materials

Article Acoustic Metasurface-Aided Broadband Noise Reduction in Automobile Induced by -Pavement Interaction

Hyeonu Heo 1 , Mathew Sofield 1, Jaehyung Ju 2,* and Arup Neogi 1,*

1 Department of Physics, University of North Texas, P.O. Box 311427, Denton, TX 76203, USA; [email protected] (H.H.); mathewsofi[email protected] (M.S.) 2 UM-SJTU Joint Institute, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China * Correspondence: [email protected] (J.J.); [email protected] (A.N.)

Abstract: The primary noise sources of the vehicle are the engine, exhaust, aeroacoustic noise, and tire–pavement interaction. Noise generated by the first three factors can be reduced by replacing the combustion engine with an electric motor and optimizing aerodynamic design. Currently, a dominant noise within automobiles occurs from the tire–pavement interaction over a speed of 70–80 km/h. Most noise suppression efforts aim to use sound absorbers and cavity resonators to narrow the bandwidth of acoustic frequencies using foams. We demonstrate a technique utilizing acoustic metasurfaces (AMSes) with high reflective characteristics using relatively lightweight materials for noise reduction without any change in mechanical strength or weight of the tire. A simple technique is demonstrated that utilizes acoustic metalayers with high reflective characteristics using relatively lightweight materials for noise reduction without any change in mechanical strength or weight of the tire. The proposed design can significantly reduce the noise arising from tire–pavement interaction

 over a broadband of acoustic frequencies under 1000 Hz and over a wide range of vehicle speeds  using a negative effective dynamic mass density approach. The experiment demonstrated that the

Citation: Heo, H.; Sofield, M.; Ju, J.; sound transmission loss of AMSes is 2–5 dB larger than the acoustic foam near the cavity mode, Neogi, A. Acoustic Metasurface-Aided at 200–300 Hz. The proposed approach can be extended to the generalized area of acoustic and Broadband Noise Reduction in vibration isolation. Automobile Induced by Tire-Pavement Interaction. Materials 2021, 14, 4262. Keywords: acoustic metasurfaces; tire cavity; noise reduction; acoustic metamaterials https://doi.org/10.3390/ma14154262

Academic Editor: Theodore E. Matikas 1. Introduction Noise pollution by traffic is the most widespread environmental problem that causes Received: 25 June 2021 sleep disturbance, hearing damage, and even cardiovascular disease [1,2]. Thus, the Euro- Accepted: 26 July 2021 Published: 30 July 2021 pean Parliament and the Member States agreed to reduce road noise in 2011, introduced noise regulations, and reduced noise levels by just 3 dB (reducing sound pressure energy

Publisher’s Note: MDPI stays neutral to half) in 2013 [3]. The primary noise sources of vehicles are engine, exhaust, aeroacoustic with regard to jurisdictional claims in noise, and tire–pavement interactions [4]. Noise generated by the first three factors can published maps and institutional affil- be essentially reduced by replacing the combustion engine with an electric motor and iations. optimizing aerodynamic design. However, reducing Tire–Pavement Interaction Noise (TPIN), which dominates the total noise generated within a vehicle at a speed of over 70–80 km/h [5,6], is hugely challenging. Any proposed technique should consider the structural and mechanical integrity of the and wheels, which can be problematic because the tire cavity environment is affected by changes in loading conditions, speed, Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. and temperature [7]. Tire and automobile manufacturers are developing soundproofing This article is an open access article techniques using resonators and sound-absorbers that meet the new industry standards [3] distributed under the terms and to provide a comfortable feeling for passengers. conditions of the Creative Commons Compressed air in a tire cavity generates resonant noise and vibration at a frequency Attribution (CC BY) license (https:// range below 1,000 Hz, and the fundamental frequency is near 230 Hz [8]. Conventional creativecommons.org/licenses/by/ noise reduction techniques using thick metal plates are not applicable for isolating this 4.0/). resonant noise and vibration of compressed air in a tire cavity due to design constraints.

Materials 2021, 14, 4262. https://doi.org/10.3390/ma14154262 https://www.mdpi.com/journal/materials Materials 2021, 14, 4262 2 of 12

