Sustainable Membrane-Based Acoustic Metamaterials Using Cork and Honeycomb Structures: Experimental and Numerical Characterization

Abstract

This work presents the experimental and numerical investigation of a novel acoustic metamaterial based on sustainable and biodegradable components: cork membranes and honeycomb cores made from treated aramid paper. The design exploits the principle of localized resonance induced by tensioned membranes coupled with subwavelength cavities, aiming to achieve high sound absorption at low (250–500 Hz) and mid frequencies (500–1400 Hz) with minimal thickness and environmental impact. Three configurations were analyzed, varying the number of membranes (one, two, and three) while keeping a constant core structure composed of three stacked honeycomb layers. Acoustic performance was measured using an impedance tube (Kundt’s tube), focusing on the normal-incidence sound absorption coefficient in the frequency range of 250–1400 Hz. The results demonstrate that increasing the number of membranes introduces multiple resonances and broadens the effective absorption bandwidth. Numerical simulations were performed to predict pressure field distributions. The numerical model showed good agreement with the experimental data, validating the underlying physical model of coupled mass–spring resonators. The proposed metamaterial offers a low-cost, modular, and fully recyclable solution for indoor sound control, combining acoustic performance and environmental sustainability. These findings offer promising perspectives for the application of bio-based metamaterials in architecture and eco-design. Further developments will address durability, high-frequency absorption, and integration in hybrid soundproofing systems.

1. Introduction

Noise pollution is one of the main forms of environmental disturbance in contemporary urban and industrial areas [1]. According to the European Environment Agency, approximately 20% of the EU population is exposed to noise levels above recommended limits, with documented health consequences, including sleep disturbances, cardiovascular problems, cognitive difficulties and chronic stress [2,3]. In this scenario, noise control and the improvement of acoustic comfort in living environments—domestic, working and public—have become strategic objectives for sustainable architecture and environmental engineering [4,5].Traditionally, noise mitigation has relied on the use of porous or fibrous materials such as rock wool, expanded melamine or polyurethane foams, which act by sound absorption through viscous phenomena in the pores [6,7]. However, these materials have several limitations: high thickness required for low frequencies, degradation over time, potential environmental impact and poor recyclability [8]. Specifically, some traditional absorbers, particularly certain foams and fibrous materials, may degrade over time under environmental stress, but not all absorbing materials exhibit this behavior. Considering these critical issues, there is a need to develop new high-performance, sustainable, compact and lightweight acoustic materials capable of responding to the needs of contemporary design.

Over the past two decades, research on acoustic metamaterials has opened a new avenue in the design of advanced materials for sound control [9,10]. These unconventional materials, whose structure is engineered at the sub-wavelength scale, enable acoustic properties that would otherwise be unattainable with traditional materials [11]. Their most promising applications include low-frequency absorption performance, selective wave guidance, resonant absorption, and manipulation of acoustic propagation [12].

A distinct class of acoustic metamaterials is represented by membrane-based metamaterials [13,14,15], in which thin, flexible films—typically made of polymers—vibrate to couple incident sound waves with local resonant modes. Such devices, in certain configurations, show peaks of sound absorption even in otherwise difficult-to-treat frequency regions (e.g., 100–800 Hz), with thicknesses less than one-tenth of the wavelength [16]. Some variants involve the coupling of the membrane with concentrated masses (Membrane-Type Acoustic Metamaterials, MTAM), cavities, or rigid or porous supports [17].

In parallel with the functional progress of metamaterials, the need to orient their design in an eco-friendly direction is becoming increasingly urgent. The use of natural materials, which are recyclable or derived from production waste, represents a concrete response to the need for technical solutions that combine performance and environmental responsibility. Cork, a natural material obtained from the bark of Quercus suber, is light, elastic, durable and has a closed cellular structure that also makes it a good thermal and acoustic insulator [18]. These properties make it an excellent candidate for applications in metamaterials, especially in flexible configurations such as membranes [19]. Furthermore, cork is completely biodegradable, recyclable and its extraction does not involve cutting down trees, making it one of the most sustainable materials available today [20].

Aramid paper impregnated with phenolic resin has good electrical insulation ability. It is appreciated for its characteristics of lightness and extreme rigidity [21]. It is often used in decorative or artistic fields, has a high specific stiffness, good workability and a controllable surface [22]. If properly worked into honeycomb structures, it can act as a light and robust support for acoustic membranes [23]. The use of paper in a structured form, in addition to reducing the weight of the system, allows for modular and low-cost use in industrial and architectural applications [24]. The coupling of cork membranes and paper honeycomb supports can therefore generate a lightweight, modular and recyclable metamaterial platform, with potential benefits in both acoustic and environmental terms.

Several recent studies have demonstrated the effectiveness of membrane metamaterials in selectively absorbing low-frequency sound waves [25,26]. However, much of the literature focuses on systems based on synthetic materials such as elastomers, silicones, or plastic films, rarely considering materials of natural origin. Furthermore, metamaterials with structured cellular supports, such as honeycombs, are poorly explored in combination with natural lightweight membranes. Some studies have focused on rigid cavities or additional masses as mechanisms to introduce multiple resonances [27,28], but a systematic evaluation of the effect of the number of membranes and the layered configuration on fully natural and sustainable devices is lacking. Finally, few works combine systematic experimentation (e.g., with Kundt tube) with numerical modeling in an integrated way [29,30]. This limits deep understanding of the physical mechanisms underlying the observed performances and prevents guided design optimization.

