Computational fluid dynamics analysis and transfer matrix optimisation for evaluating the noise absorption performance of tessellated polyform structure

Abstract

This study presents the design, development, and acoustic characterisation of a tessellated polyform absorber composed of perforated panels (PPs) made from jute-reinforced rigid composites. A full factorial optimisation involving 72 combinations—spanning 12 geometric variants, six cavity depths, multiple perforation ratios, and orifice diameters—was conducted using impedance tube measurements. Integration of jute fleece within the backing cavity, combined with an L-tromino tessellation, enabled noise absorption (NAC ≥0.9) across 400–6300 Hz in a single modular structure. To explain deviations from the classical Maa model, the transfer matrix was progressively refined: T₁ accounted for orifice irregularities caused by jute-fibre fraying; T₂ incorporated additional damping from jute fleece in the cavity. CFD simulations were conducted to qualitatively examine the influence of tessellated geometry on local airflow patterns and edge-induced vortical structures around the L-tromino elements. The analysis highlights how geometric discontinuities influence local viscous interaction, supporting the proposed topology-driven acoustic design. The resulting tessellated polyform structure demonstrates high acoustic efficiency along with favourable mechanical strength and fire-retardant characteristics of SMC-based natural fibre composites. This integrated approach offers a sustainable, geometry-driven solution suitable for precision acoustic environments such as recording studios and controlled architectural spaces.

Keywords

Computational fluid dynamics-CFD L-tromino geometry perforated panels (PPs)transfer matrix viscous and inertial effects

Introduction

The increasing demand for effective noise mitigation in built environments aligns with UN Sustainable Development Goal 11.6,^1,2 which aims to reduce the adverse per capita environmental impact of cities, including noise pollution. Noise is the unwanted sound^3,4 that can be controlled through two primary methods: sound absorption and sound insulation,^5,6 each serving a different purpose.

Sound insulation focuses on blocking the transmission of sound from one space to another.⁷ It involves the use of dense, airtight materials and structural techniques to prevent noise from entering or leaving a room, making it ideal for creating soundproof environments such as recording studios, industrial enclosures, or private offices. In contrast, sound absorbers are materials or structures designed to reduce echo and reverberation within a space. They work by absorbing a portion of the sound energy, converting it into heat, and thereby improving the acoustic quality of the room. While they may offer some level of noise reduction, their main function is to enhance clarity and reduce unwanted reflections within the same space. The choice between using an absorber or an insulator depends on the application area, for example, absorbers are preferred in classrooms, auditoriums, or home theatres where internal acoustic clarity is key, while insulators are essential in settings where preventing noise leakage or intrusion is critical like hospital operation theatres.^8,9

The Figure 1 illustrates the varying acoustic requirements of different room types such as recording studios, classrooms,^10–13 and auditoriums, based on reverberation time (RT60) and noise absorption coefficient (NAC) across different frequency ranges.^14,15 It highlights that each space has distinct acoustic characteristics, requiring specific materials to manage sound energy effectively. The shaded regions indicate the desired acoustic conditions for each environment, while the reverberation zone shows how architectural elements like macro-structures and diffusers influence sound control. The Figure 1 establishes that different frequency ranges necessitate different materials for optimal sound absorption, as no single material can effectively manage the entire frequency spectrum. This underscores the importance of a multi-material approach in acoustic design, ensuring that low, mid, and high frequencies are adequately absorbed or diffused based on the functional needs of a given space.¹⁶

Figure 1.

Acoustic demand of different room types and implementation strategy.

Among various sound absorption approaches, perforated panels (PPs) have emerged as an effective solution for controlling mid-to-high frequency reverberation.¹⁷ PP absorbers are widely used in architectural acoustics, classrooms, auditoriums, soundproof studios, quite office, and clean environments like hospitals or food processing areas due to their aesthetic flexibility, hygiene, and fire resistance.¹⁸ However, PPs have limitations chief among them is that their sound absorption is typically narrowband.¹⁹ No single panel is capable of effectively controlling the entire audible frequency spectrum due to the frequency-dependent nature of sound absorption.^19,20