Tire manufacturers and researchers add a absorber glued around the tire’s inner liner to reduce noise [9,10]. A resonator attached to the rim has been used to reduce the tire cavity’s resonant sound [11–13]. The pitch arrangement of the tire tread patterns has also been optimized to minimize the noise [14,15]. However, these noise reduction methods mainly focused on the resonator for the tire cavity resonance, i.e., a narrow bandwidth sound absorption capability of porous materials. A different approach is necessary for better noise reduction of the sound generated at low frequency and the wideband noise caused by tire–pavement interaction. Acoustic metasurfaces (AMSes) or metalayers are artificially designed 2D materials of subwavelength thickness that provide a non-trivial local phase shift and alter the direction of propagation of the incident wave. Some recent reports utilize AMSes for extraordinary sound absorption [16] using Helmholtz resonators [17], membranes [18–20], and 3D space coiling metastructures [21]. The membranes have shown over 200 times noise reduction for a specific frequency range and can be optimized for the desired application by modifying the geometry [18]. Lightweight yet soundproof acoustic metasurfaces were used within an airplane framework to reduce noise [20]. The structure consisted of a perforated, stiff, periodic pattern and thin, soft materials on a periodic structure. AMSes can be designed with a negative effective dynamic mass density (ρe f f < 0) when the frequency is below the fundamental frequency of a thin plate. AMSes provide anti-resonance, out of phase with   −1/2 the incident wave and exponential decaying wave ∆d ∝ ρe f f , resulting in almost total reflection at the low broad frequency ranges [18,19]. The proposed AMSes may be used as an alternative method for noise reduction in tires. In this study, the AMSes were designed to maximize the sound transmission loss (STL) over a broad frequency range using lightweight materials without modifying the mechanical properties of the tire. The noise reduction in the tire was investigated using AMSes based on hexagonal unit cells attached to the rim0s circumference to reflect sound waves arising from the tire–pavement interaction aided by the absorption in the radial direction. The AMSes were optimized for a particular design parameter with a negative effective dynamic mass density for a practical car tire. Based on the parametric study of the unit cell of AMSes, the noise reduction capability of AMSes is demonstrated through static tests using the tire cavity model and through a dynamic field test. The acoustic foam was considered as a comparison. The results showed that AMSes have 2–3 times (3 dB) more noise reduction capability than foam. Within a few decades, various acoustic metamaterials have been proposed and their remarkable properties have been investigated extensively, e.g., complete bandgap at a particular band [22,23], or nonreciprocity (one-way transmission) [24,25]. However, the proven practical applications are spare and challenging due to the design constraints. Here, we first applied acoustic metasurfaces to reduce unwanted noise in the cabin. The proposed design, a lightweight and thin structure, does not affect the tire0s performance. Unlike other commonly used soundproofing methods, which have absorption capabilities of about 0.4~0.6 [26], AMSes show almost total reflection at low frequency, under 1000 Hz. Furthermore, AMSes can be easily combined with existing technologies, e.g., acoustic foam and optimal tread pitch patterns, to maximize the sound transmission loss in the cabin. The potential applications of the proposed technology are not limited to automobiles or tires. The robust and lightweight design can be modified and applied to other fields for soundproofing and vibration isolation to reduce undesirable noise issues.

2. Design and Fabrication of AMS 2.1. Design The noise generated by tire–pavement interaction is the structure-borne noise at low-frequency ranges (below 500 Hz), while the air-borne noise occurs at high-frequency ranges (500–2000 Hz). According to Chang et al. [27], TPIN becomes the primary source of noise occurring at frequencies below 500 Hz, part of the audible frequency range. The fundamental frequency, f, of the tire cavity is a function of the speed of sound of air, c, and Materials 2021, 14, 4262 3 of 12

wavelength, λ; f = c/λ = 2c/π(Do + Di) where Do is the outer diameter of the tire cavity toroid, and Di is the inner diameter of tire cavity toroid [8]. For general passenger vehicles, the cavity mode is close to 230 Hz, which needs to be reduced [28,29]. Highly reflective AMSes were specifically designed for this frequency range, as shown in Figure1. AMSes are fabricated using and are composed of a honeycomb- 0 shaped core panel attached to a tire s rim. In Figure1, for the unit cell, am is the side length of the hexagon, t is the wall thickness of the core panel, and hm and hc are the thickness of the thin plate and the height of the core panel, respectively. Hexagonal unit cell-shaped metasurfaces have a natural oscillation mode at higher frequencies than squares and triangles with identical unit cells with hydraulic diameters. Moreover, the shape and form of the periodic metasurfaces with hexagonal unit cells are not deformed across a tire’s curved plane. This also offers the best surface filling fraction, which is ideal for noise suppression. The unit cell can be considered as a clamped thin plate because the core panel is relatively rigid. Thus, when the noise occurs, the thin plate oscillates and propagates Materials 2021, 14, x FOR PEER REVIEW 3 of 13 acoustic pressure while barely passing through the core panel. The effectiveness of the unit cell hexagonal cross section was evaluated to predict the acoustic characteristics of the AMSes. Through Rayleigh0s method of a spring and a mass, the effective dynamic mass 2. Design and Fabrication of AMS density, ρeff, can be determined using the following deceptively simple equation [19,20]: 2.1. Design The noise generated by tire–pavement interaction is fthe2  structure-borne noise at low- ρ = ρ 1 − r (1) frequency ranges (below 500 Hz), whilee f f the air-bornem fnoise2 occurs at high-frequency ranges (500–2000 Hz). According to Chang et al. [27], TPIN becomes the primary source whereof noisef roccurringis the lowest at frequencies eigenfrequency below 500 of Hz, a honeycomb-shapedpart of the audible frequency thin plate, range.f isThe the sound fundamental frequency, f, of the tire cavity is a function of the speed of sound of air, c, and frequency, and ρm is the density of the thin plate. The given equation originates from ⁄ ⁄ Newtonwavelength,0s second λ; 𝑓𝑐 law,2𝑐𝜋(𝐷 𝜆 but the dynamic 𝐷), where inertial 𝐷 mass is the ofouter the diameter system becomesof the tire acav- function of ity toroid, and 𝐷 is the inner diameter of tire cavity toroid [8]. For general passenger frequency due to internal mass and spring interactions [19]. Thus, the dynamic mass density vehicles, the cavity mode is close to 230 Hz, which needs to be reduced [28,29]. differs from the conventional gravitational mass density. In the case of the hexagonal Highly reflective AMSes were specifically designed for this frequency range, as clampedshown in thinFigure plate, 1. AMSesfr is calculated are fabricated using using the followingsilicone rubber equation and are [30 composed–32]: of a honeycomb-shaped core panel attached sto a tire′s rim. In Figure 1, for the unit cell, am is πα D E h3 the side length of the hexagon, t is= the wall thickness= of the corem m panel, and hm and hc are fr 2 , D 2 (2) the thickness of the thin plate and the6am heightρh mof the core12 panel,(1 − νrespectively.m) Hexagonal unit cell-shaped metasurfaces have a natural oscillation mode at higher frequencies than wheresquaresh andm is triangles the thickness with identical of the thin unit plate, cells andwith ahydraulicm is the side diameters. length Moreover, of the thin the hexagonal plate.shape andEm andformν ofm therepresent periodic Young’s metasurfaces modulus with andhexagonal Poisson’s unit cells ratio are of not base deformed material for the thinacross plate, a tire’s respectively. curved plane. The This constant also offersα is the a nondimensional best surface filling frequency fraction, which parameter is ideal calculated byfor noise the energy suppression. approach The unit and cell convergence can be considered study as [32 a clamped]. For the thin first plate mode, becauseα isthe 3.9068. If core panel is relatively rigid. Thus, when the noise occurs, the thin plate oscillates and f < f , the frequency-dependent effective dynamic mass density becomes negative. This propagatesr acoustic pressure while barely passing through the core panel. The effective- implies that the force and the acceleration have the opposite direction. The clamped thin ness of0 the unit cell hexagonal cross section was evaluated to predict the acoustic charac- plateteristicss localof the oscillation AMSes. Through provides Rayleigh the anti-resonance,′s method of a whichspring isand out a ofmass, phase the witheffective the incident wave.dynamic Therefore, mass density, the acoustic ρeff, can wavebe determined through theusing thin the plate following ceases deceptively to propagate simple and becomes evanescent,equation [19,20]: as the negative density implies an imaginary wave vector.