In this context, the present work aims to contribute to the development of sustainable acoustic metamaterials based on cork membranes and aramid paper honeycomb supports. The main objectives of the research are as follows:

• To realize and experimentally test different metamaterial configurations, varying the number of membranes (from one to three) and keeping the number of honeycomb supports constant.
• To measure the sound absorption coefficient for each configuration by using the impedance tube method according to ISO 10534-2 [31], covering a frequency range between 250 and 1400 Hz.
• To analyze the behavior of the membranes through numerical simulations to understand the mechanisms responsible for the absorption peaks.
• To evaluate acoustic efficiency by highlighting the best performing configurations in terms of average absorption/size ratio.
• To discuss the sustainability and real-world applicability of the proposed system by comparing it with conventional solutions for effectiveness, environmental impact and potential for integration into architecture.

Through this integrated approach, we intend to demonstrate that the joint use of cork and heraldic paper, appropriately configured in multilevel metamaterial architectures, can represent a valid alternative to traditional acoustic materials in terms of performance, sustainability and scalability.

The paper is organized as follows. In Section 2, the materials, the tested configurations and the experimental methodology adopted are presented. Section 3 reports the results of the measurements of the sound absorption coefficient, with a comparison between the different configurations. In Section 3, numerical modeling is introduced, which is useful to interpret the observed resonant phenomena. Finally, in Section 4, the main results, the limitations of the work and the perspectives for future developments are summarized.

The main original contributions of this work can be summarized as follows:

• Proposal and realization of a completely bio-based acoustic metamaterial, built with readily available, lightweight and low environmental impact natural materials.
• Systematic experimental evaluation of the influence of the number of cork membranes on paper honeycomb structures, with extensive data on low-frequency sound absorption.
• Integration of measurement, analytical simulation and comparative analysis, to provide a complete picture of the physical phenomena involved.

These elements, taken together, offer an original and multidisciplinary approach to the design of new acoustic materials, positioning this work at a fertile intersection between technical physics, applied acoustics, material science and sustainable design.

2. Materials and Methods

2.1. Materials Used and Specimens Set Up

To fabricate the sound-active membranes for the metamaterial system, we employed disks of pressed natural cork, selected for its favorable combination of physical and mechanical properties. Cork is a lightweight material (density ≈ 200 kg/m³) characterized by high elasticity, low stiffness, and a good internal damping capability (the loss factor typically ranges between 0.05 and 0.12 in the frequency range of 100 Hz–1000 Hz), all of which make it particularly suitable for acoustic applications where energy dissipation and membrane flexibility are crucial [32]. The cork sheets were cut into circular membranes with a diameter of 100 mm to ensure compatibility with the standardized Kundt tube apparatus used for acoustic characterization, particularly for measuring the normal-incidence sound absorption coefficient (Figure 1a). The thickness of each cork membrane was maintained at a uniform value of 2 mm to ensure repeatability and to isolate the role of other geometrical parameters (such as the honeycomb core configuration) in the system’s acoustic response. Each membrane was mechanically clamped along its circular edge using a rigid clamping ring designed to reproduce a fixed boundary condition, thereby simulating classical membrane behavior in accordance with established models of acoustic metamaterials. Specifically, the clamping rings were made of rigid plastic with an outer diameter of 100 mm, an inner diameter of 96 mm, and a thickness of 15 mm. This boundary constraint is critical in enabling the membrane to undergo controlled out-of-plane vibrations under incident acoustic excitation, facilitating the generation of resonance effects that are essential for achieving subwavelength absorption phenomena.

As the underlying structural support for the cork membrane, we utilized honeycomb cores fabricated from aramid paper—specifically treated for enhanced dimensional stability and mechanical strength.

Aramid paper based on Nomex^®, a trademark of DuPont™, is a high-performance, flame-resistant material composed of synthetic aromatic polyamide fibers [33,34]. It is widely used in demanding engineering applications due to its unique combination of mechanical strength, thermal stability, and electrical insulation properties. In its honeycomb form, Nomex-based aramid paper provides an ideal balance between rigidity and low weight, making it suitable for aerospace, transportation, and advanced acoustic systems. Structurally, it features a regular hexagonal cell geometry that offers high stiffness-to-weight ratios while maintaining permeability to air, allowing it to function as a mechanical support and an acoustic cavity in metamaterial architectures. Its inherent porosity and low density (~48–72 kg/m³) enhance its effectiveness in acoustic applications by enabling controlled resonance behavior without significant mass addition. Moreover, Nomex is valued for its chemical inertness, dimensional stability, and sustainability, as it is recyclable and designed for long-term durability in harsh environments. While aramid paper is technically recyclable, this requires specialized industrial processes due to its thermal and chemical resistance. The honeycomb core used in this study is fully recyclable through paper recycling streams. Compared to petroleum-based polymer substrates, the combined use of bio-based cork and recyclable paper components in the proposed structure contributes to a reduced carbon footprint, though the aramid layer remains a limiting factor [35].

The honeycomb architecture was composed of regularly spaced hexagonal cells, which, upon expansion, provided a rigid yet porous scaffold. Aramid paper was selected due to its high specific modulus, thermal and chemical resistance, and its excellent weight-to-strength ratio, which is advantageous for maintaining structural integrity without adding significant mass to the metamaterial unit.

