Optimizing Controlled-Resonance Acoustic Metamaterials with Perforated Plexiglass Disks, Honeycomb Structures, and Embedded Metallic Masses

Abstract

Acoustic metamaterials offer new opportunities for controlling sound waves through engineered material configurations at the sub-wavelength scale. In this research, we present the optimization of a resonance-controlled acoustic metamaterial based on a sandwich structure composed of perforated plexiglass disks, honeycomb structures, and added metal masses. The innovative approach consists of integrating perforated plexiglass disks interspersed with honeycomb structures, which act as multiple and complex Helmholtz resonators, and adding metal masses to introduce resonances at specific frequencies. The metamaterial’s acoustic properties were experimentally characterized using an impedance tube (Kundt tube), allowing the measurement of the Sound Absorption Coefficient (SAC) over an expansive frequency selection. The results demonstrate a substantial enhancement in sound absorption at the target frequencies, demonstrating the effectiveness of the introduced resonances. Numerical simulations using an Artificial Neural Network (ANN) model in MATLAB environment were used to analyze the distribution of resonances and optimize the structural configuration. To effectively evaluate the acoustic properties of the metamaterial, various configurations were analyzed using perforated plexiglass disks combined with different layers of honeycombs arranged in a sandwich structure with a thickness ranging from 41 to 45 mm. A comparison of these configurations revealed a notable increase in the Sound Absorption Coefficient (SAC) when employing three layers of perforated plexiglass disks and adding masses to the first disk (about 14%). This study highlights the potential of resonance-controlled metamaterials for advanced applications in noise control and acoustic engineering.

1. Introduction

Controlling sound waves is a central theme in many modern technological applications, ranging from acoustic engineering to noise-reduction design to advanced communications and medical devices. Acoustic metamaterials have attracted increasing scientific and industrial interest for their ability to manipulate sound in ways not possible with traditional materials [1]. These artificial materials are engineered with periodic or quasi-periodic structures at the sub-wavelength scale, which give them unique acoustic properties, such as selective absorption of frequencies, negative refraction, and sound focusing [2]. Acoustic metamaterials are a class of materials that can be engineered to achieve unusual acoustic behaviors due to their internal structure rather than the chemical composition of the materials themselves [3]. Acoustic properties, such as bulk density and compressibility, can be engineered through the design of repeating units, often called unit cells, which form the basis of metamaterials. These materials can be used to create devices that manipulate sound waves in advanced ways, such as tunable acoustic barriers, sound-absorbing panels, and acoustic lenses [4].

Over the past two decades, various acoustic metamaterial configurations have been developed, including resonant structures, Helmholtz resonators [5], and materials with engineered mass and stiffness distributions [6]. A key feature of these metamaterials is their ability to introduce resonances at specific frequencies, enabling precise control over sound absorption and transmission. Mass-spring resonators and Helmholtz resonators [7] are particularly notable for producing narrow resonance peaks that block or attenuate targeted sound frequencies [8]. By leveraging acoustic resonance—amplified oscillations of air in cavities—these materials create absorption or stop bands, significantly attenuating sound energy within specific frequency ranges [9].

This study explores an innovative approach based on the integration of perforated plexiglass disks with honeycomb structures, arranged in a sandwich configuration, and with the addition of metal masses to control resonances. This configuration aims to exploit a combination of complex resonant effects to achieve enhanced sound absorption in specific frequency bands. Honeycomb structures are well known for their high specific stiffness and low weight, make them best for purposes where both lightness and structural strength are required. In the proposed configuration, the honeycomb structures serve not only as structural elements, but also as cavities that can participate in acoustic resonance. These cavities, when coupled with perforated plexiglass disks, form a complex network of Helmholtz resonators that can be designed to achieve resonances at target frequencies. The perforated plexiglass disks function as apertures of the resonators, with the size and distribution of the holes determining the resonant frequencies. Plexiglass is chosen for its light weight, acoustic transparency, and ease of fabrication, allowing for the precise fabrication of the apertures required for the resonant configuration. Furthermore, the sandwich configuration of these perforated disks with the honeycomb structures creates a series of interconnected cavities, each potentially operating as an individual or coupled Helmholtz resonator, depending on the spacing between the disks and the size of the holes. The addition of metal masses to the plexiglass disks provides an additional degree of freedom in the design of the acoustic metamaterials. These masses introduce additional resonances due to their inertia, creating a mass-spring system that interacts with the resonances of the Helmholtz cavities. The metal masses can be distributed to optimize absorption at specific frequencies, acting as tuning elements that modify the overall acoustic response of the system.

This combined approach allows for detailed control over the absorption properties of the metamaterial, allowing for the design of narrow or broad absorption bands depending on the application needs. For example, increasing the number or mass of metal additions can shift the resonance frequencies downwards, improving absorption at low frequencies, which are often the most difficult to handle in traditional materials. The primary objective of this study is to create and optimize a resonance-controlled acoustic metamaterial using a combination of perforated plexiglass disks, honeycomb structures, and metal masses. Specifically, the following are the aims of this research:

• Design and fabricate a sandwich metamaterial configuration that exploits the principles of Helmholtz resonators and mass-spring resonances for selective sound absorption.
• Conduct experimental characterization of the metamaterial’s acoustic properties by measuring the Sound Absorption Coefficient (SAC) using an impedance tube (Kundt tube).
• Analyze the effect of design variables, such as hole size, metal mass distribution, and disk spacing, on the resonance frequencies and sound absorption effectiveness.
• Optimize the configuration to maximize sound absorption in specific frequency bands, through numerical simulations and comparison with experimental data.
• Evaluate the application potential of the optimized metamaterial in practical contexts such as industrial noise control, reduction in reverberation in enclosed spaces, and acoustic protection in critical environments.

To characterize the acoustics of the developed metamaterial, measurements of the SAC were performed via a Kundt tube, also known as an impedance tube. This setup allows us to determine how the metamaterial interacts with plane sound waves under controlled conditions, allowing accurate measurement of the SAC at different frequencies. The Kundt tube uses microphones positioned at specific points along the tube to detect the amplitude of the sound waves reflected and transmitted by the sample, from which the absorption coefficient can be calculated. Measurements were performed over a wide range of frequencies, covering both low frequencies, which are typically difficult to attenuate, and high frequencies, where absorption is generally easier but can present challenges in terms of uniformity. The optimization of acoustic metamaterials through advanced resonant configurations represents a significant step towards the realization of materials with acoustic properties tailored to specific applications. The ability to precisely control the absorption and reflection of sound waves in certain frequency bands opens up new research perspectives.

2. State of the Art and Recent Innovations

Acoustic metamaterials, designed to control and manipulate sound in ways not possible with traditional materials, have seen a remarkable development in research and applications in recent decades. This literature review will explore the main scientific and technological contributions regarding acoustic metamaterials, focusing on several areas of innovation, such as Helmholtz resonators, honeycomb structures, metallic masses, and acoustic characterization techniques. Helmholtz resonators were one of the first and most studied types of acoustic metamaterials. Originally used for indoor sound absorption applications, Helmholtz resonators have become a fundamental element in metamaterials designed to achieve specific sound absorption bands.