Figure 1. 1. AA concept concept to to reduce reduce tire tire noise noise with with an anacou acousticstic metasurface metasurface consisting consisting of a ofhoneycomb a honeycomb core panelcore panel and and a soft, a soft, thin thin plate plate on on the the tire tire0s′s rim.rim.

𝑓 𝜌 𝜌 1 (1) 𝑓

where fr is the lowest eigenfrequency of a honeycomb-shaped thin plate, f is the sound frequency, and ρm is the density of the thin plate. The given equation originates from New- ton′s second law, but the dynamic inertial mass of the system becomes a function of fre- quency due to internal mass and spring interactions [19]. Thus, the dynamic mass density differs from the conventional gravitational mass density. In the case of the hexagonal clamped thin plate, fr is calculated using the following equation [30–32]:

𝜋𝛼 𝐷 𝐸ℎ 𝑓 ,𝐷 (2) 6𝑎 𝜌ℎ 12(1 𝜈)

Materials 2021, 14, x FOR PEER REVIEW 4 of 13

where hm is the thickness of the thin plate, and 𝑎 is the side length of the thin hexagonal plate. Em and νm represent Young’s modulus and Poisson’s ratio of base material for the thin plate, respectively. The constant α is a nondimensional frequency parameter calcu- lated by the energy approach and convergence study [32]. For the first mode, α is 3.9068. If f < fr, the frequency-dependent effective dynamic mass density becomes negative. This implies that the force and the acceleration have the opposite direction. The clamped thin Materials 2021, 14, 4262 plate′s local oscillation provides the anti-resonance, which is out of phase with the 4inci- of 12 dent wave. Therefore, the acoustic wave through the thin plate ceases to propagate and becomes evanescent, as the negative density implies an imaginary wave vector. The effective dynamic mass density of an AMS, including an elastomeric thin plate The effective dynamic mass density of an AMS, including an elastomeric thin plate having an eigenfrequency of 2,056 Hz, was obtained from Equation (1) and the numerical having an eigenfrequency of 2,056 Hz, was obtained from Equation (1) and the numerical3 simulation using COMSOL Multiphysics when hm = 0.5 mm, Em = 7 MPa, ρm = 1070 kg/m 3, simulation using COMSOL Multiphysics when hm = 0.5 mm, Em = 7 MPa, ρm = 1070 kg/m , νm = 0.49, and am = 3.65 mm (see Figure 2). The effective dynamic density can be numerically νm = 0.49, and am = 3.65 mm (see Figure2). The effective dynamic density can be numerically obtained by dividing the out-of-plane surface averaged stress, 𝜎, by the product of the obtained by dividing the out-of-plane surface averaged stress, σyy, by the product of the surface averaged acceleration, 𝑎 , and the thin plate thickness, ℎ , i.e., 𝜌  surface averaged acceleration, ay, and the thin plate thickness, hm, i.e., ρ = σyy/ ayhm ⁄ e f f 𝜎where 𝑎 theℎ y-axis where is thethe directiony-axis is the of wavedirection propagation of wave propagation [20]. [20].

0 FigureFigure 2. 2. TheThe clamped clamped hexagon hexagon plate plate′ss dynamic dynamic mass mass density density is is calculated calculated by by the the analytical analytical model model (solid(solid black black line) line) and and the the numerical numerical simulation simulation (sol (solidid red redline line with with marker marker).). The fundamental The fundamental reso- nanceresonance of the of thin the thinplate plate is at is2056 at 2056Hz. Hz.