The individual honeycomb panels had a thickness of 13 mm each (Figure 1b). For the experimental configurations discussed in this work, we assembled them in stacks of up to three layers, resulting in a total core thickness of 39 mm. This modular approach enabled systematic investigation of the influence of core depth on the acoustic response, particularly regarding the positioning of the localized resonances and their bandwidth. The combination of the cork membrane and honeycomb core created a composite resonant system, where the enclosed air cavities within the hexagonal cells played a crucial role in tuning the acoustic impedance and enhancing the energy trapping mechanism at specific frequencies.

Furthermore, the open yet periodic structure of the honeycomb allowed for partial air permeability, which facilitated the coupling between membrane vibrations and the internal cavity resonances, a phenomenon central to the operation of many hybrid membrane-based acoustic metamaterials.

The integration of these two bio-based and engineered materials—pressed cork and aramid honeycomb—thus enabled the development of a lightweight, modular, and potentially sustainable solution for passive sound absorption applications across low-to-mid frequency ranges.

In

Table 1. Summary of physical-mechanical parameters of materials used to prepare the specimens.

Material	Density (kg/m3)	Thickness (mm)	Elastic Module (MPa)	Porosity (%)	Sustainability
Cork	~200	2	~10	~5–10	Recyclable, bio-based
Aramid paper (HC)	~48–72	13 for each layer	~50–300	~90–98	Recyclable

, a summary of physical-mechanical parameters of materials is shown.

Aramid paper is not biodegradable but is recyclable under certain conditions. It is durable, lightweight, and contributes to energy savings in transport. Environmental sustainability may be improved when used in long-life applications or combined with bio-based components (e.g., cork).

Three configurations of multilevel metamaterials were studied:

• Configuration A: a single cork membrane, coupled with three honeycomb layers (1M–3H).
• Configuration B: two cork membranes, each separated by a honeycomb layer (2M–3H).
• Configuration C: three cork membranes, alternating with three honeycomb layers (3M–3H).

All configurations have an external diameter of 100 mm, to ensure compatibility with tube impedance, and a constant total thickness of about 45 mm, allowing a direct comparison in terms of acoustic efficiency. The cork discs were cut using a mechanically controlled die to ensure geometric regularity. The honeycomb modules were cut to size and carefully pressed between the membranes, avoiding glues or synthetic materials, to maintain the 100% sustainable nature of the system. The assembly was performed under controlled conditions, with precise axial alignment of the various layers. The membranes were rigidly constrained at the edges by means of PVC rings and acoustic sealing tape, to avoid air leaks during the measurements.

2.2. Experimental Apparatus: Kundt Tube-Based Measurement

Accurately quantifying a material’s ability to dissipate incident sound energy is essential for evaluating its effectiveness in mitigating acoustic reflections and reverberations. Among the most informative parameters for this purpose is the Sound Absorption Coefficient (SAC), which represents the proportion of acoustic energy absorbed by a surface relative to the total energy striking it. This metric plays a crucial role in various fields—including building acoustics, transportation engineering, and industrial noise control—where optimizing the acoustic environment is a priority.

To determine the SAC under controlled conditions, this study employed the impedance tube method, a widely recognized and standardized approach for characterizing the acoustic properties of materials under normal incidence. The method involves generating a one-dimensional sound field within a rigid cylindrical tube and placing the test specimen at one end. Sound pressure levels are captured at two distinct points along the axis of the tube, enabling the separation of incident and reflected wave components.

The experimental setup included a precision cylindrical impedance tube system SCS 9020B/K (Figure 2), chosen for its reliability and high-fidelity measurement capabilities. The tube had an internal diameter of 100 mm, which allowed for accurate analysis of acoustic behavior over a frequency range typically extending up to 2000 Hz. The total length of the tube was 560 mm. Two 1/4-inch condenser microphones were flush-mounted along the wall of the tube and spaced 50 mm apart. This configuration ensures optimal phase resolution of the standing wave field, particularly in the mid-to-high frequency domain.

The core principle behind this setup is the formation of standing waves because of interference between the incident sound wave and its reflection from the sample surface. By capturing the pressure signals at two points, the two-microphone transfer function method can be used to derive the complex reflection coefficient and the normal incidence sound absorption coefficient. This method is especially advantageous because it eliminates the need for direct measurement of sound intensity or impedance, relying instead on the spatial pressure variation within the tube.

For excitation, a white noise signal was employed to ensure consistent energy distribution across the entire frequency range of interest. This type of excitation improves the statistical reliability of the data and allows for a more comprehensive assessment of the material’s absorption characteristics across multiple frequencies.

Overall, the impedance tube methodology provided a robust framework for evaluating the acoustic response of the tested samples. The precise control over boundary conditions, combined with the simplicity of the experimental configuration, made it an ideal choice for benchmarking the performance of the cork-based acoustic metamaterial developed in this study.

All specimens were fabricated with a standardized thickness of 45 mm, a value selected to align with common installation practices and to provide relevant performance data for real-world applications. Particular care was taken to ensure tight coupling between the membrane-based samples and the internal walls of the impedance tube. This airtight fit was essential, as even minor discontinuities or leakage around the edges can lead to significant distortions in the measured absorption coefficients, particularly at lower frequencies where pressure gradients are more sensitive.

Experimental measurements were conducted under controlled ambient conditions, with temperature maintained at 25 °C and relative humidity stabilized at 50%. These environmental parameters are in accordance with the recommendations outlined in ISO 10534-2:2023 [36], which governs the measurement of sound absorption using the transfer-function method in an impedance tube. Continuous monitoring of these conditions was implemented throughout the test campaign, and any deviations from the reference values were documented and considered during post-processing to minimize their impact on data accuracy.

