Pneumatically-Actuated Acoustic Metamaterials Based on Helmholtz Resonators

materials

Article Pneumatically-Actuated Acoustic Metamaterials Based on Helmholtz Resonators

Reza Hedayati * and Sandhya Lakshmanan

Novel Aerospace Materials group, Faculty of Aerospace Engineering, Delft University of Technology (TU Delft), Kluyverweg 1, 2629 HS Delft, The Netherlands; [email protected] * Correspondence: [email protected] or [email protected]

Received: 24 February 2020; Accepted: 19 March 2020; Published: 23 March 2020

Abstract: Metamaterials are periodic structures which offer physical properties not found in nature. Particularly, acoustic metamaterials can manipulate sound and elastic waves both spatially and spectrally in unpreceded ways. Acoustic metamaterials can generate arbitrary acoustic bandgaps by scattering sound waves, which is a superior property for insulation properties. In this study, one dimension of the resonators (depth of cavity) was altered by means of a pneumatic actuation system. To this end, metamaterial slabs were additively manufactured and connected to a proportional pressure control unit. The noise reduction performance of active acoustic metamaterials in closed- and open-space configurations was measured in different control conditions. The pneumatic actuation system was used to vary the pressure behind pistons inside each cell of the metamaterial, and as a result to vary the cavity depth of each unit cell. Two pressures were considered, P = 0.05 bar, which led to higher depth of the cavities, and P = 0.15 bar, which resulted in lower depth of cavities. The results showed that by changing the pressure from P = 0.05 (high cavity depth) to P = 0.15 (low cavity depth), the acoustic bandgap can be shifted from a frequency band of 150–350 Hz to a frequency band of 300–600 Hz. The pneumatically-actuated acoustical metamaterial gave a peak attenuation of 20 dB (at 500 Hz) in the closed system and 15 dB (at 500 Hz) in the open system. A step forward would be to tune different unit cells of the metamaterial with different pressure levels (and therefore different cavity depths) in order to target a broader range of frequencies.

Keywords: active noise control; acoustic metamaterial; broadband noise attenuation; pneumatic actuation; Helmholtz resonators

1. Introduction Metamaterials are periodic designer materials which offer physical properties not found in nature [1]. Particularly, acoustic metamaterials can manipulate sound and elastic waves both spatially and spectrally in unpreceded ways [2]. Such properties include super-focusing [3], super-lensing [4], active membrane structures [5,6], cloaking [7,8], phononic plates [9], fluid cavities separated by piezoelectric boundaries [10], and tunable noise attenuation based on Helmholtz resonators [11–15]. The capability of metamaterials to tune their physical behavior just based on their geometrical characteristics offers a great benefit over conventional materials for application in various high-demand industries such as aerospace, automobile, and construction. Increase in importance of customer comfort in transportation and construction sectors as well as consumer goods has been a driving force for recent advancements in acoustic metamaterials in the field of noise control. Acoustic metamaterials can generate arbitrary acoustic bandgaps by scattering sound waves, which is a superior property for insulation properties. Initially, the acoustic metamaterials were passive; their performance remained unchanged and it was in accordance to the design values [16–18]. More recently, the concept of tunable acoustic

Materials 2020, 13, 1456; doi:10.3390/ma13061456 www.mdpi.com/journal/materials Materials 2020, 13, 1456 2 of 11