2.2.2.2. Fabrication Fabrication ToTo demonstrate the noise reductionreduction ofof AMSes,AMSes, wewe used used the the AMSes AMSes attached attached tire tire cavity cav- itymodel model and and conducted conducted a fielda field test test with with tires tires covered covered with with AMSesAMSes toto proveprove their noise reduction capability. Based on the parametric study (see Section 3.1.), we first fabricated reduction capability. Based on the parametric study (see Section 3.1.), we first fabricated AMSes made up of a honeycomb core panel and silicone rubber. The aramid honeycomb AMSes made up of a honeycomb core panel and silicone rubber. The aramid honeycomb core panel has a 1/800 cell with a density of 3 lb/ft3 and 1/400 thickness (ACP Composites, core panel has a 1/8″ cell with a density of 3 lb/ft3 and 1/4″ thickness (ACP Composites, Inc, Livermore, CA, USA). The silicone rubber, called the dragon skin (Smooth-On, Inc, Inc, Livermore, CA, USA). The silicone rubber, called the dragon skin (Smooth-On, Inc, Easton, PA, USA), is low viscosity cure silicone that does not require vacuum degassing. Easton, PA, USA), is low viscosity cure silicone that does not require vacuum degassing. The silicone rubber consists of two resins which should be mixed at a ratio of 1 to 1. To The silicone rubber consists of two resins which should be mixed at a ratio of 1 to 1. To place the thin rubber plate on the core panel, first, the silicone rubber was poured as evenly place the thin rubber plate on the core panel, first, the silicone rubber was poured as as possible on the clean surface of the wood plate like a mold, which was prepared with evenly as possible on the clean surface of the wood plate like a mold, which was prepared a 0.04” (1 mm) deep channel utilizing a CNC router. It was then smoothed over with an with a 0.04″ (1 mm) deep channel utilizing a CNC router. It was then smoothed over with 11” paint shield which rested on the edges of the channel, resulting in a thickness of the ansilicone 11″ paint rubber shield of about which 0.04”. rested Next, on the the edges quarter-inch-thick of the channel, honeycomb resulting in core a thickness panel is put of theon thesilicone rubber rubber layer of and about cured 0.04 for″. Next, 2 hours the at quarter-inch-thick room temperature, honeycomb i.e., the silicone core panel rubber is putcovered on the one rubber side oflayer the and panel cured (see for Figure 2 hours3 (right)). at room temperature, i.e., the silicone rubber coveredVarious one side experimental of the panel techniques (see Figure have 3 (right)). been used to measure the soundproofing capa- bility in the lab, e.g., directly measuring sound with microphones in the cavity resembling the actual structures [7,33], or indirectly measuring vibration of the structures induced by the impact [34]. The cavity model was used for the lab test due to its simplicity and convenience. The manufactured AMSes were attached to the inner layer of the tire cavity model, mimicking a real tire, 235/65R18, for the lab test referring to O’Boy’s design [7], and the rim of each tire ( Tires), 185/65R15, of the Toyota Prius hybrid 2008, for the field test. The tire cavity model consisted of medium density fibreboard (MDF), aluminum metal sheets, and acrylic panels, as shown in Figure3 (left). The outer and the inner metal sheets represent the tire rubber and the rim of a wheel where the outer and inner diameters 00 00 are Do = 30 and Di = 18 , respectively. The thickness values of Al sheets, MDF, and Materials 2021, 14, 4262 5 of 12

acrylic panels, are 0.06000, 0.75000, and 0.43700, respectively. We added a rubber seal to the edge of the aluminum sheets to isolate the cavity. The Rode NT-USB mini microphone (RØDE Microphones LLC, Long Beach, CA, USA), which has a sampling rate of 48 kHz and a frequency range of 20 Hz–20 kHz, was mounted in the center of the inner cavity and connected to the computer with the USB cable. A hole was made at the bottom for a speaker emitting white noise which was generated by the Minirator MR2 audio generator from NTi Audio (NTi Audio AG, Schaan, Liechtenstein), which has a resolution of 0.1 Hz. The foam Materials 2021, 14, x FOR PEER REVIEW 00 5 of 13 and the AMS were bonded on the circumference of the rim, 3.5 width. The densities of the foam and the AMS are approximately 10.0 lb/ft3 and 14.5 lb/ft3, respectively.