The validity of the acoustic characterization relies not only on the precision of the instrumentation but also on rigorous compliance with the standardized testing methodology [37,38,39]. The ISO protocol prescribes detailed procedures for system calibration, environmental stabilization, and precise alignment of both the test specimen and the measurement microphones. Failure to adhere to these guidelines can introduce substantial uncertainty, particularly due to phase and amplitude errors in the captured pressure signals.

In addition to procedural accuracy, physical aspects of the testing system—such as tube wall material, surface roughness of the sample, and alignment tolerances—were carefully accounted for. These factors can influence boundary conditions and acoustic impedance, thereby altering the propagation of standing waves and leading to misrepresentation of the sample’s intrinsic behavior. Where necessary, correction algorithms and calibration adjustments were applied to counteract such effects and enhance measurement fidelity.

The acoustic data obtained through this protocol offer valuable insights into the material’s behavior under normal incidence conditions. Such information is instrumental for predicting performance in real-world environments where directional sound absorption is critical. Applications include architectural acoustics, interior vehicle design, recording studios, and industrial facilities where noise mitigation is essential. The quantitative results derived from this methodology not only validate the absorption potential of the tested metamaterial but also reinforce its suitability for integration into advanced acoustic systems.

2.3. Simulation Based on Mass–Spring–Damper Systems

The aim of this part of the study was to develop a physical model that accurately describes the acoustic behavior of layered metamaterials consisting of cork membranes coupled to aramid paper honeycomb structures (Nomex). The experimentally investigated configurations included

• 1M–3H: a single membrane coupled to three honeycomb layers;
• 2M–3H: two membranes intercalated by three honeycomb layers;
• 3M–3H: three membranes intercalated by three honeycomb layers.

The acoustic behavior of these structures was characterized in the laboratory by measuring the sound absorption coefficient in narrow bands. To interpret and predict these data, a physical model based on the dynamics of coupled linear mass–spring–damper systems was developed.

For the development of the numerical simulation model, the mass–spring–damper model was adopted. Each membrane was modeled as a surface mass, m, while each cavity between membranes or between membrane and rigid wall (i.e., the honeycomb layers) is represented as a spring with linear damping, with spring constant k and viscous coefficient c [40,41,42,43].

The resonance frequency of a single mass-spring module is given by

$$f_0={\displaystyle \frac{1}{2\pi }}\sqrt{{\displaystyle \frac{k}{m}}}$$

(1)

In this Equation (1)

k is the constant spring

c is the viscous coefficient.

Therefore, given a surface mass, m, it is possible to define the spring constant k as

$$k=(2\pi f_0{)}^2\cdot m$$

(2)

Viscous damping is modeled according to the classical formulation:

$$c=2\zeta \sqrt{km}$$

(3)

where

• c is the damping coefficient [Ns/m],
• ζ is the damping ratio (dimensionless),
• k is the stiffness of the system [N/m],
• m is the mass [kg].

This parameter was used to adjust the height and width of the absorption peak to better match the observed experimental behavior, where configurations with more membranes show a higher absorption but are distributed over a wider band.

To simulate the acoustic behavior of the two- and three-membrane configurations, a dynamic matrix formulation was employed, representing the system as an N-degree-of-freedom (DoF) mechanical model, where N corresponds to the total number of membranes integrated into the structure. The dynamical system is written in the form

$$\mathbf{M}\ddot{\mathbf{u}}\left(t\right)+\mathbf{C}\dot{\mathbf{u}}\left(t\right)+\mathbf{K}\mathbf{u}\left(t\right)=\mathbf{F}\left(t\right)$$

(4)

In Equation (4),

• $\mathbf{u}\left(t\right)$ is the vector of membrane displacements;
• $\mathbf{M}$, $\mathbf{C}$ and $\mathbf{K}$ are the mass, damping and stiffness matrices;
• $\mathbf{F}\left(t\right)$ is the vector of the external force (incident sound pressure).

In the frequency domain, the system in Equation (4) transforms into

$$\left[-{\omega }^2\mathbf{M}+i\omega \mathbf{C}+\mathbf{K}\right]\mathbf{U}\left(\omega \right)=\mathbf{F}\left(\omega \right)$$

(5)

In this formulation, each matrix element represents the dynamic interactions between the masses and the connected springs. Matrices are constructed according to the scheme of masses coupled with springs and dampers in series.

To calculate the acoustic impedance and absorption, for each frequency of interest $\omega =2\pi f$, the system is solved numerically to obtain the frequency response $\mathbf{U}\left(\omega \right)$. The velocity of the first mass $v$ (i.e., the membrane exposed to the incident wave) is calculated as

$$v\left(\omega \right)=i\omega \cdot U_1\left(\omega \right)$$

(6)

From the speed, we obtain the specific impedance of the metamaterial:

$$Z_{\mathrm{eq}}(\omega )={\displaystyle \frac{p_{\mathrm{in}}}{v\left(\omega \right)}}={\displaystyle \frac{1}{v\left(\omega \right)}},$$

(7)

having assumed an incident pressure unit $p_{\mathrm{in}}=1$ Pa.

The acoustic absorption $\alpha \left(\omega \right)$ is calculated as

$$\alpha (\omega )=1-{\left|{\displaystyle \frac{Z_{\mathrm{eq}}-Z_0}{Z_{\mathrm{eq}}+Z_0}}\right|}^2$$

(8)

where $Z_0={\rho }_0{c}_0$ is the characteristic impedance of air.