Acoustic membrane metamaterials are a novel class of materials designed to manipulate sound waves in ways that go beyond the capabilities of traditional materials. These metamaterials use thin, lightweight membranes, often with additional mass, to create local resonances that allow for high sound attenuation, especially at low frequencies, where conventional materials are less effective. Due to their structure, membrane metamaterials can break the law of mass, providing superior sound insulation without requiring large thicknesses or heavy weights. They hold promise for applications in acoustical engineering, noise control, and improving acoustic comfort in enclosed spaces. Li et al. [10] presents a sandwich structure that combines dual membrane-type acoustic metamaterials with a Helmholtz resonator, providing outstanding mechanical properties and effective low-frequency sound insulation. Theoretical calculations and numerical simulations of resonant frequencies, out-of-plane displacements, and sound transmission loss demonstrate that this new structure’s average sound insulation performance from 50 Hz to 1600 Hz is 30% higher than single-membrane types and 24.8% better than double-membrane structures without increased cavity height. This structure allows flexible modifications to meet engineering needs for lightweight, load-bearing, and sound insulation. Li et al. [11] introduces a lightweight multilayer honeycomb membrane-type acoustic metamaterial (AM) and experimentally examines its transmission loss. The results show that these honeycomb sandwich panel AMs can exceed the mass law, achieving high sound transmission loss while remaining lightweight. The metamaterial has a mass per cell area of only 0.29 and a total thickness of 4.2 mm, yet achieves an average sound transmission loss (STL) of 17 dB. Impedance tube experiments demonstrate that the STL peak frequency can be adjusted by modifying the cell structure and membrane properties. Xing et al. [12] developed membrane-type acoustic metamaterials featuring negative pressure cavities, enabling near-perfect sound absorption and tunable low-frequency sound absorption. To improve durability, a PET membrane was used as the substrate, replacing the softer membrane. The membrane material exhibits significant geometric nonlinearity due to the static negative pressure within the back cavity. This nonlinearity, along with the resulting changes in geometric stiffness, is exploited to fine-tune the structural sound absorption peak in the low-frequency range. Similarly, Sun et al. [13] proposed a technique to expand the frequency range of underwater sound absorption systems (USAS) by integrating a membrane-type resonator into the cavity, creating a membrane-type underwater acoustic metamaterial. The mechanism is demonstrated theoretically and validated through simulation and experiments. Results show that embedding the resonator significantly improves the sound absorption coefficient between 2000 and 10,000 Hz, increasing it by nearly 17% on average. This approach shows potential for underwater acoustic communication and device design.

Honeycomb structures have been extensively investigated for their potential in the acoustic metamaterial industry due to their combination of lightness and strength. Gao et al. [14] proposed a deformable honeycomb acoustic metamaterial consisting of stacked honeycomb structures and ethylene-vinyl acetate (EVA) copolymer films. Finite element analysis (FEA) results closely align with experimental data, demonstrating that the structure outperforms the acoustic mass law at frequencies below 1000 Hz. The study reveals that dislocation, compression, and tensile deformation can effectively regulate sound transmission loss (STL) over a wider frequency range. Notably, the STL of a bilayer structure is, on average, 10 dB higher than that of a monolayer at low frequencies, with the maximum STL observed when the dislocation distance (b = 1.5) mm. Sui et al. [15] introduced a class of lightweight yet highly soundproof honeycomb acoustic metamaterials. Their design, validated both theoretically and experimentally, achieves a mass per unit area of only 1.3 kg/m² while maintaining an STL exceeding 45 dB at low frequencies (<500 Hz). Additionally, a sandwich panel using this metamaterial as the core achieves STL values above 50 dB in the same frequency range, highlighting its potential for applications requiring lightweight, soundproof structures. Wang et al. [16] developed a composite structure combining a curved shell sandwich design with acoustic metamaterials to enhance mechanical and acoustic performance. Using the harmonic expansion method and the principle of virtual work, a theoretical model was constructed to analyze STL performance. The study further investigates how structural geometry and material parameters influence the STL of the composite. Xie et al. [17] introduced a new composite structure by filling Nomex honeycomb with polyester fiber to improve acoustic performance. The sound absorption coefficient (SAC) of the porous materials was measured using the impedance tube method, showcasing the material’s potential for sound absorption applications.

The study examined the effects of honeycomb specifications, fiber porosities, and filler amounts on SAC. The results indicate that increasing the porosity of the filler improves SAC, while variations in honeycomb specifications have a minimal impact, potentially due to additional sound absorption from material contact. Adjusting the filler amount alters SAC, though significant improvements at high frequencies are not observed. Zhang et al. [18] explores how structural insights at macro-, micro-, and nano-scales have advanced the design of honeycomb structures. This study also highlights recent advancements in micro- and nano-technologies, which demonstrate significant potential for the development of bioinspired honeycomb structures. It explores emerging applications in biomedicine, such as tissue engineering and regenerative medicine. Gaining a deep understanding of these design principles and the associated technological developments is essential for creating bioinspired materials and devices based on honeycomb structures for a wide range of practical applications.

The introduction of metal masses into acoustic metamaterials is an innovative and promising area of research. Metal masses, when integrated into a metamaterial system, can modify the resonant frequencies and improve the sound absorption in specific bands. A composite that allows relative motion between its components can have an inertial response that is different from that of a rigid body. A common situation where mass density dispersion can occur is the anti-resonance condition, which occurs at a frequency between two resonances. Composites with these frequency dispersion properties are of interest for both fundamental studies and practical applications. This behavior is initially achieved through an acoustic metamaterial with local resonances, simply by adding free-vibrating masses [19]. Active acoustic metamaterials exploit external control, such as electric, magnetic, mechanical, or thermal fields, to achieve effective material properties that cannot be achieved with traditional passive structures. These metamaterials enable the development of materials that can be dynamically reconfigured, allowing real-time adaptation to different acoustic conditions, improving versatility and efficiency in sound manipulation. Furthermore, active acoustic metamaterials can compensate for energy losses, maintaining high acoustic performance, and can be designed with equal-time symmetries, opening new possibilities for directional sound control, sound insulation, filtering, and the creation of advanced acoustic devices such as diodes and acoustic isolators [20]. Nakayama et al. [21] investigated the elastic wave band dispersion in acoustic metamaterial sheets, designing interconnected stub structures where each stub functions as a spring-mass resonator, creating out-of-plane acoustic bandgaps. Experimental results demonstrate that these materials, when properly integrated, outperform the mass law in noise insulation at resonant frequencies. Finite element method (FEM) numerical analysis, which couples the structures with acoustics, was used to explore the sound insulation mechanism, focusing on sound fields, vibrational fields, and dynamic effective mass. Additionally, it was shown that the insulation frequency can be tuned across a wide range by adjusting the physical and structural parameters of the resonators.

