Influence of structural and geometric parameters on the sound absorption performance of carbon fiber–Onyx acoustic panels

Abstract

In acoustic engineering, sound absorption is important in mitigating noise pollution in constructed environments. With the introduction of fused deposition modeling (FDM) based additive manufacturing, it is now more possible to create customizable, lightweight acoustic panels with optimized geometric configuration. This paper examines the acoustic behaviour of 3D-printed perforated polymer composites in terms of the effect of the most important geometrical and physical factors, including perforation ratio, thickness, air gap, layering, and backing conditions on the sound absorption coefficient (SAC). An impedance tube was used to conduct experimental measurements in line with ASTM E1050-19, over the frequency range of 50 Hz–5,000 Hz. The parameters investigated were: perforation ratio of 7.8% and 20.9%, sample thickness of 5–20 mm, air-gap thickness of 10–30 mm, 20 mm PET foam backing, and layered panel configurations. The findings indicated that the SAC improved with the perforation ratio and the sample with 2 mm holes (20.9% perforation ratio) had the highest SAC of 0.735 at 5,000 Hz. The increase in thickness of 10 mm–20 mm resulted in a substantial increase in low-frequency absorption resulting in a maximum SAC of 0.994 at 3,400 Hz. The addition of an air gap shifted the absorption peak to lower frequencies up to 550 Hz as a result of Helmholtz-type resonance, and a 10 mm air gap produced SACs up to 0.92 at 950 Hz. Substitution of air gaps with porous PET foam further extended the bandwidth of absorption to better SAC to 0.9 at 1,200 Hz. The layering of the material was also effective where the split samples exhibited improved absorption in low and high-frequency bands. Also, Delany-Bazley model was applied to predict SAC of solid samples, and it produced a satisfactory fit with an RMSE of 0.1078, particularly at low to mid frequencies. Such results can be used to design tunable acoustic panels that are specifically designed to control broadband noise.

1 Introduction

The need to have effective acoustic materials has increased tremendously because of the increased concern about noise pollution and its effects on human health and the quality of the environment. Acoustic materials are critical in soundproofing and noise management in diverse environments, such as buildings, automobiles, and industrial facilities, where they assist in improving comfort and safety by reducing undesired sound transfer (Lavrentjev, 2021). In the recent past, there has been a growing concern to substitute the traditional, petrochemical-based acoustic insulators with more sustainable and low-cost synthetic and natural-fiber-based insulators (Prabhune et al., 2022). The alternatives have similar or even better acoustic performance but less environmental impact and contribute to the circular economy (Prabhune et al., 2022). The use of such materials is growing at a high rate, particularly in automotive, construction of buildings, and aerospace industries, where lightweight and eco-friendly materials are highly demanded (Cai et al., 2021; Bilir et al., 2025). 3D-printed synthetic composites enable the fabrication of complex internal architectures—such as periodic lattices and graded porosity—that enhance sound wave dissipation, offering tunable acoustic performance, batch-to-batch consistency, lightweight yet strong multilateral hybrid structures, and customizable geometries (Sekar et al., 2024).

On the other hand, Natural fiber composites exhibit structural irregularity, limited geometric customizability, constrained tunability across acoustic frequency bands, and performance variability due to fluctuations in fiber diameter, density, and moisture content; furthermore, they are biodegradable and prone to moisture and microbial degradation, lack effective multi-material integration, and often require greater thickness to achieve equivalent mechanical strength (Sekar et al., 2024).

Basic acoustical characteristics such as the sound absorption coefficient, transmission loss and acoustic impedance are important pointers to the efficiency of a given material in absorbing and managing sound. The sound absorption coefficient is a ratio of the amount of sound energy absorbed by a material to the amount of sound energy incident on the material, whereas transmission loss is the ratio of the amount of sound energy transmitted through a material to the amount of sound energy incident on the material. Acoustic impedance, in its turn, reflects the opposition faced by sound waves when moving through a substance, which affects the reflection and transmission processes (Sakamoto et al., 2022). Material thickness and porosity also play a very significant role in these acoustic properties. Thicker materials generally improve low-frequency absorption and transmission loss because of increased internal energy dissipation, and higher porosity allows better acoustic properties through increased airflow resistivity and higher internal surface area to cause viscous and thermal losses (Biboud et al., 2024). Standardized techniques to characterize these properties experimentally include the impedance tube technique (usually called Kundt tube). Under the control of ASTM and ISO standards, these techniques allow one to measure normal-incidence acoustic parameters with high accuracy over a wide frequency range and are invaluable both in academic research and industrial material validation (Biboud et al., 2024; ASTM E1050-19, 2019; ISO 10534-2:1998, 1998).

Numerous theoretical and numerical models have been formulated to model the acoustic behaviour of porous materials, some more complex and accurate than others. The most popular ones include the Delany-Bazley, Miki and Johnson-Champoux-Allard (JCA) models. The Delany-Bazley and Miki models can be used to provide empirical formulations that are computationally efficient and can be used in initial evaluations, whereas the JCA model is more physically based and can be used to consider viscous and thermal dissipative effects and is therefore more effective when applied to fibrous and open-cell foam materials (Periyasamy et al., 2023; Kalauni and Pawar, 2023). These models need to be validated numerically not merely to confirm experimental observations but also to expand the knowledge of material behavior in conditions that are difficult to reproduce in the laboratory. Such a combination of modeling and experimentation can better predict the acoustic performance at a wide range of frequencies and configurations (Casaburo et al., 2021; Soltani et al., 2020). Therefore, the incorporation of these models in the study of acoustic materials improves predictive power and optimization of materials.

Additive manufacturing has become a flexible manufacturing method to fabricate lightweight parts with complex geometry, which is not easy to obtain by conventional manufacturing methods. Fused Deposition Modelling (FDM) is a material extrusion additive manufacturing process in which a thermoplastic filament is melted and deposited layer-by-layer to build a three-dimensional structure. FDM is one of the most popular processes for producing functional polymer parts due to its design flexibility, low cost, and ability to customize materials. The introduction of reinforcing fibers, especially carbon fibers, into thermoplastic matrices leads to high stiffness, dimensional stability and vibration damping properties with low structural weight. The above benefits make carbon fiber-reinforced polymer composites good choices for the design of high-performance acoustic panels with tunable structural and sound absorption properties.