This mathematical formulation enables the development of a comprehensive global dynamic stiffness matrix, which is essential for accurately modeling systems composed of multiple coupled membranes [44,45]. When membranes are connected through common air cavities or share structural backing layers, their dynamic behavior becomes interdependent, and individual responses influence one another. The matrix-based approach captures these coupling effects by systematically incorporating the mass, damping, and stiffness parameters of each membrane, along with the interaction forces transmitted through the surrounding medium.

Such a model effectively accounts for key physical phenomena, including resonance behavior, energy dissipation through damping, and the acoustic coupling between membranes and cavities. By solving the system in the frequency domain, it becomes possible to evaluate the transfer of vibrational energy and predict the corresponding sound absorption characteristics across a range of frequencies. This level of analytical detail is crucial for identifying the dominant resonant modes and optimizing geometric or material parameters to enhance performance.

Overall, the dynamic matrix approach provides a robust theoretical framework for analyzing and optimizing membrane-based acoustic metamaterials. It supports systematic exploration of different configurations—such as varying membrane numbers, spacings, or boundary conditions—and guides the design of structures tailored to achieve targeted acoustic functionalities.

3. Results and Discussion

3.1. Sound Absorption Coefficient

To evaluate the normal incidence sound absorption performance of the proposed cork-based acoustic metamaterial, a series of experimental tests were conducted using a standardized impedance tube setup, following the methodology prescribed in ISO 10534-2 [36]. The test apparatus facilitated precise measurement of the sound absorption coefficient (SAC) over a wide frequency range under controlled conditions. Three distinct specimens were fabricated, each consisting of a circular pressed cork membrane fixed onto a rigid polyvinyl chloride (PVC) frame. The cork membrane, selected for its intrinsic damping, elasticity, and sustainability, was tightly secured along its edge to replicate fixed-boundary conditions. These specimens served as modular unit cells for the layered configurations tested within the acoustic tube.

The experimental campaign focused on analyzing how different internal arrangements of the metamaterial influence its acoustic response. Unit cells, each measuring 15 mm in thickness, were stacked in sets of three to create multilayered structures of 45 mm total thickness. Each unit included a cork membrane, a controlled air gap of approximately 13 mm, and, in some configurations, an inserted aramid honeycomb core. This latter addition aimed to explore how the structural rigidity and porosity of the honeycomb material interact with the vibrational behavior of the membrane, potentially introducing hybrid resonance and dissipation mechanisms.

Figure 3 shows a representation of the different configurations of the specimens grouped in a sandwich form.

To ensure data reliability, each configuration was measured multiple times—typically ten repetitions—with the sample removed and reinserted between measurements to account for positioning variability. The results were statistically processed, with outliers excluded and mean values computed, ensuring the robustness of the final acoustic characterization.

Figure 4 displays the experimental results corresponding to the various configurations of the cork-based metamaterial, showcasing the frequency-dependent behavior of the sound absorption coefficient (SAC). The plotted curves clearly demonstrate how the presence or absence of the honeycomb core alters the acoustic response of the system. Notably, the inclusion of honeycomb layers leads to distinct shifts in the resonance peaks, affecting both their amplitude and frequency location.

These variations reflect the mechanical and acoustic interplay between the flexible cork membranes and the underlying structural core. Configurations incorporating honeycomb structures exhibit broader and more pronounced absorption bands, particularly at mid and low frequencies, suggesting enhanced energy dissipation through vibroacoustic coupling and localized resonance effects. Conversely, samples without the honeycomb filler display narrower absorption profiles, indicating reduced interaction between the membrane motion and internal air volume.

The comparative trends across configurations underline the role of internal architecture in tuning the metamaterial’s performance. The honeycomb core acts not only as a mechanical support but also as a functional acoustic component, modifying the impedance conditions and contributing to the emergence of hybrid absorption mechanisms. These findings validate the potential of honeycomb-enhanced cork metamaterials for targeted noise control applications.

The configuration consisting of a single cork membrane positioned on top of three honeycomb layers (referred to as 1M–3H, Figure 4a) shows typical behavior of a resonant metamaterial tuned at low frequencies. The experimental profile shows a marked absorption peak centered around 700 Hz, with a maximum value of the sound absorption coefficient (SAC) of about 0.40. The frequency response is highly selective, characterized by a narrow bandwidth (≈200 Hz) and a rapid decay at the edges of the peak, indicating strongly resonant and poorly dissipative behavior outside the tuned frequency.

This phenomenon can be interpreted as the combined effect between the flexural vibration of the cork membrane and the air cavity confined between the honeycomb layers. The membrane, thanks to its low density and good flexibility, behaves as a mechanical oscillator that, when acoustically coupled with the underlying cavity, creates a system similar to a modified Helmholtz resonator, which is capable of trapping and dissipating acoustic energy at the resonant frequency.

For frequencies above 1000 Hz, absorption decreases dramatically (α < 0.1), consistent with the typical behavior of non-porous membrane metamaterials, which are effective only in the vicinity of their resonant frequencies. The comparison with the equivalent configuration equipped with an unfilled air cavity shows that, although the presence of the honeycomb material leads to a marginal improvement at low frequencies, it is the empty cavity that allows a broader response and higher absorption values in the range above 700 Hz, thanks to the greater freedom of vibration and the different coupling between air and membrane [46].

