Passive earplug including Helmholtz resonators arranged in series to achieve broadband near zero occlusion effect at low frequencies

Prolonged noise exposure is responsible for noise-induced hearing loss and non-auditory health effects, such as stress, disturbed sleep, increased risk of hypertension, and cardiovascular disease.¹ Regarding occupational noise, passive earplugs are commonly used to prevent workers from these risks.^2,3 However, the use of passive earplugs is often associated with the increase in the auditory perception of bone-conducted sounds, such as one's own voice, chewing, or breathing.² This phenomenon is referred to as the occlusion effect of the ear canal and is most significant at low frequencies, typically below 1 kHz.² As a notable acoustic discomfort,⁴ the occlusion effect can alter the use and, consequently, the efficiency of passive earplugs. Hence, the development of passive earplugs that do not induce noticeable occlusion effect is required.

At low frequencies, the occlusion effect is objectively characterized by the increase in the acoustic pressure generated in the occluded ear canal, compared to the open case.^5,6 The ear canal acoustic pressure originates from the vibration of the ear canal wall when the subject is submitted to a bone-conducted stimulation. For conventional earplugs made of foam or silicone, the occlusion of the ear canal drastically increases its acoustic impedance (seen by its wall), which shifts from a mass-controlled acoustic behavior in the open state to a compliance-controlled acoustic behavior in the occluded state,⁷ and results in the augmentation of the ear canal acoustic pressure.⁷ The vibration of the earplug medial surface also contributes to the acoustic pressure generated in the occluded ear canal, depending on the earplug material properties and its insertion depth.⁸ 

Until recently, the deep-insertion⁹ was the only solution able to significantly reduce the occlusion effect induced by passive earplugs while ensuring a suitable sound attenuation for hearing protection purposes. The working principle of this solution is to cover most of the vibrating ear canal wall surface to decrease the acoustic pressure radiated in the occluded ear canal.^6,8 However, the deep-insertion is associated with discomfort issues due to the mechanical pressure exerted by the occlusion device in the bony part of the ear canal.^10,11 In a recent paper,¹² the authors proposed another solution to reduce the occlusion effect at shallow/medium-insertion. This solution consisted of modifying the acoustic impedance of the earplug medial surface so that it matches the characteristic impedance of air. This was achieved by using four critically coupled Helmholtz resonators (HRs), arranged in parallel in a so-called “meta-earplug.” Its geometry was optimized for exhibiting a quasi-perfect broadband absorption behavior between 200 and 900 Hz. Hence, the meta-earplug was capable of significantly decreasing the objective occlusion effect measured on an artificial ear, compared to foam and silicone earplugs. However, the quasi-perfect broadband absorption did not lead to zero occlusion effect. In addition, the use of four parallel HRs requires the four necks to fit in the ear canal. This constrains the radius of the necks, which limits the frequency bandwidth of the acoustic resonances of the HRs that support the broadband character of the acoustic properties of the meta-earplug medial surface.

In the present paper, we explore the capability of four HRs arranged in series to induce near zero occlusion effect in a broadband frequency range (100 Hz to 1 kHz). This serial configuration of the meta-earplug is inspired by multi-layer HR metamaterials¹³ and requires a single neck to fit in the ear canal. This makes it possible to decrease the radius of the medial section of the meta-earplug so that it could fit in thinner ear canals, compared to the meta-earplug using parallel HRs.¹² In this work, the geometry of the meta-earplug is optimized to achieve a null occlusion effect based on an analytical model of the phenomenon. The motivation behind this optimization strategy is to further reduce the objective occlusion effect, compared to quasi-perfect broadband absorption,¹² by obtaining an earplug that is transparent regarding this phenomenon, similar to active hearing aids,^14,15 earplugs,¹⁶ or earbuds,¹⁷ that aim at reducing the occlusion effect. As a preliminary step before validating the concept on human subjects, this study focuses on the working principle of the proposed meta-earplug. Hence, the current geometry of the meta-earplug has not been tailored to fit into a realistic human outer ear and its performance for reducing the objective occlusion effect is evaluated using an artificial ear dedicated to bone-conducted stimulation.^12,18