Thereby, in recent years, several strategies have been proposed to achieve broadband sound absorption with perforated panels (PPs). Aperture geometry modification has been explored beyond conventional circular holes. Slit-shaped and spiral apertures alter both viscous and inertial contributions to impedance, thereby broadening the absorption spectrum.²¹ Mechanically tunable configurations such as rotating dual-panel systems and iris-type variable apertures have been developed, where the effective perforation ratio can be dynamically varied to shift the absorption peak frequency.²² Hybrid cavity designs combining PPs with parallel or coiled-up cavities enable multiple resonances, providing wideband absorption while keeping the structure compact.²³ These approaches demonstrate that broad banding can be achieved by tailoring aperture shape, mechanical adjustability, or cavity complexity. However, most existing designs require multilayer assemblies, movable parts, or intricate cavity architectures. Similar vibration and acoustic control strategies have been investigated in structural systems, including vibration attenuation in automotive seating systems, metamaterial absorbers for railway track vibration mitigation, and nonlinear impact damping mechanisms for strongly coupled systems.^24–26

In contrast, the present work investigates a geometry-driven strategy in which perforated panels with different acoustic impedances are spatially arranged in a tessellated polyform configuration. Such arrangements may redistribute local acoustic velocity fields and enhance viscous interaction near panel boundaries, thereby improving the overlap of multiple resonant absorption peaks without requiring multilayer assemblies.

Experimental

Preparation of jute composite

Jute woven cloth with an average areal density of 350 g/m² was used to produce compression-moulded composite panels with polyethylene terephthalate (PET) bottle waste based recycled unsaturated polyester resin, rUPR²⁷ as matrix material via compression moulding through sheet moulding compound (SMC) route as shown in Figure 2. The rUPR mixture was prepared by thoroughly combining an activator (1 wt%) and a catalyst (1 wt%) in a resin blender. This recycled resin paste was then fed into the 2-roll calendar of the SMC machine at room temperature to produce jute cloth-based SMC. The resulting SMC was stored for 72 h. The semi-cured SMC was then cut into dimensions of 600 × 600 mm². A square die was now placed in a 200-tonne hydraulic press. The die temperature was set between 160° ± 5°C, and the press pressure was adjusted to 50 kg/cm². The SMC was stacked into the lower part of the die and subjected to a curing process for 10 min to produce a jute cloth reinforced composite panel with a thickness of 3 mm incorporating a spacer between the upper and lower part of the die.

Figure 2.

Flow diagram of the sheet moulding compound (SMC) process using jute fabric and recycled unsaturated polyester resin (rUPR), including calendaring, SMC line, and compression moulding.

Preparation of perforated panel (PP)

The SMC based jute composite panel was drilled with three different drill bits (1 mm, 1.5 mm, 2 mm) following a simple square lattice pattern to develop Perforated Panels (PPs) with various perforation ratios (0.5%, 1.5%, 3.0%, and 4.5%), as illustrated in Figure 3. An electric handheld drill (BOSCH GSB 600) was utilised for incorporating perforations into the jute composite samples. A combination of 12 different PPs were developed.

Figure 3.

(a) Marking the positions of perforations according to the sample preparation design; (b) drilling of the panels; (c) and (d) illustrating the layout and positioning of the perforations.

Design of experiments (DOE) for optimising perforated panel parameters

Table 1 presents the full factorial design of experiments (DOE) used to optimise the design and structural parameters of perforated panels (PPs). Three key parameters were considered: cavity height, perforation ratio, and orifice diameter, each varied across multiple levels. Cavity height was tested at six levels (10 mm to 60 mm), perforation ratio at four levels (ranging from 0.5% to 4.5%), and orifice diameter at three levels (1 mm to 2 mm). The combination of these parameter variations resulted in a total of 72 experimental conditions, ensuring a comprehensive evaluation of their influence on the acoustic performance of PPs. This full factorial approach allows for the assessment of both individual effects and interactions between parameters, providing a robust dataset for identifying optimal configurations. The experimental methodology ensures systematic variation and analysis, leading to precise insights into the acoustic absorption characteristics of different PP designs.

Table 1.

Design of experiments for optimising design and structural parameters of perforated panels.

Parameters	Level	Range	Total sample
Cavity height	6	10, 20, 30, 40, 50, 60 mm	6 $\times$ 4 $\times$ 3 = 72
Perforation ratio	4	0.5%, 1.5%, 3%, 4.5%
Orifice diameter	3	1, 1.5, 2 mm

Making of tessellated polyform structure

The tessellated polyform-based PP structure was fabricated using jute-reinforced unsaturated polyester composite. Following the curing process, the composite plates were precisely cut into three square panels (200 mm × 200 mm) and two L-tromino shapes (400 mm in length) to achieve the intended tessellated configuration (Figure 4). The final tessellated panel measured 600 × 600 mm², consisting of an interlocked arrangement of these geometries with optimised perforation and cavity parameters to enhance acoustic performance.