New discoveries in material science and additive manufacturing have also allowed the creation of highly customizable acoustic materials that have improved sound absorption and sound insulation capabilities. Many works have been done on 3D-printed structures in acoustic applications, and the role of geometry, material composition, and fabrication parameters has been established. To illustrate, Zaharia et al. (2023), and Matei et al. (2024), emphasized that the internal geometries of triangular and labyrinthine patterns, as well as optimized infill densities and nozzle diameters, lead to a substantial increase in sound absorption (SAC = 0.93) and mechanical strength, which implies their applicability to the aerospace and automotive sectors. Likewise, Vigneshwaran et al. (2024), Sailesh et al. (2021) demonstrated that the geometry of the perforation, especially tapered or non-uniform cross-sections, significantly increases the sound absorption and transmission loss, and the performance is maximized at narrow or convergent-divergent holes. Patil et al. (2024), confirmed these results with a series of impedance tube tests and finite element modeling on the impact of hole orientation and geometry.

The type and structure of material also plays a vital role. Vasina et al. (2020), and Monkova et al. (2022), showed that the open-porous ABS and PLA structures have sound reflection and absorption properties that are highly porosity-dependent, excitation frequency-dependent, and air gap size-dependent. Bi et al. (2024), also investigated flax fiber-reinforced PLA composites and found that internal voids increased low-frequency sound absorption, which was confirmed by simulation.

Multifunctional and hybrid materials are also proving promising. Mallesh et al. (2024), proposed a folded core sandwich structure composed of CF-PA and graphene oxide-coated PU foam, which has 99% sound absorption over a broad frequency range (160–6,000 Hz) and enhanced compressive strength. Similarly, Zhang et al., 2025), suggested a micro-perforated sandwich composite with TPMS filled with polyurethane, which moved the peak absorption to 294 Hz and increased the low-frequency absorption bandwidth by 23.86%. Subramanian et al. (2024), and Sekar et al. (2022), showed that the PLA-based honeycomb and wood-fiber panels can be acoustically optimized by varying the infill density, thickness, and nanofiller content to attain the NRC of up to 0.377. Arjunan et al. (2021), applied this to metallic materials and demonstrated that 3D-printed Ti6Al4V micro-perforated panels with porous backing improved low-frequency absorption (400–1,600 Hz) significantly.

Some other researchers have also emphasized the importance of combining numerical modeling and experiments. Guadagno et al. (2023), and Setaki et al. (2023), used computational analysis and experimental verification to evaluate vibro-acoustic and room acoustic performance and found that there was a high level of agreement with theoretical models. Goh et al. (2022), supported this strategy with CT imaging and acoustic testing to establish the relationship between core structure and layup and enhanced energy absorption and insulation in sandwich panels.

Prior studies on 3D-printed acoustic panels have focused on the effect of perforation geometry, porous backing, or material composition in isolation, Very few studies have examined the combined effect of perforation ratio, thickness, air-gap depth, porous backing, and layered configurations in a single experimental study. Moreover, there are few investigations of Carbon Fiber–Onyx composites for acoustic applications. The present work aims to fill this gap by systematically examining these parameters in their interaction over a wide frequency range and checking the acoustic response with the Delany–Bazley model. This integrated approach offers practical design guidelines for designing lightweight, tunable and additively manufactured acoustic panels.

2 Methodology

This section contains the details about material selection, sample fabrication with FDM 3D printing, experimental setup to test the impedance tube and several configurations of the tests aimed at investigating the influence of thickness, perforation ratio, air gaps, and layering.

2.1 Material selection

In the current study, hybrid Carbon Fiber and Onyx material system was used to produce composite acoustic panels. The composite was 30 percent carbon fiber as the reinforcement phase and 70 percent Onyx as the matrix material volume wise. This particular ratio was chosen in order to maximize the trade-off between structural stiffness and acoustic damping capability (Tang and Yan, 2020; Liu and Li, 2012).

Onyx is a proprietary thermoplastic mixture created to be used in 3D printing and consists of chopped carbon fibres in an engineering grade nylon matrix. It has a good printability, dimensional stability and mechanical performance. Onyx is about twice as stiff as conventional ABS and has natural acoustic damping owing to its semi-crystalline polymeric matrix (Yun et al., 2024).

Carbon fiber was selected as the reinforcement material because it offers the highest specific stiffness and strength among the reinforcement fibers available for the Markforged printing platform. Although carbon fiber is relatively more expensive than conventional reinforcement materials such as glass fiber or natural fibers, it was chosen over other available reinforcement materials for its high specific stiffness, low density, excellent dimensional stability, and superior vibration damping properties, which are beneficial for lightweight acoustic structures. These characteristics and its compatibility with the Onyx matrix, make carbon fiber-reinforced Onyx an appropriate material for investigating the acoustic performance of high-performance 3D-printed composites.

While increasing the fiber volume fraction in synthetic fiber-reinforced composites usually enhances stiffness and mechanical strength, many studies report that benefits tend to level off or even decline beyond around 30% fiber content. This is mainly due to problems like fiber clumping, non-uniform dispersion, and weakened matrix structure, which can impact both acoustic performances negatively (such as sound absorption and impedance) and mechanical properties (like strength and stiffness) by reducing stress transfer efficiency and damping ability (Tang and Yan, 2020; Liu and Li, 2012).

The acoustic response is due to the stiffness of the Carbon Fiber–Onyx composite as well as the intrinsic damping of the material. The carbon fibers add rigidity to the structure and affect the vibrations, and the Onyx nylon matrix offers internal damping, which helps dissipate the energy of vibrations. This combination helps to enhance the acoustic stability and resonance control compared with conventional polymer-based structures.

Selecting a 30% volume fraction of carbon fiber within an Onyx matrix offers a balanced strategy, i.e., the high-modulus carbon fibers enhance stiffness significantly—as predicted by rule of mixtures models—while retaining sufficient semi-crystalline nylon matrix (Onyx) to preserve acoustic damping capabilities. Micromechanics theory (e.g., ROM or Halpin Tsai models) indicates that beyond ∼20–30 vol% fiber, marginal gains in stiffness become less efficient, while fiber-rich composites increasingly lose internal damping (Tang and Yan, 2020; Liu and Li, 2012).