Several aspects are also studied in this paper. First, the performance of the meta-earplug using four HRs for reducing the occlusion effect is compared to a simpler system made of a single HR of equivalent volume. Second, the influence of acoustic resonances resulting from the coupling of the meta-earplug to the ear canal cavity is investigated up to 2 kHz as it could significantly increase the occlusion effect.¹² Third, the experimental insertion loss provided by the serial configuration of the meta-earplug is evaluated using a standard artificial test fixture and the influence of the acoustic properties of the meta-earplug on its sound attenuation is investigated using an associated finite element (FE) model.

Overall, the present paper aims to answer the following questions:

1. How does minimizing the occlusion effect itself lead to a greater reduction of the phenomenon compared to quasi-perfect broadband absorption?

2. How does the reduction of the occlusion effect compare with a single HR versus four resonators using an equivalent volume and the same optimization process?

3. How do the acoustic resonances of the meta-earplug coupled to the ear canal influence the occlusion effect above 1 kHz?

4. How do the acoustic properties of the medial surface of the meta-earplug influence its insertion loss?

Figure 1 displays schematics of the meta-earplug made of four HRs coupled in series. The proposed meta-earplug is intended to be inserted at shallow/medium depth to not cause mechanical discomfort in the bony region of the ear canal. Each HR of the meta-earplug is composed of a neck (with circular cross section) and a cavity. Each cavity is partially filled with a layer of melamine foam, which is essential to lower the acoustic resonance frequencies of the system.¹² Compared to the parallel configuration of the meta-earplug,¹² the serial configuration presented here only requires the neck of HR#1 to be inserted in the ear canal rather than all of them. In addition to the advantages presented in the Introduction, the serial configuration proposed here allows us to optimize the length of the necks #2, #3, and #4, independently from the length of neck #1 (fixed to 15 mm). Note that necks #2, #3, and #4 connecting the cavities are bent (see Fig. 1).

The remaining structure of the meta-earplug is deemed to partially fit in the concha, just like commercial earbuds. For this purpose, the volume available for the cavities of the HRs is limited to 5.76 cm³ while the volume available in the concha is approximately equal to 4 cm³ on average.¹⁹ As mentioned in the Introduction, the geometry of the cavities is not adapted to fit into realistic concha but rather kept simple to focus on the functioning principle of the meta-earplug. In the plane $x 2 , x 3$⁠, the topology of the cavities in the HRs is defined by two geometrical parameters $e cav [ n ]$ and $h cav [ n ]$⁠, $n$ being the index of the HRs [see Fig. 1(c)], while the depth of all cavities along the $x 1$-axis is fixed to 20 mm [see Fig. 1(d)]. The thickness of foam layers is denoted $l foam [ n ]$⁠. In total, the serial configuration of the meta-earplug has 13 geometrical parameters to be optimized (versus ten for the parallel configuration in which all the necks have the same length¹²).

In this work, we developed a numerical model of the meta-earplug based on the FE method using COMSOL Multiphysics 5.6 (Burlington, MA). This model is intended to verify the theoretical model of the meta-earplug medial surface acoustic properties. Compared to the theoretical model, the FE model accounts for (i) the acoustic radiation of necks in the main waveguide and in the cavities and (ii) the curved geometry of necks #2, #3, and #4. Assuming the structure of the meta-earplug is rigid and motionless, the FE model is purely acoustic. The viscothermal losses that occur in necks and in portions of cavities not filled with foam are accounted for using the low reduced frequency model.²⁴ The foam is modeled as an equivalent fluid domain based on the Johnson–Champoux–Allard model.²⁵ The geometry is meshed according to a criterion of at least six 10-noded (quadratic) tetrahedral elements per wavelength at 1 kHz (maximum frequency of interest) to achieve convergence.