Figure 4.

Schematic representation of tessellated polyform structure showing the dimensions of square and L-tromino panels, their placement within pultruded frames at the cavity heights (C), perforation ratio (P), and orifice diameter (O).

Each section of the tessellated structure was designed with distinct cavity heights (C), perforation ratios (P), and orifice diameters (O), as specified in Figure 2. The cavity height varied between 10 mm and 60 mm, directly influencing the acoustic resonance characteristics. The perforation ratio ranged from 0.5% to 4.5%, ensuring controlled airflow resistance and sound dissipation, while a uniform orifice diameter of 1 mm was maintained across all sections to achieve consistency in perforation-induced damping effects.

To ensure structural stability and precise cavity alignment, the tessellated assembly was integrated into a rigid composite frame. This frame provided mechanical support and ensured that the cavity heights remained consistent during acoustic testing. The final assembly was designed to achieve stable noise absorption properties across a broad frequency range, making it suitable for practical acoustic applications.

Testing of noise absorption coefficient (NAC)

The absorption coefficient of all composite samples was measured using a BSWA impedance tube in accordance with ISO 10,534-2:1998 Acoustics—Determination of sound absorption coefficient and impedance in impedance tubes—Part 2: Transfer function method. Circular perforated jute composite samples were securely fitted into the sample holder of the impedance tube, and sound waves in the frequency range of 63 Hz to 6300 Hz were directed through the samples. The recorded test results were subsequently utilised for calculations, graphical representation, and further analysis. The repeatability of impedance tube measurements was evaluated by performing three independent tests for each configuration. The standard deviation of the measured noise absorption coefficient was within ±0.03 across the investigated frequency range.

Testing of tessellated polyform structure

The final tessellated were tested for reverberation time (RT60) using a sound level meter (Rion make) in a double-walled reverberation box, designed with non-parallel walls to prevent standing waves.²⁸

The sound absorption coefficient (α) was calculated using Sabine’s formula:

α = \frac{24 \ln (10) \times V}{C_{20} \times {R T}_{60}}

where V is the chamber volume,

C_{20}

is the sound velocity at 20°C, and

{R T}_{60}

is the reverberation time.

Investigation of orifice geometry

A projection microscope (Projectina Microscope 4014 BK2) was employed to examine the microstructural features of orifice of the perforated panel.

Mechanical and fire response of jute cloth reinforced composite panel

The tensile strength and modulus of jute cloth reinforced composite panel were evaluated according to ASTM D3039 utilising a Universal Testing Machine (UTM) from Instron (Model: 5982). Additionally, the cross-breaking strength (flexural strength) and modulus were assessed following ASTM D790 with the ZwickRoell Flexural Test Setup (Model: Z010). The limiting oxygen index (LOI) was assessed in accordance with ASTM D2863 utilising the Dynisco Limiting Oxygen Index Tester (Model: LOI-406).

Results and discussion

A full factorial optimisation study was conducted for 3 factors i.e., perforation ratio, orifice diameter, cavity depth where perforation ratio has 4 levels i.e., of 0.5%, 1.5%, 3.0% and 4.5%; orifice diameter has 3 levels i.e., 1 mm, 1.5 mm, and 2 mm and cavity depth have 6 levels, i.e., 10, 20, 30, 40, 50, 60 in mm as shown in Figure 5. The effect of cavity height perforation ratio and orifice diameter on noise absorption coefficient (NAC) over 72 data points is represented by Figure 5.

Figure 5.

Tabulated figures displaying effect of cavity heights, perforation diameter and perforation ratio on noise measured absorption coefficient (NAC) of perforated panels using impedance tube indicated in colour scale.

It is visible that one specific PP cannot control the entire frequency range. Therefore, a balanced combination of PPs of different cavity depth and perforation ratio is required to be tessellated to absorb the entire frequency range.

To comprehensively investigate the interaction effects between cavity heights, perforation ratios, and orifice diameters on the acoustic performance of the jute composite based perforated panel absorber, a full factorial design of experiments (DOE) was employed as described in Table 1. By systematically exploring all possible combinations of these factors, as represented in the colour-coded tabular results, the individual and interactive effects on broadband absorption were thoroughly analysed.

