Drawer-like tunable ventilated sound barrier^a) Free

In the past few decades, sound insulation and absorption have always been hot topics in acoustics owing to their great potentials in noise control. Conventional methods of sound absorption mainly rely on porous and fibrous materials,^1,2 micro-perforated structures,^3,4 and sound-absorbing sponges.^5,6 However, these types of materials and structures inevitably have relatively large sizes in the low-frequency region.

Recently, the emergence of acoustic metamaterials^7–13 and metasurfaces^14–21 has provided alternative ways for noise control. In previous works, the sound absorption was realized based on a variety of resonant unit cells, such as Helmholtz resonators,^22–24 Fabry–Perot tubes,^25–27 sound membranes,^28–32 and coupled non-local resonators,³³ in which sound energy is generally dissipated inside these unit cells. In addition, the other types of unit cells were designed to realize sound absorbers with sub-wavelength thicknesses, including splitting resonators,³⁴ ultra-thin metasurface-based structures,^35–37 and coherent perfect absorbers.^38,39 These absorber structures generally have high performance of low-frequency sound absorption. However, in some application scenarios, both functions of sound insulation and ventilation are required simultaneously. To overcome this, researchers have designed a variety of open sound insulation structures, such as resonantly coupled structures,^40,41 open sound silencers,^42,43 ultra-sparse sound-insulation walls,⁴⁴ and window structures,^45,46 to simultaneously realize both performances of ventilation and sound insulation. Generally, these designs have passive structures and fixed working bands, which are unable to apply to some special scenes with variable noise frequencies. On the other hand, broadband acoustic absorbers usually contain different resonant frequency unit cells,^47,48 which inevitably increases manufacturing difficulty and cost.

To solve this problem, tunable sound absorbers have attracted great attention in recent years.^49–52 One type is based on multi-layer ring-shaped microslit tubes,^49,50 in which the resonance frequency can be changed by tuning the rotation angle of the middle microslit tube. In these designs, rigid walls are required to prevent sound transmissions, which also forbid free exchange of air on both sides of the sound absorber. The other type is ventilated metamaterials, such as a labyrinthine-like structure with a zigzag channel composed of two interposed fingers,⁵¹ and a composite unit cell contains two identical Helmholtz resonators with spatial inversion symmetry.⁵² By moving the position of the slider in each unit cell, the working band can be modulated above 300 Hz. However, in the low-frequency region (below 200 Hz), the realization of a ventilated sound insulation structure with a tunable working band and high-performance ventilation still faces a great challenge.

In this work, we propose a type of drawer-like tunable ventilated sound barrier with low-frequency bandwidth optimization. Different from previous works, the unit cell of the bound barrier designed here is composed of a pair of oppositely oriented Helmholtz resonators. Each Helmholtz resonator has a drawer-like movable structure that can be used to control the resonance frequency of the unit cell. By arranging the unit cells into a monolayer periodic lattice, we have designed a ventilated sound barrier with low-frequency sound insulation, attributing to sound reflection and absorption caused by the coupling of symmetric and anti-symmetric modes. The fractional bandwidth (the ratio of the bandwidth to the center frequency) is around 4.5%. The working bandwidth of the ventilated sound barrier can be precisely controlled by tuning the position of the drawer-like movable structure. Furthermore, we have optimized the bandwidth of the ventilated barrier by using two types of dual-layer unit cells composed of two and four pairs of oppositely oriented Helmholtz resonators, in which the measured fractional bandwidths can be increased to 14.8% and 31.8%, respectively.