Carbon fiber, which has a very high tensile strength, low density and good acoustic impedance was chosen to improve the mechanical integrity of the composite, and also to help in reducing the vibration and better energy dissipation qualities. The carbon fibers inclusion offers not only high stiffness and strength-to-weight ratio but also contributes to the regulation of vibrational behavior of the panel, which plays an important role in regulating resonance at lower frequencies (Assarar et al., 2018; Li et al., 2025).

2.2 Sample preparation

For this study, 3D printed composite panels were prepared using Onyx filament (sourced from Markforged) with a density of 1.2 g/cm³ and carbon fiber filament (sourced from Markforged) with a density of 1.4 g/cm³. In order to study the acoustic behavior of carbon fiber-Onyx composites, 7 different panel designs were printed using 3D Printer (Model - Markforged mark two). The fused deposition modeling 3D printing was used to fabricate acoustic samples under a well-controlled set of parameters to achieve geometric consistency and structural integrity.

The printing was carried out at a nozzle temperature of 240 °C and a bed temperature of 60 °C, with a layer height of 0.2 mm. The specimen geometry, including the circular perforations, was prepared in CAD software, exported as a STEP file, and imported into the Eiger™ slicer for toolpath generation. The Onyx matrix was deposited at 100% fill density using a solid rectilinear fill pattern, with raster lines alternating between 0° and 90° on successive layers, producing a fully dense solid region between and around the perforations. Continuous carbon fibre layers were laid in an isotropic concentric-ring orientation as determined by the Eiger™ slicer. All other process parameters were maintained at Markforged Mark Two default values throughout fabrication.

These conditions were selected to maximize mechanical strength and surface finish, which are important to ensure uniform acoustic behavior across all samples. The selected additive manufacturing method was based on its capacity to accurately control geometry (thickness and hole distribution) and thus allow reproducibility of samples of different perforation ratio and internal structure. The specimens were manufactured in the form of a cylinder of fixed diameter 34.7 mm to fit the dimensions of the standard impedance tube used in the testing. The values of the thickness were varied to 5 mm, 10 mm, 15 mm and 20 mm across the samples to investigate the effect of thickness on acoustic behavior. Although visual inspection was performed to confirm dimensional consistency, quantitative void percentage measurement using microscopy or CT scanning was not conducted.

Perforations were carefully placed in chosen samples in order to introduce porosity. Typical examples of the hole distributions of ⌀1 and ⌀2 configurations are presented in Figures 1, 2 respectively.

FIGURE 1

FIGURE 2

Figures 1, 2 highlight the uniform radial distribution designed to ensure consistent porosity across the sample face.

The hole spacing for each perforation series was governed by the structural integrity of the CF–Onyx specimen during FDM printing and handling, and the circular impedance tube specimen diameter of 34.7 mm. The hole spacings were established through systematic manufacturing trials in which the centre-to-centre distance was varied from 2 mm upward. It was found that a minimum inter-hole wall thickness of 1.5 mm is required to produce geometrically clear, defect-free perforations in CF–Onyx composites on the Markforged Mark Two; wall thicknesses below this threshold resulted in hole deformation and inter-hole merging. Both the H1 series (wall = 2.0 mm) and the H2 series (wall = 1.75 mm) exceed this empirically established limit, and all printed specimens were visually inspected to confirm hole clarity prior to acoustic testing.

Manufacturing tolerance effects on hole diameter and spacing were not separately evaluated in this study and will be addressed in future optimization studies.

The detailed sample configurations are presented in the Table 1 below.

The thicknesses of the specimens (5–20 mm) were chosen in accordance with the ranges of values usually investigated in previous studies on perforated acoustic absorbers, and to systematically analyze the influence of thickness and perforation ratio on the sound absorption performance under controlled conditions (Vasina et al., 2020).

Each sample was printed in one continuous print with an enclosed FDM 3D printer that had a heated bed to minimize warping. Support structures were then removed manually after printing, and the samples were left to air-dry at room temperature for 24 h.

Three different specimens were fabricated and tested for each configuration to assess experimental repeatability. The acoustic measurements were repeated three times under the same test conditions for each specimen and the SAC values reported are arithmetic averages of all measurements. At each frequency point, the standard deviation was computed to give an idea of the experimental variability. The variation observed was within the acceptable limits, indicating good repeatability and consistency of manufacturing and testing procedures.

Three experimental replicate samples were prepared and tested under every experimental setting to ensure the reproducibility and consistency of the outcome. There was no further curing, polishing or coating to retain the native surface texture that is inherent to the FDM process.

Typical examples of hole distributions of ⌀1 and ⌀2 configurations are depicted in Figures 1, 2, respectively. These values indicate the homogeneous radial distribution that aims at maintaining the porosity of the sample face. The exact geometric specifications of the six sample configurations of 3D-printed samples under study are presented in Table 1, and they differ in thickness, hole diameter, perforation density, spacing, and perforation ratio. Figure 3 shows photographs of the samples that depict significant differences in the density of surface perforation and the thickness of the structure, which has a significant effect on acoustic response. As an example, Samples 2 and 3 are associated with 5-mm and 10-mm thick samples with 1-mm holes and 7.8% porosity, but Samples 4 to 7 use 2-mm holes to achieve greater porosity (20.92%). Figure 4 also illustrates the 3D-printed spacer rings that allow creating the accurate layered sample setups, which makes it possible to systematically explore the effect of the interaction between the geometric design and the layering of air gaps on sound absorption performance.

FIGURE 3

FIGURE 4

The outer diameter of the 3D-printed spacers was 34.7 mm (same as the impedance tube), and the inner diameter was 33.7 mm. During acoustic testing, the thicknesses of the spacers used were 5 mm and 10 mm.

2.3 Experimental test setup

The acoustic characterization of the composite panels was performed by the two-microphone impedance tube method in compliance with ISO 10534–2 and ASTM E1050, which regulates the measurement of the normal incidence sound absorption coefficients. The test apparatus (Alfa Acoustics) includes an impedance tube with an inner diameter of 35 mm, a signal generator, a power amplifier, a data acquisition (DAQ) device, and a laptop computer with special analysis software. The system supports the creation, capture, and processing of acoustic signals in the range of 50 Hz–5,000 Hz. Figure 5 displays the test configuration with the signal path between the source and the data processing unit.