Materialsmetamaterials 2020, 13, x FOR has PEER emerged REVIEW in which acoustic metamaterials are able to manipulate sound2 waves of 11 in various conditions [6–8,19–21]. Active acoustic metamaterials can be responsive to different stimuli, varioussuch conditions as electric [6–8,19–21]. field [21], electromagnetic Active acoustic field meta [6,materials22], mechanical can be loadresponsive [11], and to electricitydifferent stimuli, by means of suchpiezoelectric as electric field elements [21], electromagnetic [7]. field [6,22], mechanical load [11], and electricity by means of piezoelectricAcoustic elements metamaterials [7]. are widely preferred in applications where high efficiency in noise reductionAcoustic metamaterials is expected. As are an widely important preferred design in parameter applications in this where regard high is simplicityefficiency inin designnoise yet reductionbeing is eff expected.ective in performance, As an important Helmholtz design resonance parameter provides in this regard a lucrative is simplicity solution (Figurein design1). yet Due to beingits effective simplistic in geometricalperformance, characteristics, Helmholtz resonance Helmholtz provides resonators a lucrative have been solution incorporated (Figure 1). into Due acoustic to its simplisticmetamaterials. geometrical The Helmholtz characteristics, resonator Helmholtz is a phenomenon resonators where have been acoustic incorporated resonance into is created acoustic when a metamaterials.gas (typically The air) Helmholtz passes over resonator the opening is a phenom (also calledenon neck) where of acoustic an enclosed resonance cavity. is The created system when working a gasresembles (typically that air) of passes a mass-spring over the system.opening The (als airo called inside neck) the cavity of an works enclosed as a springcavity. andThe the system air in the workingneck resembles works as athat mass. of a When mass-s anpring incoming system. air The pressure air inside acts the upon cavity the airworks occupying as a spring the neckand the region, air init the pushes neck itworks down as into a mass. the cavity. When Hence,an incoming the air air inside pressure the cavity acts upon becomes the air compressed occupying andthe neck attempts region,to retainit pushes its originalit down volume.into the cavity. This pushes Hence, back the theair inside air inside the thecavity neck becomes and creates compressed a counteracting and attemptsacoustic to retain resonance its original with respect volume. to the This initial pu incomingshes back acousticthe air wave.inside Whenthe neck the airand pressure creates insidea counteractingthe cavity acoustic decreases, resonance it sucks airwith around respect the to neck the area initial back incoming again, and acoustic this phenomenon wave. When repeats the air itself pressureseveral inside times the making cavity the decreases, air inside theit sucks cavity workair around similar the to aneck spring. area In recentback years,again, thereand hasthis been phenomenonextensive repeats research itself in development several times of making acoustic the metamaterials air inside the constructedcavity work fromsimilar Helmholtz to a spring. resonator In recentunit years, cells there [13–15 has] to been generate extensive tunable research band in gaps. development of acoustic metamaterials constructed from HelmholtzThe Helmholtz resonator resonator unit cells equation [13–15] isto [generate23] tunable band gaps. The Helmholtz resonator equation is [23] r c A f = (1) = 2π VL (1) where c is the speed of sound in the medium (i.e., air), L is the neck length, A is the neck cross-sectional wherearea, is and theV speedis the of volume sound ofin mediumthe medium in the (i.e., cavity. air), As is it the can neck be deduced length, from is the Equation neck cross- (1), three sectionalgeometrical area, and characteristics is the volume (cross-sectional of medium in area theA cavity.and length As it canL of be neck deduced as well from as theEquation volume (1), of the threecavity geometricalV) can becharacteristics actively altered (cross-sectional to produce tunabilityarea and in length the performance of neck ofas metamaterial.well as the volume The most of theconvenient cavity ) can way be to actively actively altered adjust to the produce performance tunability of metamaterialin the performance is tuning of metamaterial. the cavity volume The as mostthe convenient actuation way system to actively would adjust not need the toperforma performnce in of the metamaterial vicinity of the is tuning neck where the cavity the metamaterial volume as theinteracts actuation the system most with would incoming not need external to perform sound in pressures.the vicinity of the neck where the metamaterial interacts the most with incoming external sound pressures.

Air at the Air jet m neck Neck of Air at Inside air bottle atmospheric compressed

FigureFigure 1. Phenomenon 1. Phenomenon of Helmholtz of Helmholtz resonance resonance where where air in airside inside the cavity the cavity is modelled is modelled as a spring as a spring massmass system system (redrawn (redrawn from from[24]). [ 24]).

Sui etSui al. et [25] al. designed [25] designed and tested and tested light-weight light-weight yet sound-proof yet sound-proof acoustic acoustic metamaetrials metamaetrials made made of of hexagonalhexagonal honeycomb honeycomb structure structure covered covered by by a arubbery rubbery memberane memberane sheet. CoveringCovering thethe sandwich sandwich panel panelwith with the the membrane membrane resulted resulted in an in increasedan increased sound sound transmission transmission loss up loss to 25updB to at25f dB= 200 at f Hz= 200. In Hz. another In anotherhoneycomb-based honeycomb-based structure, structure, Claeys etClaeys al. [26 ]et introduced al. [26] introduced a vibro-acoustic a vibro-acoustic acoustic metamaterial acoustic in metamaterialwhich they in hadwhich implemented they had implemented resonant elements resonant onto elements the unit onto cell the of unit a rectangular cell of a rectangular core structure. core Theystructure. investigated They investigated the most inﬂuencing the most influenc parametersing parameters of their passive of their metamaterial passive metamaterial using numerical using and numericalexperimental and experimental methods. Themethods. relative The mass relative of the mass added of the resonant added structureresonant tostructure the host to structure the host was structurefound was to befound the mostto be inﬂuencingthe most influe parameterncing parameter on the noise on attenuation.the noise attenuation. As one of the first examples of adaptive acoustic systems based on Helmholtz resonators, Estève and Johnson [27] implemented a motorized iris diaphragm in the neck region of a simply supported cylinder (56 cm in length and 12.7 cm in diameter) to attenuate noise. They externally altered the neck opening diameter from 9 to 58 mm, which led to narrow-band noise reduction of maximum 8 dB in frequencies of 63, 82, and 103 Hz.