To investigate the influence at low frequencies (below 1 kHz) of the acoustic properties of the meta-earplug on its sound attenuation measured on an artificial test fixture (experimental setup presented in Sec. II E), we developed a simplified acousto-mechanical FE model of the system. Compared to an analytical model, a FE model makes it possible to account for the intricate acoustic transmission through the meta-earplug, which depends on (i) its mechanical behavior as a mass–spring–damper system and (ii) the contribution of the aperture of neck #1 as an acoustic radiator or absorber, and allows for computation of acoustic power flowing through the system.

Figure 2 displays the FE model of the ear canal open and occluded by the meta-earplug. The ear canal is cylindrical, of length $l E C =25.5$ mm, and radius $r E C =3.75$ mm, and corresponds to the ear canal of the artificial test fixture used in the experimental setup (see Sec. II E). From the ear canal entrance, the ear canal cavity is partially surrounded by a 10 mm–long artificial skin layer of thickness 1.7 mm. In the occluded case, the insertion depth of the meta-earplug is equal to 9 mm and corresponds to that in the experimental measurements.

The air in the ear canal is modeled as a compressible fluid domain. Viscothermal losses that occur in the ear canal are accounted for using the low reduced frequency model.²⁴ Acoustic domains of the meta-earplug are modeled as presented in Sec. II C 2. The artificial skin, the ear tip, and the three-dimensional (3D) printed structure of the meta-earplug are modeled as linear isotropic elastic solid domains. Their material properties are summarized in Table II. The artificial skin is made of silicone and its material properties are taken from Ref. 26, except for the Young's modulus, which is assumed to increase due to the static deformation induced by the insertion of the meta-earplug. The Comply^® (Oakdale, MN) ear tip is a strongly viscoelastic foam whose mechanical properties are likely to vary with frequency and to depend on its static compression. Since a direct characterization was not possible, the frequency dependent Young's modulus of the ear tip has been adjusted for the FE simulations to approximately fit the measurement data. Finally, the material properties of the 3D printed structure are taken from the manufacturer of the resin Grey pro V1 (Formlabs, Sommerville, MA).

In the measurement, a coupler mimicking the eardrum acoustic impedance (with intact middle-ear) terminates the ear canal (see Sec. II E). In the FE model, the equivalent acoustic impedance of the coupler²⁷ is defined at the eardrum surface of the ear canal. Since the scattering effect of the head is not significant below 1 kHz, the ear canal is assumed to be embedded in a flat rigid baffle.²⁶ Hence, the incident acoustic pressure field is modeled as a blocked pressure $p b$ of arbitrary amplitude (⁠ $p b =1$ Pa here). When the ear canal is open, the blocked pressure is applied at the lateral surface of the artificial skin layer. Also, to account for both the blocked pressure and the acoustic radiation at the ear canal opening, a normal acoustic particle acceleration condition $a n =jω p b − p / Z rad$ is applied, where $p$ is the total acoustic pressure and $Z rad$ is the acoustic radiation impedance of a baffled circular piston. When the ear canal is occluded, the blocked pressure is applied at the lateral surface of the skin and all over the outer surface of the meta-earplug.

In both open and occluded cases, the artificial skin is fixed on its circumferential and medial surface and the wall of the ear canal cavity not coupled with the artificial skin is acoustically rigid. Continuity of stress vectors and displacements is assumed at the interfaces between solid domains. At fluid–solid interfaces, the continuity of normal component velocity vectors and normal component stress vectors applies. For the sake of conciseness, the FE formulations associated with the current problem are not recalled here and the reader can refer to Ref. 28 for further details. Mesh criteria and solver are the same as for the previous FE model (see Sec. C 2).

Samples of the meta-earplug used in this work are 3D printed based on stereo-lithography technique (Form 2 printer, Formlabs, MA, USA). Post-cure, the mechanical properties of the resin (Grey pro V1, 2.6 GPa Young's modulus and 1200 kg/m³ density) ensure that the 3D printed structures are acoustically rigid. Foam layers are cut manually from melamine panel and inserted in the cavities while a 3D printed back-plate, including necks #2 and #4, is glued to close the system. For occlusion effect and insertion loss measurement, neck #1 is surrounded by a Comply^® foam ear tip [see Fig. 3(a)], which adapts to the ear canal, seals the entrance, and maintains the meta-earplug in position. For impedance tube measurement²⁹ of the medial surface acoustic properties, the meta-earplug is built with an integrated circular support of 29 mm diameter [see Fig. 3(b)].