FIGURE 5

In this arrangement, the broadband acoustic system created which is sent through a speaker at one end of the tube. This signal travels along the tube and is interacted with the sample mounted at the rigidly terminated end. The incident and reflected pressure waves are recorded by two microphones that are positioned at exact distances of 65 mm (X₁) and 35 mm (X₂) to the sample surface. These pressure signals are recorded by the DAQ unit and transferred to the software where they are analyzed by the transfer function method. Figure 6 shows a simplified schematic of the internal layout of the tube and how it works, with the microphone position and sample position noted.

FIGURE 6

The system was calibrated in two steps before testing. The microphones were adjusted to be in phase and amplitude consistency with a standard reference signal. This was then checked by a system-level calibration using a rigid termination at the sample holder, to check the accuracy of the reflection coefficient under known boundary conditions. All measurements were done at controlled ambient conditions of about 25 °C and the samples were firmly mounted flush with the tube to avoid leakage of air.

Table 2 shows the main specifications of the test apparatus, such as the dimensions of the tube, standard compliance, distances between the microphones, and the distance between the speaker and sample, which is 1,000 mm. The level of sound source was kept constant at 100 dB to provide proper signal-to-noise ratio of all the frequency bands. The standardized arrangement allowed the accurate and reproducible determination of sound absorption behavior of all fabricated samples so that the effect of thickness and perforation ratio on acoustic performance could be compared directly.

In the current study, the term average SAC is used to refer to the arithmetic mean of the obtained values of the sound absorption coefficient at the frequency range of 50Hz–5,000 Hz that were measured at 50 Hz intervals. This measure was only used to allow comparative analysis between different configurations. Admittedly, this construct is not a standardized measure similar to the NRC (Noise Reduction Coefficient) or the weighted sound absorption coefficient of EN ISO 11654; however, it was adopted as a means of providing a simplified measure of broadband absorption properties.

To evaluate the air flow resistivity of the porous samples, the Wispr Flow Resistivity Measurement Setup, as shown in Figure 7, was employed. The apparatus consists of a sealed cylindrical chamber to hold the test specimen, a flow control unit, and differential pressure sensors. Each sample was placed securely in the circular sample holder, and air was passed through it at controlled flow rates of 6 L/min, 8 L/min, 10 L/min, and 12 L/min. For each flow rate, the corresponding pressure drop across the sample was recorded using the integrated pressure sensors. This pressure drop data was then used to calculate the air flow resistivity (σ) of the material according to the following relation:where ΔP is the pressure drop across the sample, A is the cross-sectional area of the sample, and Q is the volumetric flow rate of air. The air flow resistivity for each flow rate was calculated using Equation 1, and the final value reported for each sample was taken as the average air flow resistivity across all tested flow rates. This approach ensures consistent and representative measurement of the material’s resistance to airflow, a critical parameter influencing acoustic absorption performance.

FIGURE 7

2.4 Test configurations

In order to test the acoustical response of the fabricated samples, various test setups were carried out using the impedance tube configuration. These arrangements include baseline testing with no air gap between the sample and the rigid backing, configurations with a specified air gap, an interposing porous polyethylene terephthalate (PET) foam layer, and multilayer arrangements where the original sample thickness was divided into separate layers with equal or different air gaps. This enabled a thorough study of the role of spatial separation, interlayer interfaces and porous intermedia on the sound absorption characteristics of the composite panels.

All the samples of 34.7 mm diameter were placed flush in the tube holder and sealed well to avoid acoustic leakage. In the case of tests with an air gap, spacers were employed to provide uniform and accurate separation with the rigid termination plane. In foam-insert systems, a 20 mm thick PET foam pad was inserted directly behind the panel in front of the rigid backing. In multilayered structures, the initial sample thickness (e.g., 10 mm or 20 mm) was split in two panels with 5 mm or 10 mm air gaps between them, to enable the assessment of distributed resonant absorption effects.

Acoustic tests were carried out between 50 Hz and 5,000 Hz. To achieve reliability, every test case was replicated three times and the final results were achieved by calculating the average of the sound absorption coefficient of all the replications. The reproducibility of the environment and procedure in the trials was possible, and random errors in measurements were reduced.

The uncertainty of the SAC measurements was determined by repeated experimental observations. The average standard deviation of SAC was determined to be less than ±0.006 for most of the frequency range studied based on the replicate measurements. Figure 8 shows the results of repeatability test for H1T10 samples where average standard deviation recorded is ±0.005.

FIGURE 8

Figure 9 illustrates the different test configurations employed: (a) single-layer sample mounted directly on the rigid backing (no air gap), (b) sample separated from the backing by an air gap, (c) sample backed by porous PET foam, and (d) multilayer configuration with sample segments split and spaced apart by controlled air gaps.

FIGURE 9

Figure 10 shows the flowchart of experimental methodology adopted for this study.

FIGURE 10

2.5 Theoretical estimation using Delany-Bazley model

The Delany-Bazley (DB) empirical model was used in the prediction of the values of the SAC of non-perforated porous samples. The DB model is commonly used in the estimation of acoustic behavior of fibrous and porous materials with relatively high airflow resistivity. It expresses the characteristic impedance and complex wave number of a material as frequency-dependent functions based on the dimensionless parameter where is the frequency (Hz) and is the airflow resistivity (Pa·s/m² or rayl/m).

The normalized characteristic impedance and normalized complex wave number are given by Equation 2 and Equation 3 respectively:where, is the air density, is the speed of sound in air, is the angular frequency, and is the imaginary unit.

Using these, the surface impedance of a porous layer of thickness backed by a rigid wall is computed using Equation 4:

The corresponding normal-incidence sound absorption coefficient is then calculated by using Equation 5:

The equations were used to interpolate the SAC of a 10-mm thick specimen. Considering the model assumptions and the frequency-dependent nature of the model, the methodology is especially useful in explaining sound energy-dissipation processes in the low-to-medium frequencies range. The estimated values of SAC were then compared to the laboratory measurements to check their accuracy.