The insertion of a second membrane inside the structure, interposed between the three honeycomb layers (2M–3H) (Figure 4b), determines a substantial transformation of the acoustic behavior of the metamaterial. Compared to the configuration with a single membrane, a shift in the maximum absorption band towards lower frequencies is observed, with a well-defined peak between 350 and 600 Hz. The maximum value of the acoustic absorption coefficient (SAC) reaches about 0.80, indicating a high sound energy dissipation efficiency in correspondence with the resonances activated by the new configuration [47].

One of the most relevant characteristics of this configuration is the persistence of high levels of absorption along the entire frequency range analyzed (250–1400 Hz), where the SAC remains constantly above 0.40. This behavior suggests the presence of multiple coupled resonant modes, resulting from the interaction between the two membranes and the air cavities separated by the honeycomb layers. The vibrations of the membranes, now partially decoupled thanks to the presence of the intermediate layer, give rise to the phenomena of constructive interference and distributed dissipation, widening the effective absorption band [48].

The comparison with the configuration equipped exclusively with an air cavity (without honeycomb) highlights the superiority of the system with an internal structure. In particular, in the 300–500 Hz range, the difference in performance is significant: the SAC of the honeycomb configuration can exceed that of the structureless configuration by more than 0.60, demonstrating the active role of the porous and rigid core in modulating the internal acoustic impedance and promoting dynamic coupling between the membranes [49].

The configuration composed of three cork membranes alternating with three honeycomb layers, arranged in a multilayer sandwich structure (3M–3H) (Figure 4c), highlights a particularly broad acoustic response distributed along the analyzed frequency spectrum. In this configuration, the maximum absorption is concentrated in the range 400–800 Hz, with a peak of the sound absorption coefficient (SAC) reaching a value of approximately 0.85. However, the effectiveness of the system extends well beyond this band: over the entire range 250–1400 Hz, the SAC remains constantly above 0.40, indicating largely dissipative behavior suitable for the treatment of broadband noise. From a physical point of view, the insertion of three membranes mechanically coupled to three cavities partially occupied by honeycomb structures generates a complex system with multiple degrees of freedom, in which multiple coupled resonances are activated, each linked to the interaction between the membrane and the underlying cavity. The elastic properties of cork, combined with the rigidity of the aramid core, favor an energy distribution between the different layers, reducing the localization of resonances and widening the useful bandwidth [50].

The comparison with the air-cavity-only configuration (without honeycomb) highlights a clear performance improvement, particularly in the range 300–500 Hz, where the SAC of the layered configuration is up to 0.50 higher, thanks to the combined effect of viscoelastic damping and structural resonance. Compared to the two-membrane configuration, the difference in the lower range (250–500 Hz) is less marked, but the three-membrane system clearly outperforms in the range 600–1000 Hz, showing greater efficiency in the mid-tones, where environmental and vocal noise often concentrates.

The experimental results clearly highlight that the increase in the number of membranes in the structure determines significant and predictable effects on the acoustic response of the metamaterial. In particular, the following are observed:

• An increase in the average sound absorption value (SAC) over the entire frequency range analyzed;
• An expansion of the useful absorption band, with effective performance starting from 250 Hz;
• The appearance of multiple resonant peaks, attributable to distinct local vibration modes for each membrane and to the interactions between them.

From a performance point of view, when comparing the average absorption coefficient with the total thickness, the 2M–3H configuration is an excellent compromise between effectiveness and construction simplicity, while the 3M–3H guarantees the most extensive spectral coverage, making it ideal for applications requiring broadband treatment.

Although all configurations were designed maintaining a similar total thickness (about 45 mm), the increase in the number of membranes leads to

• a greater number of active vibrating surfaces, capable of intercepting and dissipating sound energy;
• the segmentation of the internal cavities, each with its own resonance frequency;
• a complexification of internal reflections and interferences, which contributes to the broadening of the absorbed spectrum.

These effects confirm how a functional and controlled stratification of simple and natural materials allows the effective modulation of the acoustic response, without increasing the overall size of the system—a strategic advantage for architectural or integrated acoustic design applications.

The peaks observed in the absorption curves are consistent with local resonance phenomena: the cork membranes behave as elastic flexural masses, while the cavities formed by the honeycomb modules act as compressible air springs, recalling behavior similar to that of modified Helmholtz resonators. The position and intensity of the peaks are sensitive to several physical parameters, including the following:

• the stiffness of the membrane, a function of the elastic modulus and thickness;
• the density of the material;
• the depth of the underlying cavity;
• the dynamic coupling between adjacent resonators.

In particular, the 3M–3H configuration seems to activate coupled eigenmodes, in which the vibrations of one membrane directly influence those of the other two, generating constructive and destructive interferences that explain the presence of multiple and non-equidistant peaks.

It should be noted that

• the absorption values have an average uncertainty of ±0.03 on α, which is fully acceptable for laboratory tests;
• possible assembly imperfections or microstructural heterogeneities of natural materials (particularly cork) can affect the performance;
• the absence of diffuse porosity limits the absorption at high frequencies (>1400 Hz), as expected for non-fibrous metamaterials.

However, the repeatability of the results is high (standard deviation <5%), and the experimental trend is perfectly consistent with the expected behavior based on known physical models.

In summary, the evidence collected confirms that

• the progressive increase in membranes allows a fine and controlled modulation of the acoustic response;
• high performance can be achieved with natural and sustainable materials, without resorting to metallic elements or synthetic polymers;
• the system exhibits the typical characteristics of membrane metamaterials, with highly effective localized resonances at low frequencies (<1000 Hz).

These results provide a solid basis for the development of predictive models and for the design optimization of the metamaterial—topics that will be addressed in the subsequent sections of this work.