To assess the sound attenuation provided by the meta-earplug, insertion loss measurements are performed using a commercial artificial test fixture (G.R.A.S. 45CB, G.R.A.S. Sound & Vibration AS, Denmark) in a reverberant room [see Fig. 3(d)] based on ANSI/ASA S12.42-2010.³¹ The ear simulator (G.R.A.S. 40AG, G.R.A.S. Sound & Vibration AS, Denmark) is composed of a cylindrical ear canal (radius of 3.75 mm) and partially covered by a 10 mm–long silicon layer from the ear canal entrance. The ear canal is terminated by a coupler (IEC 60318-4, G.R.A.S Sound & Vibration AS, Holte, Denmark) simulating the eardrum impedance in the reference plane. The pinna is not included since the geometry of the meta-earplug is not adapted to fit into it. In the reverberant room, the acoustic stimulation is ensured by four speakers (type JAMO^® S628, Klipsch Group, Inc., Denmark). Using the microphone included in the coupler, sound pressure levels are measured in open and occluded ear canals and, respectively, denoted $L p , A C open$ and $L p , A C occl$⁠. The experimental insertion loss is then calculated using Eq. (12).

For both occlusion effect and insertion loss measurements, the insertion depth of the meta-earplug is approximately equal to 9 mm from the ear canal entrance, which corresponds to a shallow insertion of the meta-earplug in the cartilaginous region of the ear canal. Also, measurements are repeated three times (earplug inserted and removed each time) to assess the variability of the insertion conditions.

We first investigate the acoustic properties of the meta-earplug medial surface resulting from the optimization process described in Sec. II B. For this purpose, Fig. 4(a) displays the corresponding magnitude of the normalized specific acoustic impedance calculated (i) analytically using the TMM approach (see Sec. II C 1), (ii) numerically using the FE method (see Sec. II C 2), and (iii) experimentally measured using a classical impedance tube (see Sec. II E). According to Fig. 4(a), analytical and numerical results are in good agreement (differences lower than 1.5 dB), which verifies the TMM approach, despite its simplifications. In addition, experimental measurement compares well to the models, even though slight discrepancies (lower than 1 dB compared to the FE model above 125 Hz) exist and are more likely due to geometry inaccuracies related to the 3D printing process.

In Fig. 4(a), the local minima of the input impedance magnitude are indicated by vertical-colored lines, denoted $f 1$ to $f 3$⁠, and correspond to acoustic resonances of the meta-earplug. To minimize the magnitude of the occlusion effect, Fig. 4(a) shows that the input impedance of the meta-earplug medial surface approximately matches the open ear canal input impedance $Z E C open S E C$ weighted by the volume velocity ratio $Ψ q$ [see the dashed curve of equation $Z s = Z E C open S E C Ψ q$ in Fig. 4(a)]. This impedance match is achieved from the first resonance of the meta-earplug that occurs around 300 Hz to approximately 800 Hz. Below 300 Hz, the input impedance of the meta-earplug is governed by the compliance effect of its whole volume and cannot reach the target value. Above 800 Hz, the meta-earplug input impedance departs from $Z s = Z E C open S E C Ψ q$ to attenuate the acoustic resonances of the meta-earplug coupled to the occluded ear canal cavity, which can significantly increase the resulting occlusion effect.¹² 

In the serial configuration proposed here, the 4 degrees of freedom (DoFs) of the meta-earplug are intrinsically coupled. Hence, each resonance of the system is not governed by a single HR, like in the parallel configuration,¹² but rather by the four HRs. To illustrate this aspect, Fig. 4(b) displays the acoustic pressure field along the “unwrapped” meta-earplug (with straight necks instead of curved ones) computed using the FE model at the resonant frequencies $f 1$ to $f 3$ of the system. At each resonance, we can see that all HRs are activated and describe a particular distribution of the acoustic pressure corresponding to an acoustic mode of the system. It is noteworthy to mention that in this 4 DoFs system, the fourth resonance exists but occurs above 1 kHz (i.e., out of the frequency range of interest) and has little influence on the acoustic properties of the meta-earplug medial surface (not shown here).

