sound barrier and the high-speed train, and improve the noise reduction performance of the sound barrier. As shown in Figure 17(a), the built-in conch-shaped absorber Compared with double-layer aluminum panels and concrete walls, the sounder panels are at low frequencies below 1000 Hz, which can effectively increase the sound transmission loss. As shown in the sound pressure level test results of the three test points in Figure 17(b), the increase in the number of sound absorbers can further improve the noise reduction of the sound barrier, where (25, 3.5) has the largest change range, combined with the sound field cloud diagram in Figure 17(c). It is proved that increasing the number of sound absorbers can effectively increase the amount of noise reduction and has the greatest impact on the sound field in the high-frequency cut-off region. In practical applications, it can effectively prevent high-speed railways from sound pollution of surrounding high-rise buildings.

Figure 17.

(A) Sound insulation comparison, (B) The influence of the number of sound absorbers, (C) sound field cloud diagram of different number of sound absorbers.

The influence of sound barrier geometric design

The sound source of the sound field behind the sound barrier is mainly the top-side diffracted sound, the transmitted sound penetrating the sound barrier, and the reflected sound from the ground and the vehicle body. So we can increase the insertion loss by reducing the diffraction sound and transmission sound.

The existing standard sound barrier thickness of Chinese railways is 0.14 m. From the changes of the three field points, it can be found that the insertion loss of the sound barrier will not change significantly as the thickness changes from 0.1 m to 0.4 m, as shown in Figure 18(a). This is because increasing the thickness of the sound barrier mainly increases the loss of transmitted sound, but the transmission loss is not the main source of noise. Increasing the height of the sound barrier can effectively improve the diffraction of sound waves, thereby increasing the amount of sound insulation, as shown in Figure 18(b). According to the overall law of the sound pressure cloud diagram, the sound pressure level of the field point decreases with the increase in height at all frequencies, which has a greater impact on the rear far field, as shown in Figure 18(c).

Figure 18.

(A) The influence of thickness, (B) The influence of height, (C) sound pressure cloud graph with height.

In order to further realise the qualitative to quantitative, the relationship between the sound path difference and the height of the sound barrier is analyzed:

$$P_s^2=P_d^2{\displaystyle \frac{1}{3+{10}^N}}$$ (5)

$$D_{IL}=-10lg{\displaystyle \frac{1}{3+{10}^N}}$$ (6)

$$D_{IL}=10lg{\displaystyle \frac{\lambda }{3\lambda +{10}^{d_i}}}$$ (7)

Where $D_{IL}$ represents the sound insulation effect, N is the Fresnel number, P_S is the sound pressure of the diffracted sound field, P_d is the sound pressure of the direct sound field, λ is the wavelength, and d_i is the sound path difference.

The sound insulation effect is expressed by DIL (the logarithm of the insertion loss), so that the relationship function between the sound attenuation and the sound path difference can be obtained. It can be seen from Table 5 that as the sound attenuation increases, the sound path difference increases faster, so a larger sound path difference is required in exchange for the equivalent sound attenuation. However, when the positions of the noise source and the sound receiving point are determined, the external form can only be achieved by increasing the height of the sound barrier to achieve the amount of noise reduction. Moreover, it can be seen that the height of the sound barrier and the noise reduction effect is not a simple linear relationship, and only a certain height can have an actual impact on the noise reduction effect. Otherwise, increasing the height will only cause waste of engineering and materials.

Table 5.

The relationship between sound path difference and sound attenuation.

Sound loss (DIL)	7	8	9	10	11	12	13	14	15	16
Fresnel number (N)	0.13	0.26	0.5	0.8	1.2	1.8	2.5	3.3	4.2	5.7
Sound path Difference (di)	0.044	0.088	0.17	0.272	0.408	0.612	0.85	1.122	1.428	1.938

Conclusions

A resonant sound-absorbing structure (CICS) with good SAP and SIP at multiple frequencies was designed. The structure is easy to prepare and shows stability and an extremely strong SAP at low frequencies, allowing significant reductions in the thickness of noise barriers. Moreover, by adjusting various structural parameters of combinations of cavity forms, it is possible for the CICS to show multiple high-order peaks at intermediate frequencies (1000 to 3500 Hz). The main conclusions are drawn as follows:

1. The resonance frequency is only related to the cavity volume while remaining uncorrelated with the shape of the cavities. The shape of partitions between cavities does not influence the resonance frequency and SAC;

2. The number of divisions in the CICS directly affects the number of sound absorption peaks and the peaks will shift towards a higher frequency. By observing the frequency bands above 1000 Hz, it is seen that the area of micro-perforated panels changes the peak frequency and allows the left-shift thereof. As a result, more high-order peaks can be attained within the target frequency range.

3. When keeping the rate of perforation unchanged, the SAP is gradually enhanced in high-frequency bands and the peak SAC of the CICS gradually shifts to low-frequency bands with decreasing panel aperture diameter, thus, the sound absorption bandwidth of the CICS broadens;

4. The size of the apertures in micro-perforated panels and the rate of perforation exerts a significant influence on the SAP of the CICS. Within a certain range, the corresponding frequency of the sound absorption peak decreases while the SAC increases with increasing rate of perforation and panel thickness. The bandwidth of the CICS increases compared to that in conventional superimposed composite structures; the CICS can realise the broadband absorption of over 68.7% at frequencies below 3000 Hz; the first sound absorption peak at around 920 Hz exceeds 0.99, which is regarded as a nearly perfect absorption peak.

5. The panels of this structure can effectively increase the amount of noise reduction and have the greatest impact on the sound field in the high-frequency cut-off zone. In practical applications, it can effectively prevent high-speed railways from sound pollution of surrounding high-rise buildings.

Above all, compared to sound absorption materials with similar performances, the CICS allows a lower panel thickness and more sound absorption peaks; they also represent a simple structure at a low manufacturing cost As for the CICS, there are not only absorption peaks at low frequencies but also additional absorption peaks at relatively high frequencies. The metamaterials will find their extensive application in reducing noise in vehicle bodies and designing noise barriers in the rail-transit industry. Future research is recommended to attempt corresponding optimisation of the sound-absorbing structure aiming at various noise sources and their spectral characteristics in trains.