3.2. Analytical Modeling and Acoustic Performance Predictions

To complement the experimental analysis and gain deeper insight into the acoustic behavior of the proposed metamaterial, an analytical simulation was developed based on a mass–spring–damper (MSD) model. This approach, commonly used in the analysis of membrane-type acoustic metamaterials, allows for the representation of each membrane as a lumped mass connected to a spring and a damper, capturing its dynamic response under harmonic excitation. The system was modeled as a multi-degree-of-freedom (MDoF) structure, where each membrane corresponds to a discrete oscillating element, and the honeycomb layers were treated as coupled acoustic cavities with effective stiffness and damping characteristics [51].

The MSD model enables the prediction of resonance frequencies, absorption peaks, and the overall frequency response of the system as a function of key physical parameters, such as membrane stiffness, mass, cavity depth, and internal damping. By adjusting these parameters to reflect the experimental conditions (e.g., membrane material properties and geometry), it was possible to simulate the expected sound absorption coefficient (SAC) under normal incidence.

The model was implemented in MATLAB. v. R2023b For each configuration, a dynamic matrix of the system was created as a function of the number of membranes. The solver function calculates the frequency response, impedance and absorption on a frequency grid from 250 to 1400 Hz, with direct comparison with experimental data collected in one-third octave bands.

The parameters used for the simulations were calibrated to reflect the measured experimental behaviors. It was observed that

• the resonance frequency decreases with the increase in the number of membranes, except for the medium configuration;
• the damping ratio also increases, consistent with the hypothesis that more complex structures disperse more acoustic energy.

The values used in the model are reported in

Table 2. Summary of the parameters employed in the analytical simulations, including material properties, resonance frequencies, and damping ratio [52].

Configuration	f0 [Hz]	$\mathit{\zeta }$	m [kg/m2]
1M–3H	700	0.2	0.1
2M–3H	550	0.35	0.1
3M–3H	600	0.5	0.1

.

Figure 5 presents the results of these simulations, comparing different configurations—single, double, and triple membrane systems—and highlighting the influence of structural composition on the acoustic performance. The outcomes provide a valuable theoretical basis for interpreting the experimental findings and guiding future design improvements.

The results presented in Figure 5 highlight the effectiveness of the mass–spring–damper (MSD) model in simulating the acoustic response of the cork–honeycomb metamaterial across the different tested configurations. The model, based on a lumped-parameter mechanical analogy, was calibrated using physical properties derived from the experimental setup—such as membrane mass, stiffness, damping, and cavity dimensions—and proved capable of replicating key features observed in the measured sound absorption coefficient (SAC) curves.

In the 1M–3H configuration (Figure 5a), which consists of a single cork membrane coupled to three honeycomb layers forming a single cavity, the MSD model yields a response that follows the general shape of the experimental absorption curve. The resonant peak centered around 700 Hz is accurately predicted in terms of frequency location, though the amplitude of the peak is slightly underestimated. This discrepancy is likely due to material imperfections, variations in membrane tension, or minor air leakage, which may not be fully captured by the idealized model. Notably, the numerical simulation provides a smoothed response, filtering out minor fluctuations observed in the experimental data, which are often attributed to sample irregularities or measurement uncertainty inherent to the Kundt tube methodology.

In the case of the 2M–3H configuration (Figure 5b), where a second membrane is inserted within the layered honeycomb structure, the model begins to show more evident limitations, particularly in the low-frequency band between 250 and 450 Hz. Here, the measured absorption is significantly higher than predicted, suggesting that the model may not fully capture complex coupling effects such as inter-membrane interactions, multiple internal reflections, or higher-order vibrational modes. However, in the mid- and high-frequency ranges, the agreement improves, with the MSD model reproducing the general trend and the bandwidth of the absorption curve, even if it slightly over- or underestimates certain portions. These results indicate partial compensation for modeling errors and reinforce the model’s qualitative predictive capability [53]. The deviation observed between the numerical and experimental results in the 250–450 Hz range for the 2M–3H configuration can be attributed to multiple factors. First, the simplified boundary conditions used in the numerical model—particularly the assumption of perfect clamping—do not fully replicate the mechanical behavior of the experimental setup, which may allow for slight frame compliance or unintended energy leakage. Second, at lower frequencies, the coupling between the membrane dynamics and the enclosed air volume becomes increasingly sensitive to small variations in geometry, material properties (e.g., damping, stiffness), and pre-stress in the membrane, all of which are difficult to model with high accuracy. Furthermore, the numerical model currently treats the cork material as homogeneous and isotropic, while in reality, cork exhibits frequency-dependent damping and slight anisotropy, especially at low frequencies where viscoelastic effects are more pronounced.

Finally, in the 3M–3H configuration (Figure 5c), involving three membranes alternated with three honeycomb layers, the correspondence between simulation and experimental data is considerably improved. The broader and more distributed absorption profile, resulting from the activation of multiple coupled resonances, leads to a system response that aligns well with the assumptions of the MSD model. The interaction between each membrane and its corresponding cavity becomes more uniform across the structure, reducing sensitivity to local anomalies and allowing the model to effectively capture the global acoustic behavior. The multi-resonant nature of the system, with overlapping modes in the 400–900 Hz range, contributes to the more accurate and stable agreement observed [54].

Overall, while the MSD model presents certain limitations in resolving complex dynamic interactions, it successfully predicts the key features of the acoustic response across all configurations. It thus provides a valuable tool for guiding design optimization and understanding the resonance-based absorption mechanisms characteristic of membrane-type metamaterials.