Effect of cavity depth

The cavity depth, defined as the linear distance between the rear surface of the PP and the rigid backing wall, plays a crucial role in determining the frequency of the primary absorption peak. At shallow cavity depths (e.g., 10–20 mm), the absorption peaks occur at higher frequencies. This phenomenon arises because the cavity depth influences the resonance characteristics, with smaller depths corresponding to higher resonant frequencies. As the cavity depth increases, the frequency at which the peak absorption occurs shifts toward lower frequencies. This behaviour is attributed to the Helmholtz resonance effect, wherein a deeper cavity increases the acoustic compliance of the system, enabling sound absorption at lower frequencies.

The data presented in Figure 6 confirm that increasing the cavity depth results in a downward shift of the primary absorption peak frequency, consistent with the principles of Helmholtz resonance.²⁹ The relationship was found to be logarithmic.

Figure 6.

Figure showing effect of cavity depth (left), and perforation ratio and orifice diameter (right) on NAC.

Effect of perforation ratio

The perforation ratio, defined as the ratio of the perforated area to the total panel area, was evaluated at four levels: 0.5%, 1.5%, 3.0%, and 4.5%. An increase in the perforation ratio generally broadens the absorption coefficient across a wider frequency range. Panels with lower perforation ratios (0.5%) exhibit narrow absorption bands that are restricted to specific frequency ranges as shown in Figure 5.

An initial increase in perforation ratio improves noise absorption, with peak performance observed at a perforation ratio of 1.5%. However, as the perforation ratio increases further (to 3.0% or 4.5%), the amplitude of the absorption diminishes, particularly at higher frequencies as shown in Figure 6. This reduction in absorption efficiency is attributed to decreased acoustic resistance; higher perforation ratios allow sound waves to pass through the panel more freely, thereby reducing energy dissipation. Although increasing the perforation ratio enhances the surface area for sound interaction, it simultaneously reduces viscous losses, thereby limiting the overall absorption efficiency. This effect is particularly pronounced at the highest perforation ratio (4.5%), where the absorption peaks are less distinct. Excessive perforation reduces resistance, lowering absorption amplitude while maintaining the same peak frequency. Similar effects were observed in experimental studies of acoustic materials, where optimal porosity balanced energy dissipation and structural integrity trade-off emphasizes the importance of tuning perforation ratio to achieve the desired absorption performance.³⁰ These findings underscore a critical trade-off between perforation density and absorption efficiency, emphasizing the importance of optimizing the perforation ratio to achieve the desired acoustic performance. In addition to these resistive effects, variations in perforation ratio also alter the inertial reactance of the air within the perforations, thereby influencing the resonance frequency and bandwidth of absorption.

Increasing the perforation ratio spreads airflow across more openings, which lessens both viscous resistance and mass reactance—reducing both damping and inertial effects in the panel. At low ratios, few perforations intensify boundary-layer friction (resistive effect) and increase acoustic mass, shifting absorption peaks to lower frequencies and enhancing both resistance and reactance. High perforation ratios, in contrast, produce less damping and decreased inertial reactance, shifting absorption toward higher frequencies and broadening the absorption band.

Effect of orifice diameter

Acoustic power dissipated while moving through the opening governs by the resistance offered to the sound energy under the influence of the viscous effect near the hole wall and initiation of oscillatory motion of the air particles inside the perforation which is inertia of the air inside the hole.

The orifice diameter significantly influences the viscous and thermal dissipation within the perforations.³¹ In this study, orifice diameters of 1.0 mm, 1.5 mm, and 2.0 mm were analysed. Panels with smaller orifice diameters (1.0 mm) consistently demonstrated higher absorption coefficients across all perforation ratios. This enhanced performance is attributed to increased viscous losses within smaller perforations, which facilitate greater energy dissipation. Smaller hole diameters amplify viscous drag, as most of the air interacts with the perforation walls, leading to stronger resistive and inertive effects. This enhances energy dissipation and increases the acoustic mass, resulting in higher absorption at lower frequencies. Larger holes decrease wall friction and the amount of oscillating air mass, causing reductions in both resistance and reactance, which typically shift absorption peaks up in frequency but may lower the peak amplitude.