Ciaburro et al. [22] developed a novel layered membrane metamaterial consisting of three layers of reused PVC membranes with metal washers attached, fixed to a rigid support with cavities between the layers. The sound absorption coefficient was measured using an impedance tube for various configurations, altering the number and arrangement of attached masses. The data collected were used to train an artificial neural network model to predict the sound absorption coefficient and identify the optimal metamaterial configuration for maximum performance. The resulting metamaterial demonstrated effective acoustic absorption, even at low frequencies. Ning et al. [23] designed tunable acoustic metamaterials with resonating elements embedded in an elastomeric matrix containing circular holes. By applying equibiaxial compression, deformation-induced geometric and material nonlinearities were used to tune the dynamic responses. Numerical analysis indicated that deformation shifts and broadens low-frequency band gaps, improving noise and vibration control. Ciaburro et al. [24] created a membrane-type acoustic metamaterial using a recycled cork membrane with masses made from reused thumbtacks and buttons. A total of 42 samples with varying mass configurations were tested to measure the sound absorption coefficient using an impedance tube, with a 50 mm cavity added to enhance resonance absorption. The data collected were used to train a regression tree model to predict sound absorption performance. The results suggest that these metamaterials are suitable for acoustic correction in rooms.

The reviewed studies demonstrate that acoustic metamaterials have made significant progress in design and applications. Future directions of acoustic metamaterial research include the optimization of existing configurations, exploration of new materials and structures, and integration of emerging technologies for advanced practical applications. With the continuous evolution of research and technologies, acoustic metamaterials promise to revolutionize the field of acoustic engineering and provide innovative solutions for a wide range of sonic challenges.

3. Materials and Methods

In this section, the materials used and the methodologies adopted for the measurement of the acoustic properties of the metamaterial and for the optimization of the geometries are described.

3.1. Description of Materials

Helmholtz resonators are a crucial and innovative concept in the field of acoustics, used to manage and control sound in a wide range of applications [25]. Named after the German physicist Hermann von Helmholtz, these devices have been studied since the 19th century and continue to be fundamental in the design of optimized acoustic environments and in solving noise problems. The Helmholtz resonator is essentially a system that uses resonance to absorb specific sound frequencies. The device consists of a cavity (or chamber) with a narrow mouth that acts as an opening [26]. When sound waves enter the cavity through this opening, they create vibrations within the volume of air. Resonance, which occurs when the frequency of the sound waves matches the natural frequency of the resonator, amplifies these vibrations, allowing the resonator to effectively absorb and attenuate sound waves at that frequency. The operating principle of Helmholtz resonators can be described through an analysis of the vibrations of the cavity and the opening [27]. The cavity acts as a mass-spring system, where the air inside the cavity represents the mass and the mouth represents a spring that resists the movement of the air (Figure 1).

When sound waves hit the mouth of the resonator, it oscillates and causes compressions and rarefactions of the air inside the cavity. The frequency at which the system oscillates most effectively corresponds to the resonant frequency of the resonator, and it is at this frequency that the resonator offers maximum sound absorption.

The fundamental equation for determining the resonant frequency of a Helmholtz resonator is based on the principle of acoustic resonance. The resonant frequency f of a Helmholtz resonator can be expressed by the following formula:

$$f={\displaystyle \frac{c}{2\pi }}\sqrt{{\displaystyle \frac{A}{VL}}}$$

(1)

In Equation (1):

• f is the resonant frequency of the resonator (in Hz).
• c is the speed of sound in air (about 343 m/s at room temperature). This represents the speed at which sound waves travel through air and directly affects the resonant frequency.
• A is the area of the resonator opening (in m²). The larger the area of the opening, the more efficient the resonator is at absorbing sound waves.
• V is the volume of the resonator cavity (in m³). The volume of air inside the cavity affects the frequency at which the resonator resonates.
• L is the effective length of the mouth, which can be approximated by the length of the duct (in m). The length of the duct connecting the opening to the cavity modulates the resonant frequency.

Equation (1) is a simplification that assumes that the air inside the resonator behaves as an ideal gas and that the aperture and cavity are of simple shape. In practice, variations in the geometry of the resonator may require adjustments to this formula to obtain a more accurate estimate of the resonant frequency.

Helmholtz resonators are widely used for improving acoustics in various applications:

• Room Acoustic Treatment: In spaces like theaters, recording studios, and concert halls, they help reduce unwanted frequencies, enhance sound quality, and create balanced acoustic environments by absorbing specific resonant frequencies.
• Industrial Noise Control: In industrial and automotive settings, they reduce noise from machines and vehicles, improving safety and comfort by attenuating disruptive noise frequencies.
• Acoustic Structure Design: Helmholtz resonators are integrated into noise barriers and sound-absorbing panels to optimize sound management in architectural and engineering projects.
• Advanced Technology Applications: In modern technologies, such as active noise reduction and intelligent acoustic devices, resonators enhance acoustic performance in dynamic environments.

Designing Helmholtz resonators requires a thorough understanding of acoustic principles and device geometry [28]. The resonant frequency of the resonator is influenced by several factors, including cavity dimensions, aperture diameter, and material properties [29]. Engineers and designers must consider these parameters to create resonators that meet the specific needs of their applications: Cavity Size: The size of the cavity directly affects the resonant frequency of the resonator. Larger cavities tend to resonate at lower frequencies, while smaller cavities resonate at higher frequencies. Therefore, the choice of cavity size should be based on the frequency of the sound you want to absorb. Aperture Diameter: The resonator’s opening, often called the “mouth”, plays a crucial role in determining its ability to absorb sound. A larger opening allows more sound to enter the cavity, but can also affect the resonant frequency and overall response of the device. Cavity Material: The materials used to construct the cavity can affect the acoustic properties of the resonator. Materials with high sound-absorbing characteristics can improve the efficiency of the resonator, while stiffer materials can alter the resonant frequency and absorption capacity.

In recent years, Helmholtz resonators have seen significant technological innovations and improvements. Some examples are given as follows. Miniaturized Helmholtz Resonators: New technologies have enabled the miniaturization of Helmholtz resonators, making them suitable for applications in electronic devices and compact environments. These miniaturized resonators maintain their acoustic properties even at smaller scales [30]. Complex-Shaped Helmholtz Resonators: Advances in design have led to the creation of resonators with complex shapes and innovative geometries, which offer greater versatility and improve sound absorption capabilities [31]. Active and Adaptive Resonators: Active and adaptive resonators use modern technologies to change their resonance properties in real time. These devices can dynamically respond to changes in acoustic conditions and optimize absorption performance [32].

Helmholtz resonators are essential tools in the field of acoustics, offering effective solutions for sound control and noise management [33]. Their ability to absorb specific frequencies makes them valuable in a wide range of applications, from designing optimized acoustic environments to reducing industrial noise. With recent technological innovations and advanced design capabilities, Helmholtz resonators continue to evolve, offering new opportunities to improve sound quality and address modern acoustic challenges [34].

In this work, we developed an innovative acoustic metamaterial by coupling 0.2 cm-thick plexiglass sheets with honeycomb structures to create an effective system for sound absorption based on Helmholtz resonators. The plexiglass sheets were precisely drilled to obtain optimal resonator configurations, which, once assembled with the honeycomb structures, exploit acoustic resonance to effectively absorb specific sound frequencies. This combination of materials aims to improve acoustic performance, especially in the frequency ranges that are more difficult to attenuate with traditional methods. The coupling between the sheets and the honeycomb structures allows to exploit the properties of the Helmholtz resonator, where the air contained in the cavities and holes acts as a resonant mass that vibrates at certain frequencies, transforming the sound energy into heat and reducing the noise level.