To look at the optimized values of the geometrical parameters that support the acoustic properties shown in Fig. 4(a), Table III summarizes the optimized values, as well as the lower and upper limits, of the geometrical parameters. Note that upper limits were dictated by the maximum size of the system whereas lower limits rather came from manufacturing constraints. Regarding the foam layers, we can see that their thickness is equal to the upper limit for all HRs. This is understandable since it maximizes the compliance of the cavities which (i) shifts towards lower frequencies the acoustic resonances of the system and (ii) further decreases the magnitude of the input impedance of the meta-earplug below the first resonance. According to Table III, we can see that the radius of neck #1 is also equal to the upper limit. This can be explained by the fact that it maximizes the quality factor of the energy leakage of the meta-earplug, which depends on the surface ratio between neck #1 and the ear canal, and increases the bandwidth of the acoustic resonances of the system.³² Hence, for next optimizations, both the foam layers and the radius of neck #1 could be fixed at their maximum value to decrease the number of parameters to be optimized and speed up the optimization process.

We now investigate the performance of the meta-earplug proposed in this paper for reducing the occlusion effect. For this purpose, Fig. 5(a) displays in the third octave bands both experimental and simulated objective occlusion effect of the meta-earplug when neck #1 is open and when neck #1 is closed (i.e., acoustically rigid condition at the meta-earplug medial surface). Experimental results, denoted “Exp.,” were measured on the artificial ear dedicated to bone-conducted stimulation (see Sec. II E) while simulation results, denoted “Sim.,” were calculated using the EA model of the occlusion effect (see Sec. II B). Note that the acoustically rigid configuration is used to highlight the influence of the acoustic properties of the meta-earplug medial surface (when neck #1 is open) on the occlusion effect. In Fig. 5(a), the acoustic resonance frequencies of the meta-earplug determined in Sec. III A are indicated by vertical-colored lines.

According to Fig. 5(a), the experimental occlusion effect induced by the acoustically rigid configuration (i.e., meta-earplug with neck #1 closed) is shown to decrease with frequency from approximately 35 to 5 dB. This decrease aligns with experimental data found in the literature from studies involving human subjects using conventional earplugs.^5,6,33 The change in the character of the acoustic impedance of the ear canal seen by its wall from the mass-controlled open state to the compliance-controlled occluded state provides an explanation of the phenomenon.⁷ In Fig. 5(a), the simulation is consistent with the measurement data of the occlusion effect. Indeed, the ratio of volume velocity imposed to the ear canal cavity between open and occluded cases was adjusted in the EA model (see Sec. II B) for the simulation to approximately fit with experimental measurement in the configuration of the acoustically rigid occlusion of the ear canal. In the model, this ratio was taken constant with frequency. However, it is more likely to exhibit a frequency dependence due to its reliance on the structural modes of deformation of the ear canal surrounding tissues.

When neck #1 of the meta-earplug is open, Fig. 5(a) shows that the experimental occlusion effect is significantly reduced compared to the acoustically rigid configuration. This reduction varies from 13 dB at 100 Hz to 5 dB at 1 kHz and reaches almost 25 dB around 300 Hz. The EA model is shown to accurately predict the reduction in occlusion effect provided by the meta-earplug, despite the simplicity of the model. Indeed, the EA model does not account for the mechanical behavior of the artificial ear used in the experimental setup, which contributes to explaining the discrepancies that exist between simulations and measurements. Overall, the EA model adequately captures the acoustic behavior of the system, allowing it to be used in the optimization process. The EA model also provides a valuable tool for explaining the reduction in occlusion effect achieved by the meta-earplug.