The comparison between the model results and the experimental data showed a good correspondence in terms of the following:

• frequency of the absorption peaks,
• maximum amplitude of the SAC coefficient,
• qualitative shape of the curves.

The differentiation of the parameters for each configuration allowed the model to faithfully represent the observed trends, in particular, the higher efficiency of the structures with two and three membranes, which show a higher and more distributed absorption.

The developed model, although simplified with respect to the real metamaterial structure, provides a solid physical basis to understand the dynamic behavior of layered configurations. The multi-degree-of-freedom approach is effective in capturing the multi-resonant characteristics of multi-membrane systems. The possibility to separately calibrate the parameters f₀, z, and m makes it a useful tool for the design of new acoustic metamaterial architectures. In perspective, the model can be further extended to include the dynamic response of honeycomb materials as distributed viscoelastic materials or to explicitly model the wave propagation in the cavity. However, even in its current form, it represents a valuable predictive tool in the design and analysis phase [55].

4. Conclusions

This study presented the design, fabrication, and characterization—both experimental and numerical—of a novel acoustic metamaterial based on natural cork membranes and aramid honeycomb cores, aimed at achieving effective low-frequency sound absorption with sustainable materials and compact geometries. The main objective was to evaluate the acoustic performance of different multilayered configurations using a combination of impedance tube measurements and a mass–spring–damper (MSD) model to simulate the system dynamics.

The experimental results demonstrated that the introduction of flexible cork membranes, coupled with structured honeycomb layers acting as resonant cavities, leads to the formation of localized resonance peaks in the range of 250–900 Hz. These peaks are highly dependent on the number and arrangement of the membranes and cavities. The 1M–3H configuration, with a single membrane atop three honeycomb layers, exhibited a sharp and narrow absorption peak around 700 Hz, indicative of a single-degree-of-freedom resonator. In contrast, the 2M–3H and 3M–3H configurations introduced multi-resonant behavior, significantly broadening the absorption band and enhancing the average sound absorption coefficient across a wider frequency range.

The use of natural cork proved to be particularly advantageous due to its low density, inherent damping capacity, and structural flexibility. These properties enabled the cork membranes to behave as effective flexural resonators, while the honeycomb core materials—derived from aramid paper—acted as partially confined air cavities that contributed both mechanical stability and additional spring-like acoustic compliance. The combination of these materials provided a lightweight, sustainable alternative to conventional membrane metamaterials that often rely on synthetic polymers or metal components.

From a modeling perspective, the implementation of a mass–spring–damper system allowed for a compact representation of the mechanical-acoustic behavior of the different configurations. The MSD model successfully reproduced the general trend of the experimental absorption curves, particularly in configurations where the system’s behavior remained predominantly linear and the resonances were well separated. The agreement was most accurate in the 1M–3H and 3M–3H configurations, where the model captured both the frequency location and relative amplitude of the absorption peaks with reasonable precision. The 2M–3H configuration, which involves more complex membrane-cavity interactions, revealed some limitations of the model at very low frequencies, where coupling effects and higher-order modes become more relevant.

Nonetheless, the good overall fit between measured and simulated data confirms that the MSD framework is suitable for preliminary design optimization and for understanding the dominant vibroacoustic mechanisms governing the behavior of layered metamaterial systems. These insights will be valuable for tailoring future designs, especially when compact, tunable sound-absorbing structures are needed in architectural acoustics, automotive interiors, or lightweight noise control panels.

A key contribution of this work lies in showing that increased layering—specifically, the number of membranes—leads to

• enhanced average absorption over a broader frequency band;
• the appearance of multiple, non-equidistant resonances, associated with localized vibration modes;
• a modular strategy to tune the response without increasing the system’s overall thickness.

Furthermore, the study highlights that the best spectral coverage is obtained with the 3M–3H configuration, while the 2M–3H layout represents an excellent compromise between performance and simplicity. The use of simple, scalable fabrication techniques and readily available natural materials makes this approach not only technically effective but also ecologically and economically sustainable.

Despite the promising results, some limitations remain. The experimental setup, based on a standardized Kundt tube, does not account for off-axis or diffuse field effects, which may be relevant in real-world applications. Moreover, the MSD model, while effective, does not fully capture nonlinearities or edge effects arising from irregularities in handcrafted samples.

Future research will focus on refining the numerical model through finite element simulations, incorporating fluid-structure interaction and more detailed material modeling. Additionally, ongoing work includes testing the metamaterial in full-scale environments, such as reverberation rooms or in situ installations, to verify its performance under realistic boundary conditions.

In conclusion, this work demonstrates that cork-honeycomb acoustic metamaterials represent a viable, sustainable solution for low-frequency sound attenuation, and that their acoustic response can be effectively tailored by modulating their internal architecture. The integration of experimental and numerical approaches provides a solid foundation for future developments in the design of next-generation acoustic materials. The hybrid metamaterial developed in this study shows high potential for application in environmentally conscious sectors such as precision packaging, interior architecture, and eco-product design. For instance, in the transport of precision instruments, the structure could replace traditional polyurethane foam, combining acoustic damping and protective functions with improved sustainability. In architectural retrofits and modular interior partitions, its performance in the low-to-mid frequency range, low thickness, and lightweight nature make it a suitable candidate for space-efficient and reversible installations. Finally, its use in furniture design and interior components aligns with the principles of eco-design, offering biodegradable or recyclable end-of-life scenarios.