The proposed approach stands out for its ability to tailor acoustic properties by varying parameters such as hole size, distribution and number of resonators, as well as the cell configuration of the honeycomb structure. This study provides a new perspective on the design of advanced acoustic materials, with potential applications in several sectors, including architecture, civil engineering, and the transportation industry, where noise control is essential.

The samples were prepared with the aim of being inserted into an impedance tube for the measurement of the sound absorption coefficient [35]. For this purpose, plexiglass disks with a diameter of 10 cm and a thickness of 0.2 cm were used. To optimize the resonant effect, two sets of holes with a diameter of 0.5 cm were drilled on the disks (Figure 2a). The first set includes 16 holes equally spaced along a circumference with a radius of 4 cm from the center of the disk. This arrangement maximizes the interaction between the sound waves and the resonators distributed along the outer edge of the sample. The second set of holes, composed of 8 equally spaced holes, was drilled along a circumference with a radius of 2 cm from the center, favoring additional resonant modes at different frequencies than the first set. Finally, an additional hole was drilled in the center of the disk to complete the configuration, increasing the complexity of the resonant system (Figure 2a). This hole configuration was chosen to create a spatial distribution that promotes effective absorption over a wider range of frequencies. The interaction between the Helmholtz resonators generated by the holes and the plexiglass structure allows acoustic energy to be transformed into heat, improving absorption performance. The design was optimized to exploit multiple resonances, creating a highly efficient system that can be adapted to different noise control applications.

The perforated plexiglass discs is interspersed with a honeycomb structure with 3 mm hexagonal cells, composed of a series of cells that have the shape of regular hexagons, with all sides of equal length (Figure 2b). Each hexagonal cell has the following characteristics:

• Geometry: Each hexagon is made up of six sides of equal length, in this case, 3 mm each. The internal angles of the hexagon are all 120°. The hexagons are arranged in a repeating grid and fit perfectly together with no gaps between them.
• Size and Area: The side length of each cell is 3 mm. The area of a single hexagonal cell can be calculated using the formula for the area of a regular hexagon:

$$S={\displaystyle \frac{3 \sqrt{3}}{2}} {side}^2$$

(2)

Here:

S = surface;

side = side of the hexagon (for a side of 3 mm, the area of each hexagon is approximately 23.38 mm²).

• Thickness of the structure: When applied to a panel or material, the thickness of the honeycomb structure may vary depending on the application, with a depth of cells that can affect the stiffness and mechanical or acoustic properties of the material. In our case, the thickness of the structure is 13 mm.
• Material: The structure can be made of different materials, such as aluminum, plastic, or composites, which provide specific properties such as lightness, strength, and sound absorption or thermal insulation capacity. In this study, resinated aramid paper was used.
• Mechanical and Acoustic Properties: The hexagonal configuration distributes loads evenly, making the structure light but strong. In the acoustic context, this configuration can help dissipate sound waves, improving sound absorption and vibration reduction.

Resinized aramid paper is an advanced composite material that combines the strength of aramid fibers with the enhancing properties of a resin. Used in a wide range of industrial and technical applications, resinized aramid paper is distinguished by its exceptional mechanical, thermal and chemical properties. The basis of aramid paper is made up of aramid fibers, a family of synthetic polymers characterized by a molecular chain of aromatic rings that gives them high mechanical strength and thermal stability.

Among the most well-known brands of aramid fibers are Kevlar (produced by DuPont) and Nomex [36]. These fibers have unique characteristics that make them highly appreciated in composite materials. High tensile strength: Aramid fibers are extremely strong, with a tensile strength up to five times that of steel at the same weight. Heat resistance: Aramid fibers can withstand high temperatures without rapidly degrading, with a decomposition point above 500 °C for Kevlar and approximately 370 °C for Nomex. Low density: Aramid fibers are lightweight, making them ideal for applications where a combination of light weight and strength is needed.

However, aramid fibers alone are not easy to handle or shape into more complex applications. To improve their workability properties and to provide additional characteristics such as stiffness and resistance to deformation, aramid paper is treated with a resin [37].

Resin treatment is essential to stabilize and reinforce the structure of aramid fibers. Resin treatment occurs by impregnating the aramid paper with resin, usually of the thermosetting or thermoplastic type. Among the most used resins are the following. Epoxy resins: These are the most widely used due to their excellent adhesive properties and chemical resistance. They offer high rigidity and hardness, making the finished material very resistant. Phenolic resins: Often chosen for high temperature applications, where heat resistance is essential. Polyurethane resins: Used when a balance between flexibility and wear resistance is sought. Polyamide resins: They offer excellent chemical and thermal resistance, but with greater elasticity than other resins.

The application of resin not only strengthens the aramid paper, but also allows the modification of its properties, such as stiffness, resistance to moisture and the ability to resist chemical agents [38].

Resin-coated aramid paper combines the properties of aramid fibers with the benefits of resin, creating a material that possesses a range of exceptional properties:

• High Mechanical Strength: Combines the tensile strength of aramid fibers with the compressive strength of resin, making it ideal for lightweight, rigid panels in sandwich structures and composites.
• Thermal Resistance: Withstands high temperatures without structural degradation, suitable for aerospace and electronic applications requiring thermal stability.
• Thermal and Electrical Insulation: Natural insulating properties enhanced by resin, widely used in transformers, cables, and electric motors for thermal and electrical insulation.
• Lightweight: Low density compared to metals like steel or aluminum, advantageous in aerospace, automotive, and high-performance industries focused on weight reduction.
• Chemical Resistance: Offers durability against acids, bases, and solvents, making it suitable for use in chemically aggressive environments.
• Vibration and Sound Absorption: Effectively dissipates energy from vibrations and sound waves, ideal for acoustic panels and noise reduction applications.
• Fire Resistance: Naturally flame-resistant aramid fibers combined with flame-retardant resin provide enhanced fire safety for public transport, building materials, and defense applications.

Resin coated aramid paper is an extremely versatile material that combines the mechanical and thermal properties of aramid fibers with the advantages of resin. Its resistance to tensile stress, heat, chemicals and vibration, combined with its light weight and insulating capacity, makes it ideal for a wide range of high-performance applications. In

Table 1. Physical and chemical properties of resinated aramid paper ([36,37,38]).

Property	Value	Unit of Measure	Description
Density	30–80	kg/m3	Varies based on the amount of resin used and the density of the aramid paper.
Compressive strength	1.0–3.5	MPa	Depends on the direction of compression (normal to the hexagonal cell) and the resin used.
Elastic modulus (compression)	50–150	MPa	Describes the stiffness of the structure in the direction of compression.
Shear strength (plane)	0.5–1.5	MPa	Ability of the structure to resist shear forces.
Shear modulus (plane)	20–60	MPa	Measure of the stiffness of the structure in response to shear forces.
Operating temperature	−60–180	°C	Resistance to extreme temperatures due to the thermal stability of the aramid fibers and resin.
Flame resistance	Alta	-	Aramid fibers are flame retardant and the resin can be treated to further improve this property.
Water absorption	<1	-	Low moisture absorption, useful in environments with high exposure to humidity or water.
Chemical resistance	Good	-	Resistant to oils, solvents and many chemicals, even in harsh conditions.
Dimensional stability	Excellent	-	Retains its shape even under thermal or mechanical stress.
Thermal insulation	Good	-	Due to the low thermal conductivity of the aramid fibers.
Sound insulation	Good	-	The honeycomb structure contributes to sound attenuation, useful in acoustic applications.

are listed some physical and chemical properties of resinated aramid paper.