Figure 3. Figure(Left) Tire3. (Left cavity) Tire model cavity representing model representing a tire, 235/65R18. a tire, 235/ At65R18. the bottom,At the bottom, there is there a hole is fora hole the for speaker which generatesthe white speaker noise towhich represent generates TPIN. white The Rode noise NT-USB to represent mini microphoneTPIN. The Rode was mounted NT-USB inmini the microphone center of the inner cavity was mounted in the center of the inner cavity and connected to the computer with the USB cable. and connected to the computer with the USB cable. (Right) The rim of the tire (Pirelli Tire), 185/65R15, of Toyota Prius (Right) The rim of the tire (Pirelli Tire), 185/65R15, of Toyota Prius hybrid 2008. The foam and the hybrid 2008. The foam and the AMS were bonded on the circumference of the rim, 3.500 width. AMS were bonded on the circumference of the rim, 3.5″ width. For the field test, AMSes were bonded on the rim inside each tire of the vehicle Various experimental techniques have been used to measure the soundproofing ca- (see Figure3). A commercial soundproofing foam ( sponge foam rubber from pability in the lab, e.g., directly measuring sound with microphones in the cavity resem- Lazy dog warehouse) with the same thickness of the honeycomb core panel was used as bling the actual structures [7,33], or indirectly measuring vibration of the structures in- a comparison. duced by the impact [34]. The cavity model was used for the lab test due to its simplicity and convenience.3. The Results manufactured AMSes were attached to the inner layer of the tire cavity model, mimickingA parametric a real tire, study 235/65R18, of the for unit the cell lab was test conductedreferring to to O’Boy’s evaluate design the effects of design [7], and the rim parameters,of each tire (Pirelli such as Tires), side length185/65R15, and of thickness the Toyota of thePrius unit hybrid cell0s 2008, thin plate,for density, and the field test. Thesound tire cavity transmission model consiste loss (STL)d of (see medium Figure density4). Then, fibreboard AMSes were (MDF), fabricated alu- based on the minum metal sheets,parametric and acrylic study topanels, maximize as shown STL yetin Figure remain 3 lightweight(left). The outer and wereand attachedthe to the tire inner metal sheetscavity represent model the and tire an rubber actual tireand for the the rim laboratory of a wheel and where field the tests. outer The and performance of the inner diameters AMSesare Do = was 30″ comparedand Di = 18 to″, arespectively. commercial foamThe thickness with the values same thickness. of Al sheets, MDF, and acrylic panels, are 0.060″, 0.750″, and 0.437″, respectively. We added a rubber seal to the edge 3.1.of the Design aluminum Map of sheets the Unit to Cellisolate of the the AMS cavity. The Rode NT-USB mini mi- crophone (RØDE MicrophonesThe unit cell LLC,0s parametricLong Beach, study CA, USA), was carriedwhich has out a usingsampling the rate numerical of simulation 48 kHz and a frequency(COMSOL range Multiphysics) of 20 Hz–20 with kH thez, was pressure mounted acoustics in the and center the solidof the mechanics inner modules to cavity and connectedpredict to thethe effectcomputer of the with design the USB parameters cable. A on hole acoustic was made properties, at the bottom such as dynamic mass for a speaker emittingdensity white and STL.noise Thewhich thickness, was generatedhm, and by side the length, Miniratoram, ofMR2 the audio thin plate gen- were examined. erator from NTi TheAudio clamped (NTi Audio hexagonal AG, thinSchaan plate, Liechtenstein), was considered which the unithas a cell resolution of the AMS, of and the linear 0.1 Hz. The foamelastic and the model AMS for were the siliconebonded rubber on the wascircumference occupied. Figure of the4 rim,a illustrates 3.5″ width. thegeometry of the The densities of unitthe foam cell, and where the the AMS thin are plate approximately is placed in 10.0 the middlelb/ft3 and of 14.5 the pipe.lb/ft3, Therespec- maximum element tively. size of the pipe is 0.1λ where λ is the wavelength. The number of elements along the For the fieldthickness test, AMSes of the were thin bonded plate is on five. the Before rim inside and after each the tire thin of the plate vehicle there are(see boundary layers Figure 3). A commercialregarding soundproofing viscous layer thickness. foam (neoprene The perfectly sponge matched foam rubber layer (PML)from Lazy is placed on the back dog warehouse)of with the the receiver same thickness side to avoid of the the honeycomb reflection fromcore panel the wall. was The used boundary as a com- condition of the parison.

3. Results A parametric study of the unit cell was conducted to evaluate the effects of design parameters, such as side length and thickness of the unit cell′s thin plate, density, and sound transmission loss (STL) (see Figure 4). Then, AMSes were fabricated based on the parametric study to maximize STL yet remain lightweight and were attached to the tire cavity model and an actual tire for the laboratory and field tests. The performance of the AMSes was compared to a commercial foam with the same thickness.

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Materials 2021, 14, x FOR PEER REVIEW 6 of 13 sidewall is hard wall. On top of the pipe, the plane wave propagates through the structure. Then, the transmitted sound pressure was measured at the bottom.