As schematically shown in Fig. 1(a), we designed a type of tunable low-frequency ventilated sound barrier composed of a single layer of periodic unit cells. Figure 1(b) shows the cross section of the unit cell that is composed of two oppositely oriented Helmholtz resonators. Each Helmholtz resonator consists of a central rectangular cavity surrounded by two coiling-up channels. The drawer-like structure (red solid) can be flexibly moved along the y direction, and therefore, by moving the drawer-like structure with the distance of d, we can change the size of the central cavity, thus realizing the control of the resonance frequency. In addition, the distance between two adjacent unit cells l, the length of the resonator a, the wall thickness e, and the width of the channel t are selected as 400, 100, 2, and 6 mm, respectively. It is worth noting that the distance l is twice as long as the length (2a) of the unit cell and the ventilation ratio (the ratio of the open length to the overall length) is 50%, indicating high-performance ventilation of the ventilated barrier. The unit cell is fabricated with epoxy resin by three-dimensional (3D) printing technology, as shown in Fig. 1(c). Throughout this work, we use the software of comsol multiphysics (COMSOL AB, Stockholm, Sweden) to simulate sound characteristics. In the models, we use the module of thermoviscous acoustic-solid interaction in the internal region of the unit cell and the module of acoustic pressure in the other region for less calculation. The density and longitudinal and transversal wave velocities of epoxy resin are selected as ρ = 1180 kg/m³, c_l = 2720 m/s, and c_t = 1460 m/s, respectively, and the density and the sound velocity of air are determined by ρ = p₀M/RT and $c0=γRT/M$⁠, respectively, in which the parameters γ, M, T, R, and p₀ are selected as 1.4, 28.97 × 10⁻³kg/mol, 293 K, 8.31 J/(mol/K), and 101.325 kPa, respectively.

To verify the performance of the tunable low-frequency ventilated sound barrier, we conduct an experiment to measure its performance. The details of the experiment set-up and measurement method are presented in Note 1 in the supplementary material. Figure 2(a) shows the measured transmittance spectrum (the red open circles) of the ventilated barrier with d = 0 mm, and the simulated results (the blue solid line) are plotted for comparison. We observe that there exists a valley at 155 Hz in the transmission spectrum, and the transmittances are below −5 dB in the range of 151–158 Hz (the black shaded region), and the fractional bandwidth is about 4.5%. The measured results agree well with the simulated ones. To further present the performance of the ventilated barrier, we measure the absorptance and reflectance spectra caused by the ventilated barrier. As shown in Fig. 2(b), the maximum absorptance can reach about 0.65 and the maximum reflectance is about 0.3, indicating that the sound insulation arises from both sound absorption and reflection caused by the ventilated barrier. In addition, we discuss the feasibility of optimizing the performance of the ventilated sound barrier by tuning structural parameters of the unit cells. Here, we take the folding times of the coiled-up channels and the width of the central cavity as examples, and the simulated results are presented in Note 2 in the supplementary material. Furthermore, we investigate the influence of the distance between adjacent unit cells on the sound insulation of the ventilated sound barrier. The simulated results are presented in Note 3 of the supplementary material.

To provide an insight into the mechanism of sound insulation, we simulate the pressure and phase eigenfunctions of the unit cell with d = 0 mm. As shown in Figs. 2(c) and 2(d), there exist two types of eigenmodes at 153.7 and 157.7 Hz for the unit cell, which are denoted as symmetric and anti-symmetric modes, respectively, owing to their distribution characteristics. For the symmetric mode, the pressure and phase distributions in both cavities of the unit cell are the same [Fig. 2(c)]. However, for the anti-symmetric mode, the phase distributions are opposite in both cavities [Fig. 2(d)]. Both modes are closely related to the structure characteristics of the unit cell. Figure 2(e) shows the simulated pressure and phase distributions of the unit cell under the excitation of the normal incidence of sound (the red arrows) at 155 Hz. We can see that the pressure and phase distributions are similar to those of the anti-symmetric mode [Fig. 2(d)], but the phase difference of the two cavities (less than π) is between those of the symmetric and antisymmetric modes, and so does the frequency of the excited mode. Thus, the excited mode at 155 Hz arises from the coupling of the symmetric and anti-symmetric modes. Furthermore, we simulate the velocity and viscous loss density distributions of air in the unit cell at 155 Hz. As shown in Fig. 2(f), the velocity of air in the coiling-up channels is larger than that in the center cavities, and the viscous loss density of sound energy around the inner wall of the channel as well as the interface between the channels and the center cavities are very strong, indicating that the sound absorption arises from the loss of sound energy in the unit cell with narrow space. Thus, we demonstrate that the sound insulation arises from both sound reflection and absorption caused by the coupling of the symmetric and anti-symmetric modes, and part of the sound energy is dissipated in the coiling-up channels due to viscous loss. Here, we also theoretically study the sound absorption based on the symmetric and anti-symmetric modes of the unit cell, which is presented in Note 4 in the supplementary material.