The accuracy of the model was assessed by calculating the Root Mean Square Error (RMSE) between the measured and predicted SAC over the range of frequencies investigated (50–5,000 Hz). The RMSE was calculated using all the measured frequency points for the 10 mm thick with 2 mm hole sample used for model validation.

3 Results and discussion

The section contains and discusses the experimental results concerning the sound absorption capability of carbon fiber-Onyx composite panels. The effect of geometric parameters, air gap configurations, porous backing and model predictions are discussed with respect to their acoustic behavior at various frequency ranges.

3.1 Effect of perforation ratio

The experimental analysis of the influence of perforation ratio on sound absorption in three specimens of the same thickness (10 mm) but with different hole diameter and perforation ratio (0%, 7.8% and 20.9%) shows the main acoustic behaviors related to physical mechanisms of absorption. Sample details are provided in Table 3. As can be seen in the results (Figure 11), Sample H0T10 (non-perforated) shows overall lower SAC values, it exhibits comparable absorption up to approximately 3 kHz, with some peaks surpassing the others in specific low and mid-frequency bands. It exhibits a maximum SAC of 0.259 at 2,950 Hz and an average SAC of 0.127. Sample H1T10, which had 1 mm holes and 7.8% perforation ratio, showed a better mid-frequency absorption with a peak SAC of 0.507 at 3,900 Hz and an average SAC of 0.224. Sample H2T10 with 2 mm holes and 20.9% perforation ratio exhibited the superior high-frequency performance with a maximum SAC of 0.735 at 5,000 Hz and an average SAC of 0.162. The evolution of the absorption with perforation ratio increase is shown, especially in the high frequency range.

FIGURE 11

The higher the perforation ratio, the more the incident sound waves will interact with the inside surfaces of the perforations, and the more viscous and thermal dissipation losses will occur. The larger perforation area provides more movement of air particles in the holes, which increases the conversion of sound energy into heat. But, too high a perforation ratio will decrease the resistance to airflow and the acoustic impedance, and therefore the energy dissipation at some frequencies.

The physical explanation is the interaction between airflow resistance, tortuosity and viscous-thermal boundary layer effects in the perforations. Perforated surfaces add new mechanisms of energy dissipation (viscous losses in the holes and friction at the internal surfaces). As the hole size and perforation ratio are increased, more air can be exposed to the surface area of the material, and more energy can be dissipated at higher frequencies. However, excessive perforation ratio can lead to a decrease in flow resistance and loss of low-frequency absorption, as seen with Sample H2T10, which has less performance in the low to mid-frequency ranges than H1T10. These results agree with Maa’s theory of micro-perforated panel absorbers, where the ratio of hole diameter to thickness and the perforation ratio are the key factors in determining the peak frequency and amplitude of absorption (Kim and Mendoza, 2013).

These results are supported by comparative studies in the literature. For example, Liu et al. (2022) showed that perforated porous metamaterials can improve the high frequency absorption by using the Helmholtz-type resonance mechanisms and dissipative coupling between the perforations and neighboring porous layers. Similarly, Carbajo et al. (2016) demonstrated that dead-end slit perforations enhance absorption by increasing the effective acoustic path length and thus increasing viscous losses - a principle which is still relevant to perforations with larger diameters.

The practical consequences of these results depend on the target frequency band. Sample H0T10 has a broad but relatively low absorption profile, making it most suitable for low-sensitivity applications or in situations where high-frequency sound insulation is not a priority. Sample H1T10 has good performance in the medium frequency range, which makes it suitable for office paneling or automotive interior applications. Sample H2T10, which has good high frequency absorption, is suitable for applications where there are high or sharp noise sources such as machine shops or HVAC ductwork. Importantly, the averaged SAC values suggest that sample H1T10 provides a more uniform absorption performance in the spectrum, suggesting that a moderate perforation ratio level (ca. 7%–10%) may provide the most multifunctional acoustic properties.

Application wise, the sample H0T10 exhibiting reduced SAC with flatter response in low to high bands can be used in structural components where sound absorption is not required or in an application where low noise is required. Sample H1T10 provides the best combination between medium (500 Hz - 1 kHz) and high (2 kHz–4 kHz) frequency absorption and perforation ratio of the material, making it suitable in general purpose acoustic panels in the office, classroom or industrial environment with moderate noise levels. Sample H2T10, conversely, exhibits good and rising performance especially in the high frequency range and beyond, thus suitable in an environment heavily populated by high-pitched noise, e.g., mechanical rooms, HVAC ducting, or in the car engine compartment.

These findings support the broader understanding that the careful tuning of perforation ratio, hole size, and thickness can significantly optimize acoustic panel performance across desired frequency bands (Liu et al., 2022; Cavalieri and Van Damme, 2024).

3.2 Effect of sample thickness

The influence of sample thickness on acoustic performance was systematically studied by four test conditions, namely, H2T5, H2T10, H2T15, and H2T20, which included samples with the same perforation ratio (20.9%) obtained by all 2 mm perforations but with different thicknesses of 5 mm, 10 mm, 15 mm and 20 mm respectively. As the Figure 12 indicates, the experimental results indicate a substantial improvement in the sound absorption of low to mid-frequency with the increase in the sample thickness. In particular, the mean SAC increases to 0.084 of H2T5 to 0.162 of H2T10, 0.328 of H2T15, and reaches its highest point of 0.419 of H2T20. The good SAC frequency range also extends and moves downward, 4,950 Hz in H2T5 to 2,800–4,400 Hz in H2T20, which is a sign of better broadband absorption.

FIGURE 12

Physical processes that can explain this trend include long paths of interaction of sound waves and high viscothermal losses of the perforated channels and porous matrix. Thicker samples permit more friction and interaction of sound waves with internal structures, and result in more energy dissipation. Moreover, the greater the thickness, the better the resonance behavior of the Helmholtz type, in particular, with the support of a sufficient depth of the cavity, the higher the absorption peaks of low frequencies. The maximum SACs of H2T15 and H2T20 are 0.995 at 4,500 Hz and 0.993 at 3,400 Hz, respectively, which indicate that both can be used to offer high-efficiency absorption in the mid-to-high frequencies. As the thickness increases, the low frequency absorption increases, which is believed to be due to the increased propagation path for sound waves inside the structure. Thicker samples offer more potential for frictional and thermal losses, and also increase the effective cavity depth, which lowers the resonance behavior to lower frequencies and improves low frequency sound attenuation.