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As one of the first examples of adaptive acoustic systems based on Helmholtz resonators, Estève and Johnson [27] implemented a motorized iris diaphragm in the neck region of a simply supported cylinder (56 cm in length and 12.7 cm in diameter) to attenuate noise. They externally altered the neck opening diameter from 9 to 58 mm, which led to narrow-band noise reduction of maximum 8 dB in frequencies of 63, 82, and 103 Hz. Different types of actuation systems have been explored in previous studies for altering various dimensional parameters of active Helmholtz resonators (see Table1). Birdsong and Radcli ffe [28] designed a tunable semi-active Helmholtz resonator (SHR) that was able to reduce the resonance frequency and peak magnitude of noise in the frequency range of 60–180 Hz effectively. Their system was designed to be most effective in reducing noise in primary acoustic systems, such as ducts or pipes, by actively changing the cavity depth using electronic actuators. Bedout et al. [29] proposed another tunable resonator design that operated on the basis of radially blocking parts of cylindrical cavity volume by means of a rotary-actuated moving plate. Their design demonstrated up to 29 dB noise reduction in the frequency range of 65–150 Hz. Nagaya et al. [30] introduced a rotary two-stage Helmholtz resonator that had auto-tuning control capabilities at both low (100–3000 Hz) and high frequencies (1000–3000 Hz) for application in typical blowers.

Table 1. Comparison of performance and actuation technique of metamaterials based on Helmholtz resonators.

Range of Range of the Type of Volume Decrease in Type (self-Tuning, Frequency Actuation Type Changing Ref. Change (neck/cell). Noise (dB) Active, Adjustable) (Hz) Parameter Cavity length 100% 80–170 Pneumatic N/A Adjustable [28] Rotary-actuated Neck diameter 4.2 dB 75–115 9–58 mm Adjustable [27] aperture Volume (Sector 29 dB 65–150 Rotary-actuated walls 1491–14,093 cm3 Self-tuning [29] angle change) Cavity length 20 dB - Hydraulic 43–243 mm Active [31] 50–500 Electromagnetic Internal pressure - N/A Active [32] (Max-160) diaphragm/piezoelectric 0–400 Cavity length 18 dB - 60–90 mm Adjustable [33] (Max-226) Neck length - 3–75 Hydraulic 39–60 cm Adjustable [34] 560–940 cm3 Length of cavity 30 dB 80–140 Pneumatic Adjustable [35] 1.8–17 cm Area of neck 25 dB 100–3000 Rotary - Self-tuning [30]

Due to reasons mentioned above, the most logical way to control the dimensions of a Helmholtz resonator in an active system would be to change the volume of the resonator cavity. In this study, this method is realized by altering one dimension of the resonators (depth of cavity) by means of pneumatic actuation system. To this end, metamaterial slabs are additively manufactured and connected to a proportional pressure control unit. The noise reduction performance of active acoustic metamaterials in closed- and open-space conﬁgurations are measured in diﬀerent control conditions.

2. Materials and Methods

2.1. System Design Two types of systems were considered for acoustic measurements: an open system and a closed system (Figure2). The closed system consisted of a cube, 5 walls of which was made up of 8 8 arrays × of unit cells together constructing a plate metamaterial. Each unit cell had a cavity with a depth of 42 mm and a cross-section of 14 14 mm2 and a neck of diameter of 1.2 mm and length of 14 mm. × A speaker was placed in the middle of the system, and the noise mitigation was measured outside the cube and 15 cm away from the walls of the cube. The open system composed of two long aluminum Materials 2020, 13, 1456 4 of 11 channels with square cross-section linked together via a 4-walled cubic metamaterial in the center. Materials 2020, 13, x FOR PEER REVIEW 4 of 11 A speaker was placed at one side of the main channel and the noise was measured at the other end of thethe tube. tube. The The noise noise attenuation attenuation levels levels were were measured measured with with a a microphone microphone for for different diﬀerent frequencies to determine the performance of the metamaterials metamaterials at different diﬀerent frequencies. A Sennheiser Sennheiser e908B e908B cardioid cardioid condenser microphone (frequency (frequency response response of of 40 40–20,000–20,000 Hz, Hz, Sennheiser, Sennheiser, Wedemark, Wedemark, Germany) was used as the recording instrument. The The sound sound pressure pressure levels levels (SPL) (SPL) were were obtained by by taking a fast Fourier transform (FFT) (FFT) of of the recorded sound clips, thus changing the output from a time domain plot to a frequency domain plot. These These plots plots were were normalized with with respect respect to a reference ambient pressure plot.