Finally, metal masses (split pins) have been used to improve the acoustic properties of the material. Split pins, also known as split clips or paper clips, are small mechanical devices used to fasten together materials such as paper, cardboard or thin metal sheets. Consisting of a metal shank with two separate ends, these can be bent to lock objects in place (Figure 3). Their operation is simple: once inserted through a hole, the ends are separated and bent in opposite directions, ensuring secure fastening.

This type of pin is particularly useful in applications where a temporary or reversible solution is required, as the ends can be easily bent back to remove the fastening. Split pins find application in a variety of contexts: from crafts and office use to mechanical engineering, where they are used as a safety catch on moving components, preventing accidental disassembly of bolts and pins. They are available in different sizes and materials, including steel and brass, depending on the need for resistance or corrosion.

3.2. Measurement of Acoustic Properties of Metamaterial

Sound absorption coefficient measurements were performed following the guidelines of ISO-10534-2:2023 [39]. These measurements are essential for understanding the acoustic properties of materials and play a key role in designing spaces with optimal acoustic performance. The impedance tube is one of the most reliable and widely used methods for calculating the sound absorption coefficient, commonly applied across various technical fields. Sound absorption refers to the process by which a material dissipates acoustic energy, reducing sound reflections. The absorption coefficient, which quantifies the ratio of absorbed to incident energy, is a key parameter in industries such as construction and automotive. A thorough understanding of how materials interact with sound waves is essential for engineers and designers to create acoustically optimized environments. These measurements are important for adjusting the reverberation time in spaces such as auditoriums or for developing materials that improve acoustic comfort, both in vehicle interiors and in other contexts.

The impedance tube is an essential instrument for measuring the acoustic properties of materials and the speed of sound in gases. A typical example of this device is the SCS type 9020B/K (Figure 4). This instrument works by generating standing waves that interact with the tested material, measuring its vibration response at specific frequencies. The underlying principle is acoustic resonance, which allows parameters such as the sound absorption coefficient to be calculated accurately. ISO 10534-2:2023 describes in detail the procedures for measuring sound absorption coefficients using impedance tubes, specifying the need for a controlled environment.

The impedance tube compliant with ISO 10534-2:2023 provides a reliable and standardized system for measuring the acoustic properties of materials. This method allows for accurate and reproducible data, making it possible to compare results from different laboratories and application contexts. It is particularly useful in sectors such as construction, acoustic engineering and the automotive industry, where optimizing the acoustic performance of materials is crucial. Despite its advantages, the use of the impedance tube presents some operational challenges. For instance, the choice of tube material can affect the accuracy of measurements, as can defects in the tested material, such as air leaks or variations in composition. To minimize these sources of error, it is crucial to follow the guidelines outlined in ISO 10534-2:2023, with careful attention to the experimental setup. In this study, an impedance tube with an internal diameter of 10 cm was employed, capable of measuring frequencies up to 2000 Hz. The tube length of 56 cm, combined with two ¼″ microphones positioned 5 cm apart, enables accurate measurements above 200 Hz. This configuration covers a broad frequency range, providing a comprehensive representation of the acoustic properties of the tested material. The strategic placement of the two microphones ensures the precise detection of sound pressure variations, enhancing the reliability of the sound absorption coefficient data. Through proper calibration and careful adherence to the experimental protocols, it is possible to minimize errors and obtain accurate and reproducible results. This facilitates data comparison between different studies, making the impedance tube an essential tool for acoustic research and development.

3.3. Artificial Neural Network (ANN) Based Modeling

Artificial neural networks (ANNs) are adaptable computational models that can modify their structure, including nodes and connections, in response to various internal and external stimuli [40]. These networks aim to replicate the operational principles of biological neural systems, where artificial neurons are linked in ways that allow them to receive, process, and respond to input signals. Each neuron takes multiple inputs, which are scaled by specific factors known as “weights”, and the resulting weighted sum determines the neuron’s activation. If this sum surpasses a predetermined threshold, the neuron produces an output signal. Weights reflect the significance of each input, with higher weights assigned to inputs deemed more important and lower weights for less influential ones [41].

One common type of artificial neural network is the multilayer perceptron (MLP), which is structured with multiple interconnected layers of perceptron’s [42]. An MLP consists of an input layer that receives data, an output layer that provides predictions or classifications, and one or more hidden layers, which perform the core processing tasks. In these networks, each neuron is linked to every neuron in adjacent layers, creating a structure known as a “fully connected” network [43].

Within a simple neural network like the MLP, three main components are identifiable:

1.

Input Layer: This layer is responsible for accepting and standardizing input signals so they can be effectively processed by the neurons in the network.

2.

Hidden Layers: These layers carry out the computational processing, with additional layers adding complexity and improving the network’s learning capability.

3.

Output Layer: This layer compiles the outputs from the hidden layers and formats them for the network’s final response.

This layered structure enables MLPs and similar networks to perform complex tasks by breaking down inputs, processing them through weighted connections, and progressively refining responses through multiple hidden layers [44].

In a neural network, each layer contains one or more artificial neurons, which have multiple input pathways, often referred to as “dendrites”. These pathways allow each neuron to receive input values that are multiplied by a set of adaptable parameters called weights. The weighted inputs are then summed, creating what is known as the linear combination of the inputs. This linear combination is passed through an activation function, which, along with the weights, ultimately defines the neuron’s output. Learning within the network occurs as these weights are adjusted to produce the desired outputs, a process that requires extensive computation, particularly in large networks containing millions or even billions of weights [45].

In feed-forward networks, neurons at each layer receive signals exclusively from neurons in preceding layers and send outputs only to neurons in subsequent layers. There are no connections within the same layer or backward connections, ensuring a unidirectional flow of information from the input layer to the output layer. Consequently, in feed-forward architectures, the network’s current output depends solely on the current input, with no memory of previous inputs. This forward-only structure facilitates signal propagation across the network, but it also means that the network is “memoryless”, responding only to the present input without retaining information from past inputs [46].

In this study, we employed an artificial neural network (ANN)-based model to simulate the acoustic behavior of the material under investigation. The goal was to identify the optimal configuration of an acoustic metamaterial, composed of a membrane and additional masses, with the aim of maximizing the sound absorption coefficient. Our approach leverages an advanced predictive model driven by neural networks, which autonomously identifies configurations that deliver superior sound absorption performance. This model optimizes the placement of additional masses on both the internal and external circumferences, ensuring the most effective acoustic properties.

4. Results and Discussion

This research investigates the acoustic properties of an innovative metamaterial made up of perforated plexiglass disks integrated with a honeycomb structure. The study focuses on evaluating the acoustic performance of these Helmholtz resonator-based materials, providing valuable insights into their potential applications in various acoustic fields.