Below the first acoustic resonance of the meta-earplug that occurs around 300 Hz [see Fig. 5(a)], the reduction of the occlusion effect comes from the compliance effect of its whole volume. This phenomenon is comparable to the reduction of the occlusion effect provided by large earmuffs.^2,6 Then, from 300 Hz to 1 kHz, the successive acoustic resonances of the meta-earplug maintain the occlusion effect close to zero by approximately matching the input impedance of the open ear canal, weighted by the ratio of volume velocity imposed to the ear canal cavity between open and occluded cases [see Fig. 4(a) and Eq. (5) of the EA model in Sec. II B]. Although the optimization process was set to minimize the occlusion effect magnitude between 100 Hz and 1 kHz, the meta-earplug is unable to achieve zero occlusion effect below its first acoustic resonance (around 300 Hz) due to its limited volume which governs the acoustic compliance of the system (see Sec. III A).

In a previous paper,¹² the authors proposed to reduce the occlusion effect induced by earplugs using quasi-perfect broadband absorption (i.e., $Z s , E P$ tends to $Z 0$⁠). In Fig. 5(b), we compare the two strategies of optimization (i.e., minimizing the reflection coefficient $R 2$ or the occlusion effect $O E 2$ itself) on the simulated occlusion effect induced by the meta-earplug with four HRs in series. Geometrical parameters of this additional configuration are summarized in Table IV of the  Appendix. According to Fig. 5(b), the quasi-perfect broadband absorption provides a significant reduction of the occlusion effect compared to the acoustically rigid configuration, similarly to the parallel configuration of the meta-earplug.¹² However, minimizing the magnitude of the occlusion effect leads to an even greater reduction of the phenomenon [up to 10 dB in the 200–400 Hz frequency range; see Fig. 5(b)] because it further decreases the input impedance of the meta-earplug medial surface $[ Z s , E P$ is twice as low as $Z 0$ around 300 Hz; see Fig. 4(a)].

The performance of the meta-earplug minimizing the magnitude of the occlusion effect using four HRs in series is also compared to a simpler system made of a single HR of equivalent dimensions. Geometrical parameters of the single HR are also optimized for minimizing $O E 2$ from 100 Hz to 1 kHz and the resulting values are presented in Table V of the  Appendix. The simulated occlusion effect induced by the single HR is displayed in Fig. 5(b). At the resonant frequency of the single HR that occurs around 400 Hz, the occlusion effect encounters a large negative dip (up to −10 dB). Below 400 Hz, the reduction of the occlusion effect provided by the single HR comes from the compliance effect of its cavity, similarly to the meta-earplug using four HRs. From 400 Hz to 1 kHz, the occlusion effect induced by the single HR gradually increases (up to almost 10 dB at 1 kHz), driven by the Tonraum resonance that occurs in the coupled system¹² above 1 kHz. A single HR alone cannot attain a nearly zero occlusion effect across a wide range of frequencies, unlike the four HRs meta-earplug that has been optimized to minimize this phenomenon. More generally, the use of multiple HRs gives more DoFs to shape the curve of the occlusion effect as desired compared to a single HR.

As previously mentioned, acoustic resonances resulting from the coupling of the meta-earplug (or a single HR) to another finite volume (i.e., the ear canal cavity) can significantly increase the occlusion effect.¹² Below 1 kHz, coupled resonances that could occur in the system are completely attenuated since the meta-earplug input impedance was optimized for minimizing the occlusion effect magnitude. To study the influence of coupled resonance above 1 kHz, Fig. 6(a) displays the simulated occlusion effect induced by the meta-earplug (with neck #1 open) up to 2 kHz. According to Fig. 6(a), the simulated occlusion effect induced by the meta-earplug reaches 15 dB at the coupled resonance of the system near 1.5 kHz. However, when accounting for the eardrum impedance $Z T M$ in the EA model as a locally reacting impedance taken from Ref. 22 (also detailed in Ref. 34) and displayed in Fig. 6(b) (normalized magnitude), the occlusion effect significantly decreases to 5 dB at the corresponding frequency [see Fig. 6(a)]. This comes from the resistive effect of the eardrum/middle-ear, which greatly attenuates the coupled resonance. Below 1 kHz, the eardrum impedance is mainly driven by the compliance effect of the middle-ear [see Fig. 6(b)], which has little influence on the occlusion effect induced by the meta-earplug [see Fig. 6(a)]. Hence, two conclusions can be drawn regarding the optimization process. (i) It is not necessary to optimize the meta-earplug input impedance above 1 kHz to avoid the coupled system resonance since the latter is greatly attenuated by the eardrum/middle-ear. (ii) The eardrum impedance is not required in the optimization process below 1 kHz since it barely influences the occlusion effect induced by the meta-earplug.