(a) (b)

Figure 2. 2. (a) (Opena) Open and and(b) closed (b) closed systems systems design design to measure to measure the performance the performance of active of acoustic active metamaterials.acoustic metamaterials.

Four typestypes ofof noise noise samples, samples, namely namely white white noise, nois pinke, pink noise, noise, brown brown noise, noise, and a and frequency a frequency sweep of 10,000 20 Hz→ were used for the acoustic tests. A tone generator application was used to produce sweep of→ 10,000 20 Hz were used for the acoustic tests. A tone generator application was used to produceeach of the each noted of the noise noted samples. noise samples. The difference The differen betweence colorsbetween of noisecolors used of noise in this used study in this is described study is describedbelow [11 ]:below [11]: • WhiteWhite noise: noise: white white noise noise has a has uniform a uniform signal signal power power intensity intensity distribution distribution at all frequenciesat all frequencies when • whenfrequency frequency is is plotted plotted in in Hz Hz scale, scale, giving giving a a uniform uniform power power spectral spectral density. density. • Pink noise: In homogeny with white noise, the pink noise has a uniform power distribution Pink noise: In homogeny with white noise, the pink noise has a uniform power distribution if the if• the bandwidth is plotted in a logarithmic scale. Consequently, if the frequency spectrum is plotted bandwidth is plotted in a logarithmic scale. Consequently, if the frequency spectrum is plotted linearly, the sound magnitude is mainly concentrated at the lower end of the spectrum. linearly, the sound magnitude is mainly concentrated at the lower end of the spectrum. • Brown noise: In brown noise, the power amplitude decreases with a proportion of 1/, Brown noise: In brown noise, the power amplitude decreases with a proportion of 1/ f 2, with with• respect to frequency. In other words, in brown noise sample, the power amplitude decreases 6 respect to frequency. In other words, in brown noise sample, the power amplitude decreases 6 dB dB per octave. per octave. • A frequency sweep of 10,000→20 Hz to provide a diverse range of narrow-band frequency A frequency sweep of 10,000 20 Hz to provide a diverse range of narrow-band frequency tones tones• while measuring loudness in→ real time. while measuring loudness in real time. 2.2. Manufacturing 2.2. Manufacturing A metamaterial slab equipped with pneumatic actuation is demonstrated in Figure 3. In theory, A metamaterial slab equipped with pneumatic actuation is demonstrated in Figure3. In theory, each individual unit cell has the capability of having a different cavity depth. Each cavity has a piston each individual unit cell has the capability of having a different cavity depth. Each cavity has a piston the location of which can be tuned through varying the pressure of an inflatable balloon under it the location of which can be tuned through varying the pressure of an inflatable balloon under it (Figure 4). The metamaterial walls, pistons were additively manufactured using Fused Deposition Modeling (FDM) additive manufacturing (AM) technique. Polylactic acid (PLA) was chosen as the printing material, and Ultimaker 2+ and Ultimaker 3 3D printer apparatus (Untilmaker, Utrecht, Netherlands) were used. To establish a comparative device for the performance of the metamaterial, a solid plate of similar mass (430 g) was manufactured using the same manufacturing technique and