4.1. Analysis of Acoustic Characteristics of the Helmholtz Resonator-Based Metamaterial

The structure of the metamaterial, consisting of three layers of perforated plexiglass disks alternating with honeycomb structures, was studied to evaluate the performance. In the configuration studied, the disks act as the neck of a Helmholtz resonator, while the honeycomb core acts as a cavity (Figure 5).

The combination of these characteristics allows to obtain a material with excellent sound absorption and acoustic transmission reduction capabilities, in addition to ensuring excellent mechanical performance. By precisely adjusting the thickness of the core and selecting specific materials, it is possible to tailor the acoustic behavior of the metamaterial to achieve high levels of efficiency. These metamaterials are particularly effective for applications that require lightweight but high-performance solutions, such as in the aerospace, automotive and architectural sectors. In these fields, the use of materials capable of improving acoustic comfort without compromising structural properties is crucial. Furthermore, thanks to their ability to isolate and absorb sound waves, these sandwich structures are used in projects where the reduction in noise and vibrations is essential, thus contributing to the improvement of the overall performance and comfort of the environments or devices in which they are used.

To effectively evaluate the acoustic properties of the metamaterial, different configurations were examined (Figure 6); the letter of the list gives the name of the configuration:

(a)

A perforated plexiglass disk and a 43 mm cavity;

(b)

A perforated plexiglass disk and three layers of honeycomb;

(c)

Three perforated plexiglass disks and three layers of honeycomb;

(d)

A perforated plexiglass disk, three layers of honeycomb and additional masses on the disk;

(e)

Three perforated plexiglass disks, three layers of honeycomb and additional masses on the first disk.

For each measurement, the operation was performed 10 times, ensuring maximum accuracy. Each sample was removed and repositioned in the tube for each measurement, with the aim of minimizing uncertainty and obtaining precise results [47]. During these steps, special care was taken to maintain the position and orientation of the samples unchanged, minimizing any alignment errors [48]. Furthermore, between the various measurements, a check of the instruments used was performed to ensure that they were correctly calibrated and not influenced by variations over time [49]. This approach allowed obtaining consistent and reliable data, essential for subsequent analyses.

The metamaterial units were assembled inside the Kundt tube, forming a final configuration with a total thickness of approximately 45 mm. This layered structure is made up of several levels, each composed of a perforated plexiglass disk with a thickness of 2 mm, positioned in front of a 13 mm honeycomb structure. The honeycomb-shaped cavity provides both strength and lightness, helping to achieve the desired acoustic properties. The cavity behind the membrane is crucial for sound absorption, functioning through a combination of two primary effects: membrane resonance and cavity resonance [50]. Membrane resonance arises when the membrane vibrates at frequencies, dissipating sound energy. Simultaneously, the cavity amplifies absorption through internal resonance, which occurs as the trapped air inside the cavity vibrates in response to sound waves. This dual mechanism, resulting from careful design of the metamaterial, makes the structure extremely effective in reducing noise. The use of the Kundt tube for measurements allows for detailed analysis of the acoustic properties, confirming the effectiveness of the design in managing sound waves [51].

Figure 7 presents the measurement results obtained using the impedance tube, with analysis divided into one-third-octave bands.

Each curve in the figure represents data from a specific configuration of membrane layers, each supported by a honeycomb structure at the rear, as illustrated in Figure 5. The curves, identified by distinct colors, correspond to the various arrangements of the metamaterial layers. The horizontal axis displays frequencies on a logarithmic scale, grouped into one-third octave bands, while the vertical axis shows the measured values of acoustic absorption or impedance.

In Figure 7, different acoustic behaviors of the material can be observed based on the different configurations of the layers. The sound absorption coefficient (SAC) of the perforated plexiglass disk with a 43 mm cavity follows a typical bell curve, characteristic of porous materials, with a maximum peak of about 0.35 at 1000 Hz. This behavior arises from the ability of the material to dissipate sound energy through the friction generated by the sound waves passing through the holes, a typical characteristic of porous materials.

When the cavity is filled with three layers of honeycomb material, the acoustic behavior changes significantly. The curve rises, peaking at 0.55 around 800 Hz, and expands over a wider frequency range. This improvement in absorption can be explained by the increased structural complexity introduced by the honeycomb layers, which generate multiple resonances. These resonances amplify the interaction between the sound wave and the structure, increasing the effectiveness of the system in absorbing sound energy.

Finally, in the configuration with three disks and three honeycomb layers, a further improvement in sound-absorbing properties is observed. The peak reaches a maximum value of 1 at around 800 Hz, and the curve broadens further, showing effective behavior even at lower frequencies, such as 400 Hz. This increase in acoustic performance is attributable to the combination of multiple resonance effects, both at the membrane level and in the cavities behind them, which work in synergy to effectively dissipate acoustic energy over a wide frequency range. This behavior makes the material particularly suitable for noise control applications, where a broad absorption spectrum is required.

It can also be observed that the addition of the honeycomb material causes a shift in the absorption peak towards the lower frequencies, a behavior that is particularly significant since these are notoriously more difficult to attenuate [52]. This shift can be explained by the greater ability of the honeycomb structure to influence low-frequency resonances. The complex geometric arrangement of the honeycomb acts as a series of resonant cavities that interact with the sound waves, slowing them down and amplifying their absorption. At lower frequencies, sound energy has greater difficulty being dissipated by conventional porous materials, since these waves have greater lengths and require thicker structures to be absorbed effectively. The introduction of the honeycomb instead creates a resonance effect that allows to overcome this limitation, increasing the absorption efficiency without requiring a significant increase in the thickness of the material [53]. The result is a structure that can successfully address a wider frequency range, including the low frequency range, improving the overall noise control capability of the system.

Figure 8 presents the measurement results of the SAC (α) in one-third octave bands (250–1600 Hz) for two configurations: a perforated plexiglass disk combined with three layers of honeycomb, and the same setup with the addition of extra masses.

To optimize the acoustic properties of the metamaterial, we inserted additional masses, consisting of split pins, passing them through the holes in both the plexiglass disk and the honeycomb structure. This configuration is intended to increase the local resonance effect, since the additional masses interact with the incident sound waves, modifying the dynamic response of the system. The insertion of the masses introduces an additional degree of freedom in the vibrational behavior of the membrane, contributing to a greater dissipation of the acoustic energy.

In particular, the additional masses act as mass-spring resonators, improving the absorption at specific frequencies that are difficult to attenuate with traditional materials. This approach allows for a more flexible and adaptable acoustic response, increasing the effectiveness of the metamaterial over a wider range of frequencies, including the most difficult ranges to manage, such as the low frequencies.

Again, different configurations of the material were analyzed to optimize its acoustic performance. The starting point was a setup with a single plexiglass disk and three layers of honeycomb. Subsequently, one to five additional masses were progressively added, strategically positioned to study their impact on the overall acoustic behavior. The masses were first inserted into the central hole and then distributed over four holes along the outer circumference of the disc, with a radius of 4 cm.