Next, we discuss the performance of the ventilated barrier by tuning the position of the drawer-like structure in each unit cell. Figure 3(a) shows the simulated transmittance spectra of the ventilated barriers with different values of d. We can see that, with the increases of d, the working band of the sound insulation moves to the lower-frequency region, and the frequency of the valley decreases from 155 to 122 Hz, indicating that the working band of the ventilated barrier can be precisely controlled by tuning the position of the drawer-like structure. To experimentally demonstrate it, we measure the transmittance spectra of the ventilated barriers with d = 5, 15, 25, 35, and 45 mm, which are shown in Fig. 3(b). The simulated results are provided for comparison. We can observe that the frequencies of the valley are 152, 148, 142, 135, and 124 Hz for the ventilated barriers with d = 5, 15, 25, 35, and 45 mm, respectively. The measured spectra agree with the simulated ones, which are also consistent with the characteristics of the spectra in Fig. 3(a). Therefore, the working band of the ventilated barrier can be controlled by simply tuning the position of the drawer-like structure in each unit cell, showing a promising application prospect.

In addition, we simulate the excited pressure and viscous loss density distributions in the unit cells with different values of d at these valley frequencies, which are shown in Fig. 3(c). We can see that the excited field distributions in these unit cells are similar to those in Figs. 2(e) and 2(f), indicating that the sound insulation of these ventilated barriers is still closely related to the coupling of the symmetric and anti-symmetric modes.

Next, we discuss the bandwidth optimization of the ventilated barrier. As shown in Fig. 4(a), the optimized barrier is composed of periodic dual-layer unit cells, in which the interlayer distance h = 150 mm, and the parameters d₁, d₂, d₃, and d₄ represent the moving distances of the draw-type structures in each unit cell, and the other parameters are the same as those in Fig. 1(a). Figure 4(b) shows the measured and simulated transmittance spectra of the ventilated barrier with d₁ = d₂ = d₃ = d₄ = 0 mm. It is observed that, in the range of 148.7–164.7 Hz (the black dashed region), the transmittances are below −5 dB and the fractional bandwidth is 10.4%, which is about 2.3 times that in Fig. 2(a). Here, it is worth noting that the working band of the ventilated barrier can be controlled by tuning the values of d₁, d₂, d₃, and d₄. To verify it, we measure and simulate transmittance spectra of the ventilated barriers with different parameter combinations of d₁, d₂, d₃, and d₄. As shown in Fig. 4(c), by selecting d₁ = d₃ = 0 mm and d₂ = d₄ = 15 mm, there exist two valleys in the transmittance spectra owing to two different values of d₁, d₂, d₃, and d₄. Thus, the fractional bandwidth can reach about 12.3%, and both measured and simulated results basically agree with each other. Additionally, by selecting d₁ = d₃ = 15 mm and d₂ = d₄ = 30 mm [Fig. 4(d)], the working band moves to the lower-frequency region gradually and the fractional bandwidth can be further optimized to 14.8%, which is nearly about 3.3 times that in Fig. 2(a). It is therefore demonstrated that the bandwidth of the ventilated barrier can be improved by using the dual-layer structures, and the working band and bandwidth can be controlled by tuning the parameter combinations of d₁, d₂, d₃, and d₄ in each dual-layer unit cell.