For smaller orifices, such as those with a diameter of 1.0 mm, the absorption efficiency remains robust over a broader range of perforation ratios. In contrast, panels with larger orifice diameters (e.g., 2.0 mm) exhibit a more pronounced decline in absorption performance at higher perforation ratios. At the maximum perforation ratio (4.5%), the negative effect of larger orifices is particularly evident, as the increased size of the perforations reduces acoustic resistance and compromises sound dissipation efficiency.

These results are consistent with Maa’s theoretical framework, which predicts that smaller orifices exhibit superior acoustic performance due to increased viscous losses. However, the jute-based PPs studied here surpassed the performance predicted by the model, highlighting their potential as sustainable, high-performance materials for acoustic applications.

Modified impedance modelling

Microscopic analysis of the drilled orifices, as illustrated in Figure 10, confirmed the presence of fibre fringes that may introduce imperfections along the orifice walls. These non-ideal features are hypothesised to influence the interaction between incident sound waves and the orifice surface, leading to deviations from theoretical models based on smooth circular geometries. To address this, a shrinkage factor δ ∈(0,1), was introduced to refine the nominal orifice diameter ( $d_{n o m i n a l}$ ) and derive a modified diameter ( $d_{m o d i f i e d}$ ), expressed as (1):

d_{m o d i f i e d} = δ \cdot d_{n o m i n a l}

(1)

The acoustic impedance of a single orifice that incorporates both viscous resistance ( $R_{m}$ ) and inertial reactance ( $M_{m}$ ) can be expressed as^32,33:

Z_{p p} = R_{p p} + j X_{p p}

(2)

where the modified resistance,

R_{p p}

and reactance,

M_{p p}

are given by:

R_{p p} = \frac{32 η t}{σ {d_{m o d i f i e d}}^{2}} (\sqrt{1 + \frac{β^{2}}{32}} + \frac{\sqrt{2}}{8} ρ \frac{d_{m o d i f i e d}}{t})

(3)

X_{p p} = \frac{ω ρ t}{σ} (1 + \frac{1}{\sqrt{(3^{2} + \frac{β^{2}}{32})}} + 0.85 \frac{d_{m o d i f i e d}}{t})

(4)

here,

η

is the dynamic viscosity of air,

ρ

is the air density, t is the panel thickness,

ω

is the angular frequency, and

σ

is the perforation ratio. The transfer matrix of a PPs based on modified impedance becomes:

T_{p p} = [\begin{array}{l} 1 & Z_{p p} \\ 0 & 1 \end{array}]

(5)

Behind the PP, the presence of an air cavity of depth, D contributes an unaltered reactive impedance component, defined as:

Z_{C a v} = - j Z_{0} \cot (k D)

(6)

In the above,

Z_{0} = ρ c

, where,

ρ

is density of air and

c

is the speed of sound, and k =

\frac{ω}{c}

is the acoustic wave number. The transfer matrix of this air cavity segment is written as:

T_{C a v} = [\begin{array}{l} 1 & 0 \\ \frac{1}{Z_{C a v}} & 1 \end{array}]

(7)

Placement of an PP with an air cavity behind can be modelled as a series combination of the two elements and the overall transfer matrix, $T_{1}$ is obtained by multiplying the two matrices:

T_{1} = T_{p p} \cdot T_{C a v} = [\begin{array}{l} 1 & Z_{m o d i f i e d} \\ 0 & 1 \end{array}] \cdot [\begin{array}{l} 1 & 0 \\ \frac{1}{Z_{c a v i t y}} & 1 \end{array}] = [\begin{array}{l} 1 + \frac{Z_{p p}}{Z_{C a v}} & Z_{p p} \\ \frac{1}{Z_{C a v}} & 1 \end{array}] = [\begin{array}{l} A & B \\ C & D \end{array}]

(8)

[\begin{array}{l} p_{0} \\ u_{0} \end{array}] = [\begin{array}{l} A & B \\ C & D \end{array}] [\begin{array}{l} p_{L} \\ u_{L} \end{array}]

(9)

for rigid backing,

u_{L} = 0

(10)

therefore,

p_{0} = A p_{L}

(11)

u_{0} = C p_{L}

(12)

The input impedance at the front surface is

Z_{i n} = \frac{p_{0}}{u_{0}} = \frac{A}{C}

(13)

Substituting from (8):

Z_{i n} = \frac{1 + \frac{Z_{p p}}{Z_{C a v}}}{\frac{1}{Z_{C a v}}} = Z_{p p} + Z_{C a v}

(14)

The histogram Figure 7 illustrates the frequency distribution of the orifice diameter shrinkage factor (δ) for 72 experimental runs using MATLAB 2020. The distribution shows that most shrinkage factors fall within the range of approximately 0.3 to 0.6, with the highest frequency observed around 0.3, where the occurrence reaches a peak of 9.