Figure 4. TheFigure result 4. of The the result parametric of the study parametric on design study parameters, on design suchparameters, as thickness, such ashm thickness,, and side h length,m, and asidem, of the thin plate of the unitlength, cell a ofm, AMSes;of the thin (a) plate the schematic of the unit image cell of of AMSes; the unit ( cella) the used schematic in Figures image1 and of2 ;(theb unit) the cell natural used frequency in of AMSes; (c) theFigures average 1 and STL 2; of (b AMSes) the natural from 100frequency Hz to 400 of HzAMSes; calculated (c) the by average the numerical STL of AMSes simulation. from 100 Hz to 400 Hz calculated by the numerical simulation. The peak of the noise is near 230 Hz, which is the fundamental mode of the tire 3.1. Design Mapcavity. of the Unit The Cell investigation’s of the AMS frequency range was from 100 Hz to 400 Hz, to consider The unit thecell effects′s parametric on the fundamentalstudy was carried mode. out As mentionedusing the numerical above, when simulation the frequency is less (COMSOL Multiphysics)than the fundamental with the pressure mode of acoustics AMSes, and the effectivethe solid densitymechanics of AMSes modules becomes to negative. predict the effectUnder of the these design conditions, parameters the plate’s on acoustic local oscillation properties, reflects such theas dynamic incident wavemass resulting in a density and STL.substantial The thickness, noise reduction. hm, and side Therefore, length, a whenm, of the the thin natural plate frequency were examined. is shifted to a higher The clamped hexagonalfrequency thin by modifying plate was considered the design the parameters, unit cell of the the noise AMS, reduction and the linear effect is enhanced elastic model (seefor the Figure silicone4b,c). rubber Figure was4c showsoccupied. the Figure average 4a STL illustrates of AMSes the geometry from 100 Hzof to 400 Hz, the unit cell, wheredepending the thin on aplate variety is placed of design in the parameters. middle of The the AMS pipe. shows The maximum a significant ele- noise reduction ment size of theof pipe23–62 is dB 0.1atλ where the low-frequency λ is the wavelength. ranges, even The thoughnumber the of materialelements properties along the of the silicone thickness of therubber thin plate were is simplified five. Before in thisandstudy after the using thin a linearplate there elastic are model. boundary A smaller layers unit cell and a regarding viscousthicker layer plate thickness. have even The higher perfectly sound matched losses because layer (PML) the first is modeplaced is on proportional the to the 0 back of the receiverthickness side and to avoid inversely the reflecti proportionalon from to the the wall. plate Thes area boundary (see Equation condition (2)). of the sidewall is hard wall. On top of the pipe, the plane wave propagates through the struc- 3.2. The Sound Pressure Level in the Tire Cavity Model (Static Test) ture. Then, the transmitted sound pressure was measured at the bottom. The peak of theThe noise AMS is near feasibility 230 Hz, was which demonstrated is the fundamental by constructing mode of athe tire tire cavity cavity. representing an The investigation’sactual frequency tire (235/65R18), range was as from shown 100 in Hz Figure to 4003. Hz, The to model consider consisted the effects of MDF, on aluminum the fundamentalmetal mode. sheets, As andmentioned acrylic above, panels. wh Theen outerthe frequency and the inneris less metal than sheetsthe funda- represent the tire mental mode rubberof AMSes, and the rim,effective respectively. density Theof AMSes Rode NT-USBbecomes mini negative. microphone Under wasthese mounted in the inner cavity. A hole at the bottom facilitated the generation of white noise via a speaker. conditions, the plate’s local oscillation reflects the incident wave resulting in a substantial Figure5 shows the effects of noise reduction due to the AMSes. Figure5a shows the noise reduction. Therefore, when the natural frequency is shifted to a higher frequency by acoustic spectrum in log scale, and Figure5c,d depict the sound transmission coefficients modifying the design parameters, the noise reduction effect is enhanced (see Figure 4b,c). (STCs) normalized to the maximum sound transmission of the white noise of the cavity Figure 4c shows the average STL of AMSes from 100 Hz to 400 Hz, depending on a variety mode. Figure5b illustrates the tire cavity with foam and AMS. of design parameters. The AMS shows a significant noise reduction of 23–62 dB at the low- frequency ranges, even though the material properties of the silicone rubber were simpli- fied in this study using a linear elastic model. A smaller unit cell and a thicker plate have even higher sound losses because the first mode is proportional to the thickness and in- versely proportional to the plate′s area (see Equation (2)).

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3.2. The Sound Pressure Level in the Tire Cavity Model (Static Test) The AMS feasibility was demonstrated by constructing a tire cavity representing an actual tire (235/65R18), as shown in Figure 3. The model consisted of MDF, aluminum metal sheets, and acrylic panels. The outer and the inner metal sheets represent the tire rubber and the rim, respectively. The Rode NT-USB mini microphone was mounted in the inner cavity. A hole at the bottom facilitated the generation of white noise via a speaker. Figure 5 shows the effects of noise reduction due to the AMSes. Figure 5a shows the acous- tic spectrum in log scale, and Figures 5c,d depict the sound transmission coefficients Materials 2021, 14, 4262(STCs) normalized to the maximum sound transmission of the white noise of the cavity 7 of 12 mode. Figure 5b illustrates the tire cavity with foam and AMS.

Figure 5. SoundFigure pressure 5. Sound level pressure (a) and level normalized (a) and soundnormalized transmission sound transmission coefficients ( ccoefficients,d) in the tire (c,d cavity) in the model tire measured cavity model measured in the inner cavity. The background noise, black solid dashed lines, is the in the inner cavity. The background noise, black solid dashed lines, is the reference. The yellow lines represent the white reference. The yellow lines represent the white noise (WN) when the speaker is turned on. The blue noise (WN) when the speaker is turned on. The blue and red lines represent the attached foam and AMS, respectively. The and red lines represent the attached foam and AMS, respectively. The pictures (b) display the cavity pictures (b)models display with the cavityfoam or models AMS withutilized foam in orthe AMS experiment. utilized in the experiment. In Figure5, the solid black line represents background noise, and it serves as a In Figure 5, the solid black line represents background noise, and it serves as a refer- reference. The speaker generating white noise (WN) was turned on to measure the spectra ence. The speaker generating white noise (WN) was turned on to measure the spectra of of the empty inner cavity and is depicted by the yellow lines. Due to the circular symmetry the empty inner cavity and is depicted by the yellow lines. Due to the circular symmetry of the tire cavity, there are radial and azimuthal eigenmodes. The dominant contribution of the tire cavity, there are radial and azimuthal eigenmodes. The dominant contribution to automobile noise originates from the fundamental radial mode with a frequency near to automobile noise originates from the fundamental radial mode with a frequency near 184.7 Hz. There is a peak near 185 Hz in Figure5. The suppression of this peak noise in the 184.7 Hz. Therefrequency is a peak spectrumnear 185 Hz within in Figure the inner 5. The cavity suppression strongly reducesof this peak the noise noise transmitted in to the the frequency spectrumcar0s cabin. within The efficiency the inner ofcavity our metasurface-basedstrongly reduces the technology noise transmitted is compared to with existing the car′s cabin.sound The efficiency absorption-based of our metasurface-based noise reduction technology. technology Theis compared noise in a with cavity ex- filled with 1/400 isting sound absorption-basedthick foam (shown noise by reduction the blue dashedtechnology. lines) The is compared noise in a cavity with the filled cavity with wrapped using 1/4″ thick foamthe (shown acoustic by metasurfacethe blue dashed (shown lines) by is the compared red dotted with lines). the cavity It is evident wrapped from the acoustic using the acousticspectra metasurface shown in Figure(shown5c,d by that the thered noise dotted within lines). the It inner is evident cavity isfrom reduced the in both cases. acoustic spectraThe shown reduction in Figures is more 5c,d substantial that the noise in the within case ofthe the inner AMS, cavity especially is reduced near in the cavity mode (about twice (3 dB) that of the foam), and it remains effective over a broader range of frequencies. The bandwidth of the noise suppression frequency is narrower for the foam as it continues to transmit sound energy while absorbing due to thermal dissipation. The wavelength at the low frequency is much larger than the porous size of the foam. The AMS, on the other hand, reflects due to anti-local resonance below the natural frequency of the thin plate. There are several minor peaks at higher frequencies of 350 Hz, and the unit cell design can suppress that. As the dynamic mass density is a function of design parameters, the modes can be varied or specified to reflect and consequently reduce noise. Materials 2021, 14, 4262 8 of 12