Applications H2T5 and H2T10 with comparatively lower average SACs and reduced effective frequency response are more appropriate in high frequency noise mitigation where space is limited, e.g., in thin wall linings of electronic equipment or HVAC ducts. Conversely, H2T15 and H2T20 have significant benefits in those applications that demand greater frequency coverage and lower frequency response like in automotive cabin interiors, industrial enclosures and architectural sound systems.

The results are consistent with the previous studies which have stressed the importance of material thickness in improving low-frequency performance. Other works like Zheng et al. (2020) and Sanchis et al. (2022) have also demonstrated that broadband absorption and shifting absorption peaks to lower frequencies can be enhanced by increasing the absorber thickness or by adding a layered structure due to increased cavity resonance and frictional losses.

3.3 Effect of air gap

In the first (Figure 13a) the samples (1 mm holes and 10 mm thickness, 7.8% perforation ratio) were tested with 0 mm, 10 mm, 20 mm and 30 mm air gaps. The H1GT10G30 showed highest peak SAC of 0.952 at 550 Hz, followed by H1T10G20 with peak SAC of 0.937 at 700 Hz and H1T10G10 with peak SAC of 0.920 at 950 Hz compared to SAC of 0.506 at 3,900 Hz. The mass-spring resonance phenomena were observed with the introduction of air gap, which resulted in the significant change of the absorption peaks to lower frequencies, which is the evidence of the mass-spring resonance phenomena caused by the Helmholtz resonance where the air in the holes is the acoustic mass and the rear cavity is the acoustic spring.

FIGURE 13

When an air gap is introduced, it forms a coupled mass-spring system with the air inside the perforations being the oscillating mass and the enclosed cavity being the acoustic spring. This Helmholtz-type resonance mechanism causes the absorption peak to move to lower frequencies and enhances the low frequency absorption performance. The resonance shift caused by the air gap can be interpreted using Helmholtz-type behavior, where the perforated holes act as acoustic masses and the rear air cavity acts as an acoustic spring.

The same trend was observed in the second set (Figure 13b) where the samples with 2 mm holes and 10 mm thickness (20.9% perforation ratio) showed an increase in the peak SAC to 0.809 at 1800 Hz (10 mm air gap) as compared to 0.734 at 5,000 Hz (no air gap). The mean SAC increased significantly between 0.162 (no gap) and 0.289 (10 mm air gap) and then decreased gradually with an increase in gaps (0.254 at 20 mm and 0.236 at 30 mm). The findings indicate that an air gap can be used to improve the sound absorption at low to mid frequencies by tuning the resonant behaviour of the system, but the size of the gap giving the best average performance varies with the geometry of the hole and the thickness of the sample.

In the third set (Figure 13c) where the sample thickness was made 20 mm and the hole diameter maintained at 2 mm, addition of air gap once again resulted in low frequency peak shifts. Peak SAC decreased to 0.847 at 800 Hz (30 mm gap) as compared to 0.993 at 3,400 Hz (no gap). In the same way, average SAC fell to 0.230 (30 mm gap) versus 0.419 (no gap) and there was a trade-off between air gap increasing the low-frequency absorption but slightly impairing the overall average absorption performance. These results are consistent with the works of Wang and Huang (2011), and Gai et al. (2015), who discovered that the addition of air gaps improves the absorption in the lower frequency band because of the cavity resonance effects. Sakagami et al. (2014) also found that the resonance tuning can be successfully attained through geometric control of the air gap, and the interpretations of the mass-spring system were similar.

Therefore, when the application is related to the high frequency sound suppression, the configurations without air gap can be more appropriate, and the low- to mid-frequency noise suppression can be effectively implemented with the moderate air gaps (10–20 mm). This has a direct implication in the design of tunable acoustic panels in architectural acoustics and in automotive interiors where certain frequency bands need to be attenuated.

3.4 Effect of porous backing

The study of the effect of porous backing was performed on a 10 mm thick composite sample with 2 mm diameter holes (Sample H2T10 with 20.9% perforation ratio) under two conditions: with a 20 mm air gap and with a 20 mm PET foam backing. Both configurations have high SAC in low-to-mid frequency range as illustrated in Figure 14, but the PET-backed configuration has a wider and slightly higher performance. In particular, the sample with the PET backing has a maximum SAC of 0.9 at 1,200 Hz, as opposed to 0.75 at 1,300 Hz in the sample with an air gap, which shows increased energy dissipation caused by extra viscous and thermal losses introduced by the porous matrix. Moreover, the PET-filled structure also has a broader effective absorption band (1,000–1,500 Hz), compared to the narrower effective band (1,200–1,400 Hz) for air-gap configuration (H2T10G20), indicating its better broadband acoustic performance.

FIGURE 14

Porous PET foam provides both resistive and reactive acoustic impedance components, unlike an air cavity. The interconnected pore structure enhances viscous friction and heat transfer between the vibrating air particles and the pore walls, which leads to the greater dissipation of sound energy and the wider effective sound absorption band.

The improvements observed can be explained by the damping properties of the porous PET foam that adds resistive and reactive impedance components. Unlike the strictly reactive response of an air gap, the PET foam improves energy dissipation by friction and thermal conductivity, thereby flattening and extending the SAC response. This result is in line with the findings of other previous researchers like Okano et al. (2015), and Li et al. (2021), who found that porous backing layers may enhance significantly the low-to-mid frequency absorption of micro-perforated panels and composite systems. Physically, the air gap is a spring in the Helmholtz resonance system, but the PET layer introduces a dissipative component, in effect, converting more acoustic energy to heat over a wider frequency range.

In terms of application, the PET-backed sample has a good potential in low-to-mid frequency dominant applications like HVAC systems, industrial noise enclosures and automobile cabins where it is desirable to have compact, lightweight and broadband sound absorbers. The PET backing does not only improve acoustical performance, it also provides structural support and thermal insulation, which makes it a desirable multi-purpose material. Therefore, porous backing, such as PET is a convenient and effective alternative to mere air gaps, both acoustically and structurally.