The progressive addition of these masses allowed modulating the resonance frequencies of the system, improving the acoustic absorption in specific frequency bands. This approach allowed us to analyze the influence of the additional masses both in terms of modification of the dynamic response of the membrane and of interaction with the multiple resonances of the honeycomb structure. The configuration with masses distributed along the circumference showed a greater control on the dispersion of the sound energy, optimizing the ability of the system to attenuate the critical frequencies, especially those more difficult to manage, such as low frequencies.

The insertion of the masses led to a significant improvement in the acoustic properties of the metamaterial. In particular, the absorption peak remained at 800 Hz, but its value increased significantly, going from about 0.6 to about 0.9. Furthermore, a significant increase in the sound absorption coefficient (SAC) is evident in the frequencies between 400 and 800 Hz. This variation is explained by the introduction of additional resonances generated by the masses, which interact with the sound waves more effectively.

Looking at the transition from the insertion of one mass to that of two, a further improvement is noted around 600 Hz, suggesting the presence of a new resonance frequency that amplifies the sound absorption. In particular, the addition of only two masses causes a significant increase in the SAC at 500 Hz, which goes from about 0.1 to about 0.6. This improvement is indicative of the ability of the masses to modulate the vibrations of the system, optimizing the response of the metamaterial to the sound waves.

Interestingly, additional masses do not produce substantial improvements in acoustic performance. This suggests that the insertion of two masses is already sufficient to optimize the SAC, achieving an effective balance between weight and absorption. This result demonstrates the importance of structural design and mass distribution in maximizing the effectiveness of the metamaterial in sound absorption, confirming that a targeted strategy in mass configuration can lead to a significant increase in performance without the need for additional loading.

Figure 9 compares the SAC of the three-disk, three-honeycomb configuration with that of the same configuration with added masses.

Masses were added to the three-disk, three-honeycomb structure to modify its configuration. In this configuration, the addition of masses did not lead to a significant improvement in acoustic performance, which is different from what was observed with the single-disk, three-honeycomb configuration.

A closer look reveals that the main effect of adding masses is a shift of the sound absorption coefficient (SAC) curve towards lower frequencies. This behavior is typical of porous materials, where the distribution of additional masses affects the resonant characteristics of the system. Specifically, the peak that was initially located at around 800 Hz in the massless configuration shifted to around 630 Hz with their addition.

This shift can be justified by considering the increase in the effective mass of the structure, which reduces the resonant frequency of the system. The introduced masses contribute to lowering the frequency at which the metamaterial shows maximum sound absorption, although they do not improve the overall effectiveness in the other frequency bands [54]. This behavior reflects a greater mechanical inertia introduced by the masses, which reduces the system’s ability to respond quickly to sound inputs at high frequencies but improves performance at lower frequencies.

4.2. Optimization of the Metamaterial Configuration

Optimizing the configuration of acoustic metamaterials is a crucial step in the development of advanced materials capable of efficiently modulating sound waves for noise control and acoustic engineering applications. In this section, we present a detailed and in-depth analysis on the search for the optimal configuration of an acoustic metamaterial based on membrane and additional masses, aiming at maximizing the sound absorption coefficient. Our methodology exploits an advanced neural network-based predictive model, developed to automatically identify the configurations that offer the best performance in terms of sound absorption capacity, optimizing the placement of the additional masses on both the inner and outer circumference.

The optimization approach followed was motivated by the increasing complexity in obtaining acoustic metamaterial configurations that respond precisely to specific sound frequencies. Acoustic metamaterials, especially those structured with resonant elements as additional masses, are sensitive to even small variations in their geometrical arrangement and material characteristics. These factors directly influence their acoustic behavior, especially in low frequencies, where traditional sound absorption is often insufficient. Therefore, we chose to employ a machine learning model, capable of learning from data collected through experimental measurements, to predict the configurations that return a high efficiency in terms of absorption.

To collect the necessary data, we conducted measurements of the sound absorption coefficient using the impedance tube, known for its precision in determining the acoustic properties of material samples. We examined different configurations of the metamaterial, varying the number of plexiglass layers as well as varying the position of the additional masses, placing them alternatively on the inner and outer circumference. These variables proved to be fundamental to explore how the distribution of the masses influences the absorption characteristics of the material. The obtained measurements were used as a training dataset for the neural network model, which was subsequently implemented to identify the configurations with the maximum sound absorption.

Neural networks, thanks to their ability to model nonlinear relationships and complex data patterns, have proven to be an effective tool for the optimization of acoustic metamaterial design [55]. The developed model was trained to recognize correlations between the arrangement of additional masses and the measured acoustic performances. Subsequently, the model was tested to evaluate the predictive capacity, confirming that some configurations are particularly efficient in increasing the sound absorption coefficient, especially in certain target frequencies.

Sound Absorption Coefficient (SAC) measurements were utilized to train a regression model based on artificial neural networks (ANNs) to predict the acoustic performance of the metamaterial. The SAC prediction model incorporates 13 input features, including frequencies in one-third octave bands (ranging from 250 Hz to 1600 Hz), the number of perforated disks, the number of additional masses, and the positioning of these masses. The model’s output is the SAC value across the specified frequency bands. Given the continuous, numerical nature of the output, this confirms that the task is a regression problem with multiple predictors and a single response variable.

The acoustic measurements obtained from the impedance tube were organized into a data file with 13 columns, containing approximately 500 records. Each record corresponds to one-third octave frequency bands within the 250–1600 Hz range, as well as key configuration parameters such as the number of disks, the number of additional masses, and their respective positions. For applying a prediction model via supervised learning, a labeling process was essential. This process involved associating each Sound Absorption Coefficient (SAC) value, obtained from impedance tube measurements, with the specific configuration characteristics of the metamaterial. Labeling is a critical step in any supervised ANN methodology, as it allows the model to learn by linking input data to a target output, enabling it to predict labels for new data samples after training.

A feed-forward ANN model was developed to predict SAC values, using the Bayesian regularization backpropagation algorithm for network training [56]. This algorithm addresses training and generalization issues statistically, enabling the model to consistently generate reliable predictions. During each training session, weights are initialized randomly, and the Bayesian approach combines these diverse solutions to identify the optimal weight configuration for the best overall generalization. Unlike traditional ANN optimization methods, which consider only a single solution, Bayesian regularization merges multiple results to enhance prediction accuracy.

The SAC prediction model was implemented on the MATLAB (2022) platform by MathWorks. To validate the model, the dataset was divided into two parts: 80% of the data was allocated for training, while the remaining 20% was reserved for testing. This division ensures that the model is trained effectively while retaining a subset for independent validation. Figure 10 illustrates the training phase, showing the gradient and mean square error values, which reflect the model’s learning progress and accuracy over time.

Two key metrics were used to assess the simulation model’s performance. The Mean Squared Error (MSE) measures the difference between observed and predicted values, reflecting how closely the predictions match actual data [57]. MSE indicates the dispersion of the data points around a central tendency, with lower values signifying better accuracy and less deviation from actual measurements.

The correlation coefficient, ranging from −1 to +1, quantifies the strength and direction of the linear relationship between predicted and actual values [58]. A value of −1 or +1 indicates a perfect correlation, with −1 representing an inverse relationship and +1 indicating a direct relationship. A value of 0 denotes no correlation, meaning the variables are unrelated. Positive correlation values suggest that higher values of one variable correspond to higher values of the other, while negative values imply the opposite.