In this section, we now study the experimental insertion loss provided by the serial configuration of the meta-earplug using a standard artificial test fixture (see Sec. II E). In particular, we focus on the influence of the acoustic properties of the meta-earplug medial surface on the resulting sound attenuation. For this purpose, Fig. 7(a) displays the insertion loss (mean ± standard deviation) provided by the meta-earplug when neck #1 is open and when neck #1 is closed (i.e., filled with resin). The results are presented in the third octave band between 100 Hz and 5 kHz and, as usual in the hearing protection field, the y axis is reversed so that the insertion loss is maximum at the bottom and minimum at the top. Vertical-colored lines indicate the resonant frequencies of the system below 1 kHz. The fourth acoustic resonance that occurs above 1 kHz is not indicated since it has no significant influence on the acoustic behavior of the system.

According to Fig. 7(a), the meta-earplug (with neck #1 open) provides an insertion loss higher than 35 dB in the entire frequency range of interest, which makes it suitable for hearing protection usage. When neck #1 is blocked, Fig. 7(a) shows that the insertion loss provided by the meta-earplug is decreased up to 10 dB in the third octave band centered at 800 Hz. The minimum of the insertion loss in both configurations (i.e., neck #1 open or blocked) also occurs in this frequency band. Above 1 kHz, the insertion loss remains quite similar between the two configurations. Below 1 kHz, the influence of the acoustic properties of the meta-earplug medial surface on the insertion loss was already seen in the parallel configuration of the meta-earplug exhibiting a quasi-perfect broadband absorption.¹² In this paper, the difference in insertion loss seen between 100 Hz and 1 kHz depending on the state of neck #1 (open or blocked) is examined hereafter using the FE model presented in Sec. II D.

Figure 7(b) displays the simulated insertion loss in narrow band provided by the meta-earplug when neck #1 is open or blocked. In the FE model, the Young's moduli of the artificial skin layer of the ear canal and of the ear tip of the meta-earplug were adjusted so that the simulations approximately fit the measurement data presented in Fig. 7(a). Hence, the FE model adequately captures the vibro-acoustic behavior of the system, which allows it to be used for investigating the insertion loss provided by the meta-earplug. According to the FE model, the insertion loss minima that occurs around 700 Hz, whether neck #1 is open or closed [see Fig. 7(b)], corresponds to a piston-like mode of deformation of the meta-earplug/skin system where the 3D printed structure acts as a mass while the ear tip coupled to the skin layer of the ear canal forms a spring-damper system. This mode of deformation is illustrated in Fig. 7(d) which displays the total displacement field of the system. While this mode occurs, regardless of the state of neck #1 (open or blocked), the resulting insertion loss is 10 dB higher when neck #1 is open rather than closed [see Fig. 7(b)].