3.3. The Sound Pressure Level in the Cabin (Dynamic Test) After the lab-scale test, the field test was performed with the Toyota Prius hybrid 2008. This car was chosen to minimize the noise induced by engine and exhaust and focus on the tire–pavement interaction. The Prius hybrid has an electric vehicle (E.V.) mode up to 60 km/h (~37 mph). The tire size is 185/65R15 (Pirelli Tire), and the air pressure in the tire is 44 psi. To investigate the effectiveness of AMSes, we consider three cases—(i) without any attachment, (ii) with foam, and (iii) with AMS (Figure6). The test was performed on Materials 2021, 14, x FOR PEER REVIEW 9 of 13 the local driveway, about 7.2 miles, newly paved with asphalt in 2020 (see inset to Figure7). The noise inside the cabin was measured twice from 20 to 60 mph with a 10 mph interval.

Figure 6. 6. TheThe result result of the of sound the sound reduction reduction performanc performancee of the AMS of (red) the and AMS the (red) foam and(blue) the com- foam (blue) comparedpared to the to original the original tire (yellow) tire (yellow) without any without attachment any attachment through thethrough field test.the (a) The field sound test. pres- (a) The sound pressuresure spectra spectra from from100 Hz 100 to Hz1000 to Hz. 1000 The Hz. solid The blac solidk line black represents line represents the stopped the state. stopped At 60 state. mph, At 60 mph, yellow (solid), (solid), blue blue (dashed), (dashed), and and red red(dotted) (dotted) lines linesrepresent represent no attachment, no attachment, foam attachment, foam attachment, and and AMS on the rim, respectively. (b–f) The normalized sound transmission coefficients (N-STC) from AMS200 Hz on to the300 rim,Hz depending respectively. on the (b vehicle–f) The speed. normalized sound transmission coefficients (N-STC) from 200 Hz to 300 Hz depending on the vehicle speed.

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FigureFigure 7.7. TheThe averageaverage soundsound pressurepressure levellevel fromfrom 200200 HzHz toto 300300 HzHz versusversus thethe vehicle’svehicle’s speedspeed withwith error bars. Yellow (solid), blue (dashed), and red (dotted) lines represent no attachment, foam at- error bars. Yellow (solid), blue (dashed), and red (dotted) lines represent no attachment, foam tachment, and AMS on the rim, respectively. The inset depicts the newly paved asphalt driveway. attachment, and AMS on the rim, respectively. The inset depicts the newly paved asphalt driveway.

TheThe temporal sound sound pressure pressure was was measured measured for for 19 19 s with s with a Rode a Rode NT-USB NT-USB mini mini mi- microphone,crophone, and and the the recorded recorded data data were were processe processedd with with the the fast fast Fourier Fourier transform transform (FFT) (FFT) to toobtain obtain the the frequency frequency spectrum spectrum of of the the sound sound pr pressureessure level level (SPL) (SPL) from from 50 50 Hz Hz to to 1,000 1000 HzHz asas shownshown inin FigureFigure6 6a.a. The The cavity cavity mode mode occurs occurs near near 230 230 Hz, Hz, as as expected. expected. Although Although both both foamfoam andand AMSAMS showshow noisenoise reductionreduction effects,effects, thethe SPLSPL ofof AMSAMS isis 2–32–3 dBdB moremore thanthan foamfoam andand isis significantlysignificantly higher.higher. TheThe frequencyfrequency rangerange underunder considerationconsideration rangedranged fromfrom 200200 toto 300300 HzHz asas thethe tiretire airair cavitycavity modemode appearsappears nearnear 230230 Hz.Hz. TheThe frequencyfrequency spectrumspectrum ofof thethe soundsound transmissiontransmission coefficientcoefficient (STC) at vari variousous vehicle vehicle speeds speeds is is shown shown in in Figures Figure6 6b–f.b–f. STCSTC isis normalizednormalized byby thethe peakpeak ofof the cavity mode at 60 mph. For low speed at E.V. mode, 20–4020–40 mph,mph, thethe cavitycavity modemode0′s peakpeak valuesvalues areare similarsimilar butbut thethe noisenoise atat otherother frequenciesfrequencies inducedinduced byby engineengine increasesincreases asas thethe vehiclevehicle speedspeed increases.increases. TheThe averageaverage soundsound pressurepressure levellevel inin thethe bandband 200–300200–300 HzHz dependsdepends onon thethe vehiclevehicle speed,speed, asas shownshown inin FigureFigure7 7.. TheThe noise noise level level increases increases with with the the speed, speed, and and the the slope slope of of noisenoise changeschanges whenwhen thethe mechanicalmechanical engineengine kickskicks onon afterafter 4040 mphmph duedue toto thethe electricelectric toto gasolinegasoline powerpower modes.modes. Average valuesvalues areare usedused soso thatthat thethe foamfoam casecase showsshows moremore noisenoise thanthan thethe referencereference case.case. AlthoughAlthough thethe foamfoam reducesreduces thethe cavitycavity mode’smode’s noise,noise, moremore peakspeaks occuroccur nearnear thethe cavitycavity mode,mode, asas seenseen inin FigureFigure6 6b.b. The The AMS AMS is is 1.45 1.45 times times heavier heavier than than the the foam.foam. Nevertheless, through all speed ranges, the AMSAMS clearlyclearly providesprovides aa betterbetter noisenoise reductionreduction effecteffect thanthan thethe foam,foam, 2–52–5 dBdB nearnear thethe cavitycavity mode,mode, atat 200–300200–300 Hz.Hz.