Figure 7.

Histogram showing frequency of occurrence of shrinkage factors.

The Figure 8 presents a comparison of the root-mean-square error (RMSE) between the Maa model and the newly modified model (equation (8)). The lower RMSE of the new model suggests a significantly improved degree of fit compared to the Maa model.

Figure 8.

Comparison of root-mean-squared-error (RMSE) of acoustic resistance and reactance for Maa model and new modified model.

For such purpose, surface fitting of the curves which was obtained based on equation given by MAA model with those obtained from the experimental values in the impedance tube for the jute-rUPR composites was done employing MATLAB R2022b to obtain different values of shrinkage factors expressed as

δ

for jute-rUPR system having different perforation percentage, orifice diameter and cavity height based on experimental data. A regression equation from the observed

δ

values was obtained when data for all the jute-rUPR samples were used and it appeared from such statistical analysis that orifice diameter and perforation percentage were the influencing factors for predicting shrinkage factor,

δ

. Such relation is given below in equation (15) below,

δ = p d^{2} + q σ

(15)

where, p, q are the coefficients in the above equation, the estimated values of which lie within the upper and lower limits of their respective values at 95% confidence limits as shown in Table 2. Since the value 0 is not included within the upper and lower limits, the corresponding factors

σ

and

d

significantly influence

δ

. Therefore, equation (1) as given below relation is statistically worthwhile.

Table 2.

Coefficients of regression surface (with 95% confidence limits).

Coefficients	Estimated value	Lower limit	Upper limit
p	0.1491	0.1362	0.162
q	0.0656	0.05477	0.07639

Comparison of noise absorption coefficients (NAC) across different models

Figure 9 presents a comparative analysis of noise absorption coefficients for 12 different PP samples, varying in orifice diameter (1.0 mm, 1.5 mm, and 2.0 mm) and perforation ratio (0.5%, 1.5%, 3.0%, and 4.5%). Each subplot illustrates the measured noise absorption coefficients (black line), alongside predictions from a newly developed model (red dotted line) and the blue shaded area based on Maa model.³⁴ The results indicate that the new model closely follows the measured data across various frequency ranges, demonstrating improved accuracy over the Maa model in capturing peak absorption values and frequency shifts. Although the PPs denoted by yellow line in Figure 5 were selected for development of final polyform structure, it is very important to understand scientific reasoning behind the underestimation of NAC by classical Maa model. It was evident from Figure 10, the cross section of flow purtuber modified due to the presence of fringes surrounding the perforation introduced uneven opening.

Figure 9.

Comparison between the proposed model (red dotted line) and Maa’s model (blue shaded region) for predicting the sound absorption coefficients (black line) of 12 PPs each placed in 6 different cavity depth.

Figure 10.

Projected microscopic image of orifice of diameter (a) 2 mm and (b)1 mm at rear end of developed perforated panel.

Finite element acoustic study

An acoustic study was conducted in ANSYS 2024 R2 to investigate the effect of perforation shape on sound propagation and energy dissipation. Three single-perforation boards were modelled at a fixed distance of 60 mm from a rigid wall. The perforations had equal areas but different shapes: circular, elliptical, and octalobal. A harmonic excitation of 2 × 10⁻⁶ kg·mm² was applied to generate acoustic oscillations. The acoustic domain was meshed finely near the perforation to resolve boundary-layer effects. Element size near the perforations were kept 0.2 mm as per grid independence study in respect of acoustic velocity. Complex acoustic pressure and normal particle velocity were extracted at the perforation surface for analysis (Figure 11).

Figure 11.

Acoustic total velocity distribution for perforated boards with different perforation shapes: circular (left), elliptical (middle), and octa-lobal (right).