Materials 2020, 13, 1456 5 of 11 Materials 2020, 13, x FOR PEER REVIEW 5 of 11 settings and used a reference case. Such cases will be named as “plain isolators” in the remaining of (Figure4). The metamaterial walls, pistons were additively manufactured using Fused Deposition the manuscript.Materials 2020, 13 , x FOR PEER REVIEW 5 of 11 Modeling (FDM) additive manufacturing (AM) technique. Polylactic acid (PLA) was chosen as the Balloons create the minimum and maximum depths at respectively their inflated and deflated printingsettings material, and used and a reference Ultimaker case. 2+ Suchand cases Ultimaker will be named 3 3D printer as “plain apparatus isolators” (Untilmaker,in the remaining Utrecht, of status. The only drawback of this mechanism is that the accuracy of depths of the cavities is in Netherlands)the manuscript. were used. To establish a comparative device for the performance of the metamaterial, millimeter range, as particular air pressures can lead to slightly different balloon inflation in different a solid plateBalloons of similar create massthe minimum (430 g) was and manufacturedmaximum depths using at respectively the same manufacturing their inflated and technique deflated and unit cells depending on the friction between the piston and inner walls of each unit cell. settingsstatus. and The used only a referencedrawback case.of this Such mechanism cases will is bethat named the accuracy as “plain of isolators”depths of the in thecavities remaining is in of the manuscript.millimeter range, as particular air pressures can lead to slightly different balloon inflation in different unit cells depending on the friction between the piston and inner walls of each unit cell.

(a) (b) (c) (a) (b) (c) Figure 3. (a) Schematic of a metamaterial slab equipped with actuating balloons; (b) schematic of variationFigureFigure 3. of( a3. the) ( Schematica )cavity Schematic depths of of a metamaterialawith metamaterial balloons slabinslab the equippedequipped deflated with withand actuatinginflated actuating states;balloons; balloons; (c) (imageb) ( bschematic) schematicof actuation of of ofvariation a 3D-printedvariation of the of cavitytheunit cavity cell depths in depths the with deflated with balloons balloon and insinflated in the the deflated deflated states. and and inflated inflated states;states; (c) image image of of actuation actuation of a 3D-printedof a 3D-printed unit cell unit in cell the in deflated the deflated and and inflated inflated states. states.

Figure 4. The pneumatic actuation system used for inflating and deflating balloons in the active FigureFigureacoustic 4. TheThe metamaterial. pneumatic pneumatic actuation actuation system system used used for for infl inflatingating and and deflating deflating balloons balloons in in the the active acousticacoustic metamaterial. 2.3. Actuation Balloons create the minimum and maximum depths at respectively their inflated and deflated 2.3. Actuation status. TheThe pneumatic only drawback inlets of of each this balloon mechanism are connect is thated theto a accuracydigital pressure of depths regulator of the controlled cavities by is in a house-made software made by LabView. The pressure controller consists of different units such as millimeterThe pneumatic range, as inlets particular of each air balloon pressures are can connect lead toed slightly to a digital different pressure balloon regulator inflation controlled in different by power unit, processing unit, Input/output (IO) controller, and four proportional pressure controllers aunit house-made cells depending software on made the friction by LabView. between The the pressure piston and controller inner walls consists of each of different unit cell. units such as (VEAB-L-26-D9-Q4-V1-1R1, Festo, Delft, The Netherlands), see Figure 4. Since the number of power unit, processing unit, Input/output (IO) controller, and four proportional pressure controllers proportional pressure controllers is limited to four, a splitter (Figure 5a,b) is manufactured for the (VEAB-L-26-D9-Q4-V1-1R1, Festo, Delft, The Netherlands), see Figure 4. Since the number of outlet of each pressure controller so that pressure provided by the pressure controller can be proportional pressure controllers is limited to four, a splitter (Figure 5a,b) is manufactured for the outlet of each pressure controller so that pressure provided by the pressure controller can be

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2.3. Actuation The pneumatic inlets of each balloon are connected to a digital pressure regulator controlled by a house-made software made by LabView. The pressure controller consists of diﬀerent units such as power unit, processing unit, Input/output (IO) controller, and four proportional pressure controllers (VEAB-L-26-D9-Q4-V1-1R1, Festo, Delft, The Netherlands), see Figure4. Since the number ofMaterials proportional 2020, 13, x pressureFOR PEER controllersREVIEW is limited to four, a splitter (Figure5a,b) is manufactured for6 theof 11 outlet of each pressure controller so that pressure provided by the pressure controller can be transferred totransferred several unit to several cells of metamaterialunit cells of metamaterial (Figure5c). The (Figure closed 5c). setup The isclosed composed setup of is ﬁvecomposed metamaterial of five wallsmetamaterial each consisting walls each of 64 consisti resonators,ng of and 64 henceresonators, 80 outlets and arehence drawn 80 fromoutlets each are pressure drawn splitter.from each pressure splitter.