Furthermore, we further improve the working bandwidth of the ventilated barrier by using a type of dual-layer unit cell composed of eight oppositely oriented Helmholtz resonators. As shown in Fig. 5(a), the distance between two adjacent unit cells l₁ = 60 cm and the opening width of ventilation is the same as that in Fig. 1(a), indicating that the corresponding ventilation ratio is about 33.3%. In addition, the moving distances of eight drawer-like structures are denoted as d₁, d₂, d₃, d₄, d₅, d₆, d₇, and d₈, and the other parameters are the same as those in Fig. 4(a). Figures 5(b)–5(d) show the measured and simulated transmittance spectra caused by the dual-layer ventilated barriers with different parameter combinations of d₁, d₂, d₃, d₄, d₅, d₆, d₇, and d₈. As shown in Fig. 5(b), for d₁ = d₂ = d₃ = d₄ = d₅ = d₆ = d₇ = d₈ = 0 mm, the working band of the ventilated barrier can cover the range of 139.2–180.2 Hz (black shaded region), and the fractional bandwidth is about 25.7%, which is nearly about 2.5 times that in Fig. 4(b). In addition, by selecting d₁ = d₂ = d₇ = d₈ = 0 mm and d₃ = d₄ = d₅ = d₆ = 15 mm, the working band can extend to the lower-frequency region [133.6–179.6 Hz, the black shaded region in Fig. 5(c)], and the fractional bandwidth can reach about 29.3%. By selecting d₁ = d₂ = d₇ = d₈ = 15 mm and d₃ = d₄ = d₅ = d₆ = 30 mm, the working band moves to the lower-frequency region [124.8–172.2 Hz, the black shaded region in Fig. 5(d)], and the fractional bandwidth is increased to 31.8%, which is about 3 times that in Fig. 4(b). Compared with the results in Figs. 4(b)–4(d), the change tendency of the working band is almost the same, but the bandwidths of the dual-layer ventilated barriers are greatly improved. Moreover, we discuss the transmittance spectra of two dual-layer ventilated barriers with different values of d₁, d₂, d₃, d₄, d₅, d₆, d₇, and d₈, and the simulated results are added in Note 5 in the supplementary material. Finally, we present a comparison between the performance of our design and those of previous ventilated sound barriers, which are presented in Note 6 in the supplementary material. We obtain that the fractional bandwidth of our design is slightly lower than that in Ref. 52, but the ventilation ratio and thickness are better than those of the other types of sound barriers.

In conclusion, we have experimentally demonstrated a type of drawer-like tunable ventilated sound barrier with low-frequency bandwidth optimization. To realize the sound insulation and its manipulation, we designed a type of unit cell composed of a pair of oppositely oriented Helmholtz resonators. Each Helmholtz resonator has a movable drawer-like structure that can be used to change the size of the central cavity and control the resonance frequency. By arranging a single layer of periodic unit cells with d = 0 mm, we designed the ventilated sound barrier with the fractional bandwidth of 4.5%. Such a phenomenon arises from sound reflection and absorption caused by the coupling of symmetric and anti-symmetric modes. By tuning the position of the drawer-like structure, we can precisely control the working band of the ventilated barrier. Furthermore, by designing two types of dual-layer unit cells composed of two and four pairs of oppositely oriented Helmholtz resonators, we can optimize the working bandwidth of the ventilated barrier, and their fractional bandwidths can reach about 14.8% and 31.8%, respectively. Our work paves the way to design low-frequency sound insulation structures with both tunable and ventilated functions, which may have a great potential in the applications of low-frequency noise control and architectural acoustics.

See the supplementary material for the experiment setup and measurement method, the performances of two types of unit cells with folding times of coiled-up channel N = 4 and width of central cavity b = 54 mm, the simulated transmittance spectra of ventilated barriers with different values of l, the theoretical analysis of sound absorption for symmetric and anti-symmetric modes, the simulated transmittance spectra of two dual-layer ventilated barriers with different values of d₁–d₈, and the comparison between our work and previous ventilation sound barriers.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12274183, 12174159, 12174188, 12474293, 52479083, 11974176, and 51976079), the National Key Research and Development Program of China (Grant No. 2020YFC1512403), and the Research Project of the State Key Laboratory of Mechanical System and Vibration (Grant No. MSV202201).

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.