Table 2. SAC prediction model results.

	MSE	R2
Training	0.0115	0.9177
Validation	0.0077	0.9355
Test	0.0138	0.8518

presents the SAC prediction model results, evaluated according to these performance metrics.

The model’s accuracy in fitting measurement results can be visually evaluated with scatter plots, where measured values are placed on the horizontal axis (target) and predicted values on the vertical axis (response). In Figure 11, points clustering near the solid line—representing an ideal match—indicate the precision of the model’s predictions. To further assess the sound absorption performance of corn stem fibers, we compare the SAC trend across frequency bands between measured and simulated data.

To appreciate the results of the simulation of the acoustic behavior of the metamaterial using the ANN-based model, we compared different configurations. We first compared the acoustic behavior of the metamaterial by placing the masses in the holes of the external circumference, specifically the one with a radius of 4 cm (Figure 12).

We next examined the acoustic behavior of the metamaterial by placing the masses in the holes of the inner circumference, specifically the one with a radius of 2 cm (Figure 13).

This configuration allowed us to evaluate the impact of the mass distribution on a smaller scale, taking advantage of the proximity of the masses to the center of the plexiglass disk. Placing the masses in this strategic position enabled a more effective interaction between the sound waves and the system, favoring the generation of additional resonances at different frequencies [59]. Furthermore, this arrangement contributed to modifying the vibration dynamics of the structure, increasing the efficiency of the sound absorption in specific frequency bands [60]. This configuration provided the opportunity to explore the effect of localized masses, allowing us to determine whether a more targeted approach to the mass position could further optimize the performance of the metamaterial. The observations collected from these tests were fundamental to understand how the geometry and the arrangement of the masses influence the sound absorption capabilities of the system, opening new possibilities for the optimization of acoustic solutions in practical settings. The placement of the masses in the innermost layer introduced a new resonance frequency that interacts effectively with the sound waves, resulting in a significant improvement in sound absorption at around 630 Hz. In this case, the sound absorption coefficient (SAC) increased significantly, from around 0.25 to 0.85.

This change can be attributed to the increased ability of the masses to influence the membrane vibrations at this specific frequency. The interaction between the masses and the sound waves generates resonances that amplify the dissipated sound energy, thus improving sound absorption [61]. The internal position of the masses facilitates a more direct connection with the sound waves, optimizing the dynamic response of the system. Furthermore, it is interesting to note that once the placement of two masses is achieved, no further significant improvements in acoustic performance are observed. This suggests that the two-mass configuration is already optimal for maximizing absorption at this specific frequency [62]. In contrast, the transition from one mass at the center to two masses is instrumental in the improvement at 630 Hz, demonstrating the importance of the strategic mass configuration and distribution in enhancing the sound absorption capabilities of the metamaterial. These results highlight how a targeted design can lead to superior noise control performance.

Figure 14 shows a comparison between the two configurations with four additional masses positioned in the circumference with a radius of 2 cm.

We compared the two configurations with four additional masses, since previous tests have shown that this solution performed best. Analyzing the data, the addition of masses leads to a clear improvement in the single-disc configuration. In fact, comparing the curves of the sound absorption coefficient (SAC) for the two configurations, we note that the significant differences observed in the basic configurations (without additional masses) are largely filled thanks to the addition of the four masses.

This behavior suggests that the effectiveness of the additional masses is particularly marked in the single-disc configuration. The masses, in fact, seem to interact more optimally with the structure, improving the resonant behavior of the system and increasing the effectiveness of the acoustic absorption. It is likely that in a multi-disc configuration, the interference between the various resonances decreases the effectiveness of the masses, while in the case of a single disc, the acoustic energy is better concentrated and absorbed [63].

In conclusion, the additional masses prove to be particularly effective in improving the acoustic performance of the one-disk configuration, compensating for the limitations of the basic configuration and making it comparable, if not superior, to the three-disk solution. This behavior underlines the importance of the correct distribution of the masses and of the structure itself in determining the overall performance of the metamaterial.

5. Conclusions

This study highlighted the significant potential of resonance-controlled acoustic metamaterials as advanced tools for controlling sound waves. The research demonstrated that precisely designed sub-wavelength configurations allow for targeted control of the acoustic behavior of the material by introducing specific resonances in certain frequency ranges. The comparison between the two configurations—one with four additional masses and three perforated disks, and the other with only one perforated disk—revealed a notable 14% increase in the Sound Absorption Coefficient (SAC) when utilizing three layers of perforated plexiglass disks with masses added to the first disk.

The innovation of this project lies in the combination of perforated plexiglass disks, honeycomb structures and added metal masses, which allowed for the creation of a sandwich structure capable of acting as a complex system of Helmholtz resonators. The integration of metal elements further contributed to enhance the effectiveness of the system, allowing for the introduction of resonances tuned to target frequencies. This configuration allowed for a significant increase in the sound absorption coefficient in specific frequency ranges, as evidenced by the experimental results obtained with the impedance tube. These experimental results, in addition to confirming the effectiveness of the structure, represent a significant advancement compared to traditional acoustic material configurations, showing a significantly enhanced sound absorption capacity.

Another relevant aspect was the use of numerical simulations, which allowed us to analyze and optimize the distribution of resonances based on the structural characteristics of the metamaterial. Simulations played a crucial role in identifying the optimal arrangement of the components and in identifying the configurations that maximize sound absorption, reducing experimentation times and costs. This modeling and simulation-based approach allows for targeted design, minimizing prototyping cycles and increasing the overall efficiency of the development process.

The effectiveness demonstrated by the developed metamaterials suggests promising applications in the field of acoustic engineering and noise control, in sectors ranging from construction to transportation, up to the industrial sector. The results of this research not only validate the adopted approach, but also provide a solid basis for future optimizations and for the development of metamaterials that can be customized according to specific needs, paving the way for innovative solutions in the field of passive noise control. Finally, the integration of additional masses and honeycomb configurations represents a methodology that can be easily adapted and implemented in other types of materials to achieve optimal acoustic characteristics at sustainable costs.

In conclusion, this study has demonstrated the effectiveness of resonance-controlled acoustic metamaterials and has laid the foundation for further research and practical applications. In densely populated areas, noise pollution from traffic, construction, and industrial activities significantly impacts public health and quality of life. The metamaterial’s unique configuration offers a lightweight, cost-effective solution with high sound absorption properties, particularly in low-frequency ranges that are traditionally challenging to mitigate.

Future experiments could explore configuration and material variants to further optimize the performance, particularly in terms of efficiency and frequency range.

One of the main limitations of this study lies in the complexity of the metamaterial structure, which makes large-scale production difficult and may affect mechanical stability. Furthermore, the measurements performed cover a limited frequency range, suggesting the need for extensions to evaluate the acoustic behavior in other bands. Future developments could include configuration optimization through evolutionary algorithms, to reduce production costs. Furthermore, the use of alternative materials and modular components could be explored to increase the versatility and applicability of the metamaterial in different industrial contexts.