(a) (b)

(c)

Figure 5. ((a) Side Side and and ( (b)) bottom bottom views views of of the the splitter. splitter. ( (cc)) Drawing Drawing of of the the connection connection from the pressure outlet of the pneumatic system toto the splitters (S1,(S1, S2, S3, and S4) and then distributed to the unit cells of thethe metamaterialmetamaterial slabsslabs (walls) (walls) in in a a closed-space closed-space system. system. Each Each line line color color represents represents the the connection connection of eachof each splitter splitter to ditoﬀ differenterent cells cells of metamaterialof metamaterial slabs. slabs.

The pressurepressure outlets outlets of of the the pneumatic pneumatic system system (Figure (Figure4) are 4) connected are connected to the to balloons the balloons fixed inside fixed theinside resonators the resonators by means by means of flexible of flexible tubes. tubes. The balloons The balloons are attached are attached to the to back the back side ofside each of each unit cell,unit cell, and and each each resonator resonator cavity cavity is sealed is sealed as as the th balloonse balloons are are glued glued to to the the back back sideside ofof the pistons. Figure6 6displays displays how how pressure pressure is distributed is distributed from thefrom pneumatic the pneumatic pressure pressure provider provider system to system di fferent to resonatorsdifferent resonators by means by of means four di ffoferent four splitters.different Furthermore,splitters. Furthermore, two different two cavitydifferent depths cavity obtained depths obtained by pressures of 0.05 bar and 0.15 bar are demonstrated. The metamaterial is tested at two pressures; the pressure 0.05 bar yields the highest possible cavity depths, while 0.15 bar yields the lowest cavity depth. As the open system is composed of only four metamaterial slabs (Figure 2a), the remaining 64 outlets of the splitter are sealed.

Materials 2020, 13, 1456 7 of 11 by pressures of 0.05 bar and 0.15 bar are demonstrated. The metamaterial is tested at two pressures; the pressure 0.05 bar yields the highest possible cavity depths, while 0.15 bar yields the lowest cavity depth. As the open system is composed of only four metamaterial slabs (Figure2a), the remaining Materials64 outlets 2020 of, 13 the, x FOR splitter PEER are REVIEW sealed. 7 of 11

(b)

(a) (c) Figure 6. (a) The 3D-printed metamaterial in the open configuration with tubes connecting the inflatable Figure 6. (a) The 3D-printed metamaterial in the open configuration with tubes connecting the balloons in each unit cell to the splitters of the pneumatic actuation, (b) resonators at P = 0.05 bar, inflatable balloons in each unit cell to the splitters of the pneumatic actuation, (b) resonators at P = (c) resonators at P = 0.15 bar. 0.05 bar, (c) resonators at P = 0.15 bar. 3. Results and Discussions 3. Results and Discussions In each input pressure level, due to the non-identical response of the inflatable balloons to the pressureIn each input level, pressure the cells level, had a due range to ofthe cavity non-identical depths (withresponse variations of the inflatable of ~3 mm) balloons rather thanto the a pressuresingle cavity level, depth. the cells The had number a range of acousticof cavity tests depths conducted (with variations was limited of ~3 as mm) the fatigue rather endurancethan a single of cavitycommercially depth. availableThe number balloons of acoustic is relatively tests low, conducted allowing was only limited for a limited as the number fatigue of endurance actuations. of commercially available balloons is relatively low, allowing only for a limited number of actuations. 3.1. Open System 3.1. Open System Decreasing the input pressure from 0.15 bar to 0.05 bar (and therefore increasing the cavity depth) improvedDecreasing the noise the mitigationinput pressure in low-frequency from 0.15 bar range, to 0.05 particularly bar (and therefore for white increasing noise and pinkthe cavity noise. depth)For instance, improved for the the case noise of mitigation white noise, in at low-freque a frequencyncy of range, 100 Hz, particularly the metamaterial for white with noise higher and depth pink (Pnoise.= 0.05 For bar) instance,has 9 for dB the more case noise of white mitigation noise, at as a frequency compared of to 100 the Hz, metamaterial the metamaterial with lower with higher depth (Pdepth= 0.15 (P = bar) 0.05, seebar) Figure has 9 7dB. Similarly, more noise for mitigation the case of as pink compared noise, to the the metamaterial metamaterial with with higher lower depthdepth (P = 0.150.05 bar), bar) hassee 3.5Figure dB more7. Similarly, noise mitigation for the case as of compared pink noise, to the metamaterial metamaterial with with higher lower depth (P = 0.050.15 bar) bar), has see 3.5 Figure dB more7a. noise mitigation as compared to the metamaterial with lower depth (P = 0.15 bar), see Figure 7a. In high frequencies, on the other hand, the metamaterial with lower depth (P = 0.15 bar) demonstrates better performance as compared to the metamaterial with higher depth (P = 0.05 bar). For instance, for the case of white noise, at a frequency of 1000 Hz, the metamaterial with higher depth (P = 0.05 bar) has 5 dB more noise mitigation as compared to the metamaterial with lower depth (P = 0.15 bar), see Figure 7. Similarly, for the case of pink noise, the metamaterial with higher depth (P = 0.05 bar) has 3 dB more noise mitigation as compared to the metamaterial with lower depth (P = 0.15 bar), see Figure 7b.