3.5 Effect of air gap layering

The effect of air gap layering on the sound absorption coefficient (SAC) of acoustic panels is critical in optimizing material design for noise control across varying frequency bands. In this study, four experimental sets were conducted to evaluate the influence of splitting air gaps and introducing layered structures on SAC performance, with variations in sample thickness, hole diameter (perforation ratio), and air gap configuration. Table 4 gives the nomenclature and configuration codes that were adopted to refer to the test samples that were subjected to air gap layering analysis. The purpose of each code is to give a clear definition of the diameter of holes, the thickness of the samples, and the spatial distribution of air gaps and layers to interpret the experimental results easily.

In the first set, comparing H1T10G10 with H1T5G5T5G5 (Figure 15), the layered configuration showed a comparable peak SAC of 0.905 at 1,250 Hz versus 0.92 at 950 Hz for the single-layer configuration. However, the layered structure achieved a broader effective frequency range (1,000–1,650 Hz) and a higher average SAC of 0.394 compared to 0.230. This enhanced broadband absorption in the layered case is explained by multiple internal reflections, cavity-coupling and increased interference effects that the intermediate air layers introduce. This kind of behavior confirms the results of Ciaburro et al. (2025), who showed that sub-dividing absorptive materials into sub-layers is an effective way to introduce several Helmholtz-like resonances, thus extending the effective absorption band.

FIGURE 15

In the second set (Figure 16), H1T10G20 was compared with H1T5G10T5G10. The peak SAC for the layered configuration was 0.970 at 1,250 Hz and 0.67 at 2,350 Hz, significantly outperforming the single air gap sample (0.937 at 700 Hz). The layered configuration also provided a wider effective frequency coverage (700–1,250 Hz and 2,200–2,500 Hz), leading to an overall average SAC of 0.409 versus 0.218. The enhanced response of the layered system can be physically explained by the fact that two consecutive Helmholtz resonant systems are in parallel and, as a result of this, the resonance effects overlap and hybrid mode coupling occurs, which results in the increased energy dissipation within a broader bandwidth.

FIGURE 16

In the third set (Figure 17), involving samples with higher perforation ratio (2 mm hole diameter), H2T10G10 was compared to H2T5G5T5G5. The layered configuration again showed effective performance, with a peak SAC of 0.729 at 2,250 Hz and an average SAC of 0.276, slightly lower than H2T10G10’s peak SAC of 0.809 at 1800 Hz but comparable in terms of average SAC (0.289). Higher perforation ratio and shorter cavity lengths in layered design enhances the acoustic impedance mismatch and viscothermal losses in the perforations and cavities. These results are consistent with the previous works by Cobo et al. (2021), who highlighted the benefits of coupled-cavity systems in improving low-frequency response without adding thickness to the panel.

FIGURE 17

In the fourth comparison (Figure 18), H2T10G20 was evaluated against H2T5G10T5G10. The data presented in Figure 17 shows that the layered structure (H2T5G10T5G10) is significantly better than the monolithic structure (H2T10G20) in broadband absorption performance at frequencies between 1,000 Hz and 2000 Hz.

FIGURE 18

The mean SAC of the layered structure H2T5G10T5G10 is 0.398, and this is a significant improvement of 56.7% over the monolithic structure H2T10G20, which has a mean coefficient of 0.254. The comparison of peak values also shows a very strong improvement: the layered sample has a maximum coefficient of about 0.99 at 4,150 Hz, compared to the peak of 0.74 in the monolithic sample at 1,250 Hz. These findings indicate that the layered structure provides better low-to-mid frequency absorption and at the same time creates a new high-frequency resonance peak that broadens the acoustic bandwidth.

The above advantages can be explained by the presence of additional internal resonances and additional viscothermal losses as a result of additional interfaces in the layered system. The second Helmholtz resonator is the intermediate air cavity, which produces broader and stronger SAC peaks. In practice, samples of average SAC (that is, above 0.35) like H1T5G5T5G5 and H1T5G10T5G10) are acceptable in medium-frequency noise control in automotive or HVAC applications. The H2T5G10T5G10 design with maximum SAC of approximately 1.0 at high frequencies can be successfully applied in industrial enclosures or applications where high frequency sound suppression is needed. These results are consistent with the literature reports that indicate that multilayer structures and perforated panels with customized backing designs can be used to greatly enhance acoustic absorption by exploiting impedance mismatch, wave interference, and frictional losses (Bucciarelli et al., 2019; Su et al., 2020; Maury and Bravo, 2023).

3.6 Influence of perforation ratio in layered air-gap configurations

Perforation ratio effects on sound absorption performance of layered perforated panels (MPPs) with split air gaps were systematically examined with the help of two comparative experimental arrangements. These arrangements were the same geometrical arrangement with only the difference in the diameter of the holes: 1 mm diameter (7.8% perforation ratio) with H1 samples and 2 mm diameter (20.9% perforation ratio) with H2 samples. Figure 19a shows the sound absorption coefficient (SAC) in the frequency range of the configurations H1T5G5T5G5 and H2T5G5T5G5, and Figure 19b compares the configurations H1T5G10T5G10 and H2T5G10T5G10.

FIGURE 19

Figure 19a shows that the H1T5G5T5G5 setup has 2 different absorption peaks, the first at 1,250 Hz with a peak SAC of 0.905 and the second at 3,500 Hz with a SAC of 0.556, which means that it has a wider range of performance in the mid- to high-frequency spectrum. The average SAC of this setting is 0.394. The H2T5G5T5G5 arrangement, in contrast, shows only one dominant peak with a higher frequency of 2,250 Hz and a SAC of 0.729 and an effective absorption range of 2000–2,500 Hz with a lower average SAC of 0.276. The increase in peak frequency and decrease in broadband absorption of H2T5G5T5G5 can be explained by the higher perforation ratio of the larger hole diameter, which decreases the acoustic resistance and postpones the optimum absorption condition to higher frequencies.