To investigate this phenomenon, Fig. 7(c) displays the acoustic power (i) injected in the ear canal cavity through the ear tip (orange curve), (ii) exchanged through the aperture of the open neck #1 (green curve), and (iii) dissipated in the coupler simulating the eardrum acoustic impedance (black curve), all computed using the FE model. Solid (respectively, dashed) lines indicate that the acoustic power flows towards (respectively, outwards) the ear canal cavity. Other contributions, such as the acoustic power injected by the portion of skin that is not covered by the meta-earplug, and the acoustic power dissipated in the ear canal cavity by viscothermal effects are not displayed since they are small compared to the powers plotted on Fig. 7(c). According to Fig. 7(c), most of the acoustic power injected in the ear canal cavity flows through the ear tip of the meta-earplug in the entire frequency range of interest, except between 300 and 400 Hz where the acoustic power injected through the aperture of neck #1 is of similar amplitude. At the mechanical resonance of the system that occurs around 700 Hz, the acoustic power injected by the ear tip is maximum. In addition, most of the acoustic power injected in the ear canal cavity by the ear tip is absorbed by the meta-earplug through the aperture of neck #1 due to the high absorption of the meta-earplug medial surface whose acoustic impedance approximately matches the characteristic impedance of air from 700 Hz to 1 kHz [see Fig. 4(a)]. This absorption phenomenon is illustrated in Fig. 7(e) which shows the active acoustic intensity vectors starting from the medial surface of the ear tip and pointing towards the aperture of neck #1. As a result of this absorption phenomenon, the acoustic power dissipated in the coupler is 10 dB lower than the acoustic power injected in the ear canal by the ear tip [see Fig. 7(c)]. Hence, when neck #1 is blocked, the acoustic power injected by the ear tip cannot be absorbed by the meta-earplug and is, rather, mainly dissipated in the coupler, which decreases the insertion loss of the system [see Fig. 7(b)].

In this section, we finally discuss the main limitations of this work and outline some perspectives. First, the proposed approach for reducing the objective occlusion effect using an optimized meta-earplug was applied on a specific artificial ear for a given bone-conducted stimulation. However, the magnitude of the objective occlusion effect is known to significantly vary between individuals⁶ and also depends, to some extent, on the bone-conducted stimulation.³⁵ Since the proposed meta-earplug is a passive system, it cannot adapt to the various factors influencing the occlusion effect compared to an active device.¹⁷ Hence, several meta-earplugs could be optimized for different magnitudes of the occlusion effect adapted to different group of individuals, for example.

Second, regarding the source of the occlusion effect, we considered in this work a purely bone-conducted stimulation, such as chewing, breathing, or heartbeat in practice. Therefore, the proposed approach partially applies to speech production, which includes both air-conducted and bone-conducted components. In fact, the naturalness of one's own voice perception depends on the natural balance that exists between air-conducted and bone-conducted sounds when the ear canal is open.³⁶ Hence, in the case of speech production, another approach could be to maintain this natural balance, even when the ear canal is occluded. For this purpose, both the sound attenuation and the occlusion effect should be combined in the optimization process.

In this paper, we reported a new design of a meta-earplug made of four HRs, arranged in series, and capable of achieving near zero objective occlusion effect measured on an artificial ear in a broadband frequency range (300 Hz to 1 kHz). For this purpose, the input impedance of the meta-earplug medial surface was shown to approximately match the input impedance of the open ear canal weighted by the ratio of volume velocity imposed to the ear canal cavity in open and occluded cases. Also, the meta-earplug was shown to provide a suitable sound attenuation for hearing protection usage. In particular, at the piston-like mode of the system, we showed that, compared to the case where neck #1 is closed, the meta-earplug (with neck #1 open) significantly improves the sound attenuation by absorbing the acoustic power injected to the ear canal cavity through the ear tip. In future work, the proposed approach for reducing the occlusion effect using a meta-earplug will be tested on individuals to evaluate its benefit on the reduction of the associated acoustic discomfort.

The authors acknowledge the support of the Institut de recherche Robert-Sauvé en santé et en sécurité du travail for funding this research.

Table IV summarizes the geometrical values of the meta-earplug made of four HRs arranged in series and optimized for minimizing $R 2$ while Table V presents the geometrical values of the single HR optimized for minimizing $O E 2$⁠. For each configuration, lower and upper limits of the geometrical parameters are also provided. In both configurations, note that the length of neck #1 is fixed to $l neck [ 1 ] =15$ mm, as in the base configuration (see Sec. II A). In the configuration using the single HR, the optimized values of geometrical parameters correspond to the upper limits.