Materials 2020, 13, x FOR PEER REVIEW 8 of 11

The difference between the performance of both systems became negligible for the cases of brown noise and frequency sweep 10,000→20 Hz, see Figure 7c,d. However, both the systems are able to mitigate noise for around 10 dB for frequency range of 100 Hz to 1000 Hz (Figure 7c,d). In summary, the system with high cavity volumes (P = 0.05 bar) demonstrated a better performance at lower frequencies, while the system with low cavity volumes (P = 0.15 bar) reduced the noise more efficiently at the higher end of the frequency spectrum (Figure 7). This was an expected Materialsperformance2020, 13, 1456from the active metamaterial, since according to the Helmholtz resonance equation (i.e.,8 of 11 Equation (1)) where ∝ .

Plain isolators Plain isolators

(a) (b)

Plain isolators Plain isolators

FigureFigure 7. 7.Measured Measured sound sound pressurepressure levels in in the the open open system system for for (a) (white,a) white, (b) pink, (b) pink, (c) brown (c) brown noises, noises, as wellas well as as for for (d ()d frequency) frequency sweepsweep from 10,000 10,000→2020 Hz Hz for for systems systems with with plain plain isolators, isolators, and the and active the active → systemsystem at at two two di differentﬀerent cavity cavity depthdepth levels.

3.2.In Closed high System frequencies, on the other hand, the metamaterial with lower depth (P = 0.15 bar) demonstratesSimilar betterto open performance system, in the as lower compared end of fr toequency the metamaterial range, the system with higher performed depth better (P = when0.05 bar). Forit instance,was at its for high the cavity case ofdepth white state noise, (P = at 0.05 a frequency bar), and ofthe 1000 system Hz, performed the metamaterial better in withhigher higher depthfrequencies (P = 0.05 when bar) the has cavity 5 dB depth more noisewas lower mitigation (P = 0.15 as bar), compared see Figure to the 8. metamaterialThe maximum with noise lower depthmitigation(P = 0.15 of high-cavity-depth bar), see Figure7 .system Similarly, as compared for the caseto low-cavity-depth of pink noise, thesystem metamaterial was observed with at f higher = depth200 (PHz= for0.05 all bar)the noisehas 3 sample dB more types noise (whi mitigationte, pink, brown, as compared and frequency to the metamaterial sweep 10,000 with→20 lowerHz), in depth (P =which0.15 bar),the high-cavity-depth see Figure7b. system mitigated noise 3–4 dB better than its low-cavity-depth counterpart.The diﬀerence On the between other thehand, performance the maximum of both nois systemse mitigation became of negligiblelow-cavity-depth for the system cases of as brown compared to high-cavity-depth system was observed at f = 500 Hz for all the noise sample types noise and frequency sweep 10,000 20 Hz, see Figure7c,d. However, both the systems are able to (white, pink, brown, and frequency→ sweep 10,000→20 Hz), in which the low-cavity-depth system mitigate noise for around 10 dB for frequency range of 100 Hz to 1000 Hz (Figure7c,d). mitigated noise 8–10 dB better than its high-cavity-depth counterpart (Figure 8). In summary, the system with high cavity volumes (P = 0.05 bar) demonstrated a better performance at lower frequencies, while the system with low cavity volumes (P = 0.15 bar) reduced the noise more eﬃciently at the higher end of the frequency spectrum (Figure7). This was an expected performance from the active metamaterial, since according to the Helmholtz resonance equation (i.e., Equation (1)) 1 where f V− 2 . ∝ 3.2. Closed System Similar to open system, in the lower end of frequency range, the system performed better when it was at its high cavity depth state (P = 0.05 bar), and the system performed better in higher frequencies when the cavity depth was lower (P = 0.15 bar), see Figure8. The maximum noise mitigation of Materials 2020, 13, 1456 9 of 11 high-cavity-depth system as compared to low-cavity-depth system was observed at f = 200 Hz for all the noise sample types (white, pink, brown, and frequency sweep 10,000 20 Hz), in which → the high-cavity-depth system mitigated noise 3–4 dB better than its low-cavity-depth counterpart. OnMaterials the other2020, 13,hand, x FOR PEER the REVIEW maximum noise mitigation of low-cavity-depth system as compared9 of 11 to high-cavity-depth system was observed at f = 500 Hz for all the noise sample types (white, pink, brown, and frequencyOverall, making sweep 10,000use of metamaterial20 Hz), in which for the the clos low-cavity-depthed system led to system8–20 dB mitigated noise mitigation noise 8–10 as dB → bettercompared than itsto the high-cavity-depth system without counterpartmetamaterial (Figure (composed8). of solid walls) in the frequencies higher than 100 Hz.