4.4. Further Discussion TheThe acousticacoustic foamfoam isis generallygenerally usedused toto reducereduce noise,noise, notnot onlyonly forfor tirestires butbut alsoalso forfor stationarystationary structures,structures, e.g.,e.g., inin civilcivil engineeringengineering asas anan absorberabsorber [[35–38].35–38]. For the tire applica- tion,tion, MohamedMohamed etet al.al. validatedvalidated thethe effectivenesseffectiveness ofof foamfoam [[39].39]. However,However, thethe absorptionabsorption coefficientcoefficient isis lessless thanthan 7%,7%, andand eveneven lowerlower atat thethe low-frequencylow-frequency range.range. AsAs aa reflector,reflector, thethe AMSAMS displaysdisplays aa betterbetter noisenoise reductionreduction capability,capability, aboutabout 2–32–3 timestimes (~3(~3 dB)dB) thatthat ofof foamfoam atat thethe low-frequencylow-frequency range,range, inin thethe regionregion ofof thethe cavitycavity mode,mode, andand thethe broadband.broadband. However, the actual effectiveness of the application (~10 dB) is much lower than the preliminary the actual effectiveness of the application (~10 dB) is much lower than the preliminary results (23–62 dB) from the unit cell; the AMS can only cover 3.5” of the rim due to the results (23–62 dB) from the unit cell; the AMS can only cover 3.5″ of the rim due to the non-flat surface, so noise induced by TPIN continues to propagate through the uncovered non-flat surface, so noise induced by TPIN continues to propagate through the uncovered area. With a modified and optimized design concerning the rim, an adequate bonding area. With a modified and optimized design concerning the rim, an adequate bonding mechanism between the rim and the AMS for durability, and a suitable material selection, the efficiency of AMS noise reduction could be improved substantially.

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5. Conclusions We propose a noise-reduction method for tires using relatively lightweight acoustic metasurfaces or metalayers with high reflective and absorbing characteristics. The natural frequency of the clamped thin plate is calculated by the numerical simulation and validated by the references. The effectiveness of the AMS was demonstrated numerically and experimentally, but these were not compared to each other directly. The design guideline was provided through the parametric study. Our in-house AMS prototype was utilized for the experiment both on the laboratory scale and for actual field tests in a hybrid car. The noise reduction effect of the AMS can be manipulated by tuning the thin plate’s fundamental resonance via certain design parameters. The method in this work can substantially reduce the noise near the tire cavity mode at around 230 Hz and extends over a broader range of frequencies under 1000 Hz. The field test results demonstrated that almost-total AMS reflection provides a better noise reduction effect than absorption by foam, 2–3 dB near the cavity mode at 200–300 Hz. Even considering that AMS is slightly heavier than foam, the former is still 1.4–2 times more effective than the latter when it comes to noise reduction. Furthermore, the structure of the material used in this approach is lightweight and does not affect the tire0s performance. It can be easily combined with the existing technolo- gies to maximize the sound transmission loss. The robust and lightweight nature of the design means that it can be modified and applied to other fields for sound and vibration isolation to reduce noise issues.

Author Contributions: Conceptualization, H.H., J.J., and A.N.; methodology, H.H. and M.S.; soft- ware, H.H.; validation, H.H. and M.S.; formal analysis, H.H.; investigation, H.H. and M.S.; resources, H.H. and M.S.; data curation, H.H.; writing—original draft preparation, H.H. and M.S.; writing— review and editing, J.J. and A.N.; visualization, H.H. and M.S.; supervision, J.J. and A.N.; project administration, A.N.; funding acquisition, J.J. and A.N.; All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by National Science Foundation supported grant entitled “GOALI: EFRI NewLaw: Non-reciprocal effects and Anderson localization of acoustic and elas- tic waves in periodic structures with broken P-symmetry of the unit cell” Award #1741677. J.J. appreciates the support from Shanghai NSF (Award # 17ZR1414700), the Research Incentive Program of Recruited Non-Chinese Foreign Faculty by Shanghai Jiao Tong University. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data is contained within the article. Acknowledgments: The authors acknowledge Tracy Lynch, Mark Lanier, Richard Bates, and Lowyn Hendrickson for their help and support in this study. Conflicts of Interest: The authors declare no conflict of interest.

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