This trend is further proved in Figure 19b when a larger air gap arrangement is considered. The H1T5G10T5G10 setting has two peaks at 1,250 Hz (SAC = 0.970) and 2,350 Hz (SAC = 0.670) with a broad effective range of 700–1,250 Hz and 2,200–2,500 Hz resulting in an average SAC of 0.409. Conversely, the H2T5G10T5G10 panel once again moves the absorption to higher frequencies with the first peak at 1,550 Hz (SAC = 0.681) and the second, stronger peak at 4,150 Hz (SAC = 0.997). Its effective absorption range is spread between 1,400–1700 Hz and 3,850–4,450 Hz with a slightly lower average SAC of 0.398.

The physical process that underlies these findings is the balance of acoustic impedance controlled by perforation ratio, hole diameter and depth of the cavity. Increased perforation ratio permits more airflow and reduces the surface resistance, which slows the rate at which the system attains optimum impedance that is equal to air. Although this improves high-frequency absorption, it may impair low-frequency performance and the overall broadband effectiveness, particularly when it is not combined with sufficient cavity depth. On the other hand, reduced perforation ratio and reduced hole size keeps the resistance higher, allowing better dissipation at the mid-frequency range, and resulting in wider but slightly smaller amplitude absorption.

3.7 Influence of layering sequence on acoustic performance

The perforation and perforation ratio of acoustic panels influence the acoustic panel sound absorption properties greatly with the layering sequence; the more the air gaps the system has, the better the sound absorption properties of the panels. Figure 20 is a comparison of the SAC performance of two configurations H1T5G10H2T5G10 and H2T5G10H1T5G10. In the former setup, the sample is a lower perforation ratio H1T5 followed by a higher perforation ratio H2T5 with 10 mm air gaps between them. Two peaks of SAC are observed in this setup the first peak is 0.997 at 1,000 Hz and the second is 0.557 at 3,750 Hz with an average SAC of 0.366. Conversely, inverting the sequence (H2T5G10H1T5G10) gives a better absorption over a wider frequency range, with the first peak of 0.999 at 1,150 Hz and a second peak of 0.953 at 3,000 Hz, giving a higher average SAC of 0.513. This is because of the improved performance in terms of impedance matching and gradual dissipation of energy because of the higher perforation ratio at the front layer. The first H2T5 layer helps the incident sound waves to penetrate further enhancing low and mid frequency absorption. The results indicate that acoustic layer sequencing is an important design factor in broadband noise control optimization in engineered composite structures.

FIGURE 20

3.8 Model validation for sound absorption prediction

The Delany-Bazley (DB) empirical model was used to predict the SAC of the non-perforated 10 mm thick sample with 2 mm holes (20.92% perforation ratio) to estimate the acoustic response of the sample and compared with the experimental measurements. The DB model, developed on fibrous and porous media with comparatively high airflow resistivity, gives frequency-dependent expressions of characteristic impedance and wave number. The difference between the predicted and the measured SAC values indicates that the general trend of the sound absorption is captured by the DB model as shown in Figure 21 with a RMSE of 0.1078. The RMSE of 0.1078 suggests that the agreement is reasonable for the preliminary estimation of the SAC trends, especially at low-to-mid frequencies. But more advanced models and further experimental validation are needed for engineering design with high accuracy. It is interesting to note that the model and experiment agreement is better in the low to medium frequency region especially between 300 Hz and 4,000 Hz. The model has been able to capture the slow rise in SAC in this region and reflect the behavior of energy dissipation as observed. The Delany–Bazley model is mostly applicable to fibrous or porous media and does not explicitly consider perforation resonance or complex layered cavities. In this study, it was applied to the 2 mm hole size perforated configuration as a preliminary predictive comparative test.

FIGURE 21

The average SAC of the experiment is about 0.1620 over the frequency range whereas the DB model has a slightly higher average of 0.1875. The model differs more noticeably in the higher frequency range above 4,000 Hz where it tends to underpredict absorption but is still a useful tool in making rapid estimates. The improved fit in the low frequency range can be explained by the fact that bulk viscous losses and the comparative simplicity of the interaction of the waves with the thin material are well-covered by the empirical nature of the DB formulation. But at higher frequencies the model does not take into consideration microstructural scattering effect, surface reflections and resonance peaks that are observed in the experiment data, particularly around 5,000 Hz where SAC is maximum. The Delany–Bazley model was found to be in good agreement with the experimental results in the low to mid-frequency range (around 300–4,000 Hz), where the viscous and thermal dissipation mechanisms dominate, but larger deviations were observed at higher frequencies (above 4,000 Hz) as the empirical model does not explicitly account for the localized resonance effects, perforation-induced scattering, and complex wave interactions associated with the composite structure. Therefore, the model is suitable for preliminary prediction of acoustic trends, while more advanced numerical models would be required for accurate high-frequency analysis.

4 Conclusion

The optimized Carbon Fiber–Onyx acoustic panels were found to have peak sound absorption coefficients of nearly 0.99, which is comparable to the performance of several commercially available acoustic absorbers in their useful frequency ranges. The present panels, however, are not conventional fibrous absorbers that offer broadband absorption, but are rather structurally designed resonant absorbers that have frequency-selective absorption characteristics. According to the measured SAC values, the investigated samples can be considered as moderate to high performance sound-absorbing material depending on the structural configuration and operating frequency range.

The results obtained from this study have been obtained from laboratory scale impedance tube measurements in a controlled environment. The Carbon Fiber–Onyx composite configurations investigated are not all possible practical designs, but offer valuable insights into the effect of perforation ratio, thickness, air gaps, porous backing and layered arrangements on sound absorption performance. In addition, long-term durability, environmental exposure (including temperature and humidity changes), manufacturing variability and large-scale implementation were not explored. Conclusions should thus be considered in the context of the configurations tested. Further research is needed to test full-scale acoustic panels under real service conditions and to increase the range of the parameters investigated to enable more general design guidelines. The present study aimed at experimental assessment of the effect of geometric and structural parameters on the acoustic performance. Repeated measures were carried out to ensure reliability of data, but advanced statistical analyses including ANOVA, regression modelling and calculating effect size were not part of the current work. Such statistical methods could be useful in future studies with larger data sets and wider ranges of parameters to further quantify parameter significance and improve predictive design methods.

Further studies might investigate micro-perforation geometries, hybrid material combinations or numerical modeling methods to further improve predictive accuracy and performance optimization to a given acoustic application.

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