Plain isolators

(a) (b)

Plain isolators Plain isolators

FigureFigure 8.8. Measured sound sound pressure pressure levels levels in in the the open open system system for for (a) (white,a) white, (b) (pink,b) pink, (c) brown (c) brown noises, noises, as well as for (d) frequency sweep from 10,000→ 20 Hz for systems with plain isolators, and the active as well as for (d) frequency sweep from 10,000 →20 Hz for systems with plain isolators, and the active systemsystem atat twotwo didifferentﬀerent cavity depth depth levels. levels.

Overall,In another making study [11], use ofwe metamaterial used a stepper for motor the to closed vary the system depth led of tothe 8–20 cavities. dB noiseAs compared mitigation to as comparedlinear motor, to the the system pneumatic without mode metamaterial of actuation (composed has both of advantages solid walls) and in the disadvantages. frequencies higher In the than 100pneumatically-actuated Hz. system, a much smaller number of actuators (i.e., linear pressure providers) are neededIn another to create study non-uniform [11], we used distribution a stepper of motor cavity to depths, vary the whereas depth for of the case cavities. of actuation As compared by tomeans linear of motor, the linear the motor, pneumatic theoretically, mode ofeach actuation unit cell hasrequires both a advantages dedicated linear and actuator. disadvantages. Therefore, In the pneumatically-actuatedthe linear motor actuation system, mechanism a much smallerhas much number more oflimitations actuators regarding (i.e., linear individual pressure providers) depth of are neededcavities to in create each non-uniformmetamaterial distributionslab, if the economic of cavity point depths, of whereasview is to for be the considered. case of actuation On the byother means ofhand, the linearlinear motor,actuators theoretically, provide a better each precision unit cell in requires resonator a dedicatedlocation. linear actuator. Therefore, the linear motor actuation mechanism has much more limitations regarding individual depth of cavities in 4. Conclusions each metamaterial slab, if the economic point of view is to be considered. On the other hand, linear actuatorsIn this provide study, a betterpneumatically-actuated precision in resonator acoustic location. metamaterials based on Helmholtz resonator were developed and their acoustic performance was analyzed. The pneumatic actuation system was used to vary the pressure behind pistons inside each cell of the metamaterial, and as a result to vary the cavity depth of each unit cell. The results showed that by increasing the pressure level, the mitigation region of performance shifts from a frequency range of 150–350 Hz at higher cavity depths to a frequency range of 300–600 Hz at a lower cavity depth. The pneumatically-actuated acoustical

Materials 2020, 13, 1456 10 of 11

4. Conclusions In this study, pneumatically-actuated acoustic metamaterials based on Helmholtz resonator were developed and their acoustic performance was analyzed. The pneumatic actuation system was used to vary the pressure behind pistons inside each cell of the metamaterial, and as a result to vary the cavity depth of each unit cell. The results showed that by increasing the pressure level, the mitigation region of performance shifts from a frequency range of 150–350 Hz at higher cavity depths to a frequency range of 300–600 Hz at a lower cavity depth. The pneumatically-actuated acoustical metamaterial yielded peak attenuations of 20 dB and 15 dB in respectively closed and open systems (at 500 Hz). The results of the study demonstrate that pneumatic actuation system can be effectively implemented to mitigate a targeted range of frequencies for noise reduction applications in low frequencies such as in aircraft liners, buildings, and noise mitigation enclosures. A step forward would be to tune different unit cells of the metamaterial with different pressure levels (and therefore different cavity depths) in order to target a broader range of frequencies.

Author Contributions: R.H. conceived of the presented idea. All authors developed the theory and performed the manufacturing and tests. All authors verified the test results. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.

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