Analysis of the perforation surfaces showed that acoustic pressure remained nearly uniform near all perforations, while particle velocity varied significantly with geometry. The octalobal perforation exhibited the highest velocity, followed by the elliptical and circular shapes. The higher velocity in the perforation suggests stronger interaction with the acoustic field, indicating potentially higher sound energy loss due to viscous and thermal effects. These results demonstrate that, for similar open areas, the perforation shape strongly influences local acoustic velocity and may enhance sound dissipation.^35,36

Cavity modification using jute fleece fillers

Various researchers introduce stacking of the PPs performance (Mathur, 2016) or use of PP in combinations with metamaterial performance (Zhao & Fan, 2015) or filling of the cavities with the fibrous element³⁷ for solving the problem of narrow frequency band with single or multi modal peaks with absorption as high as 90%.

Studies^37–39 have shown that adding elastic or porous inclusions in the backing cavity significantly broadens the absorption bandwidth without sacrificing structural compactness. This can be attributed to the fibrous material within the cavity which introduces additional characteristics concerning its acoustic properties, including flow resistance, density, and porosity.^5,40 These factors alter the effective acoustic impedance and wave propagation properties of the cavity. This modification alters the dynamic response of the back cavity, offering more consistent impedance across a wide frequency range. Thereby, modified transfer matrix $T_{1}$ , as presented in equation (8), for a cavity containing air may further be refined to $T_{2}$ by filling it with a porous fibrous (equation (15)).

An electrical analogy can be employed to interpret the complex acoustic impedance, like that of a parallel RLC circuit: the perforated panel represents the resistive component (R) due to air friction at the orifices; the compressible air within the cavity behaves as an inductive element (L); and the rigid backing simulates a capacitive (C) element due to wave reflection.

When jute fleece is introduced into the cavity, it adds an additional complex impedance, modifying the overall response of the structure and offered an improved sound absorption characteristic. This additional impedance can be mathematically expressed as:

Incorporation of the modification of orifice geometry and the modification of cavity depth through the introduction of fibrous material, specifically, jute fleece in the context of this study does not suffice to achieve a NAC ≥0.9 across a broadband frequency range. The limited operational bandwidth thus poses a significant challenge in meeting diverse acoustic requirements in practical applications as depicted in Figure 1 (Brown et al., 2016). To overcome this limitation, a systematic approach was adopted involving the development of a polyform structure made by tessellation of perforated panels based on jute-reinforced composites. Panel to control low frequencies was with C: 60 mm, P: 0.5% while panel configuration of C: 10 mm, P: 4.5% was planned to use for higher frequency.

Geometrical flow analysis of tessellated polyform structure

To understand the influence of tessellated geometry on local airflow behaviour, computational fluid dynamics (CFD) simulations were performed on simplified polyform configurations. The objective of this analysis was not to compute acoustic absorption directly but to visualise how geometric discontinuities associated with the L-tromino topology influence local flow structures and potential viscous interaction regions. In the design of advanced PP absorbers with complex L-tromino geometries generate abrupt changes in flow direction due to the L-shaped configuration led to significant flow separation and the formation of unstable wakes. The 90° phase-apart limbs of L-trominoes introduce sharp edges, which act as initiation points for vortex formation as shown in Figure 12. This can be visualised through CFD simulations.

Figure 12.

CFD visualisation of airflow around (a) I-tromino and (b) L-tromino geometries illustrating the influence of geometric discontinuities on local flow structures.

The airflow navigates around an L-tromino, it generates a several number of discrete vortices perpendicular to the flow. These vortices create regions of flow stagnation, or dead spots as indicated with green colour (∼64 Pascal). The simulations reveal the formation of local recirculation zones and flow separation near the edges of L-tromino segments. Such geometric discontinuities may increase local velocity gradients near the surface, which can potentially enhance viscous interaction in oscillatory acoustic flow conditions.

In contrast, I-shaped structures, being more streamlined, allow for a more uniform and less turbulent wake, minimizing disruptions in airflow. Consequently, the sharp angles and pressure differences in L-shaped structures make them more prone to flow separation and recirculation zones compared to the relatively stable aerodynamics of I-shaped.

The total impedance of the tessellated polyform structure was estimated by considering the parallel acoustic impedance contribution of the individual perforated panel segments as shown in Equation below.

\frac{1}{Z_{3}} = \sum_{i = 1}^{3} (\frac{1}{Z_{M, i} + \frac{1}{\frac{1}{Z_{c a v i t y, i}} + \frac{1}{Z_{f i b r o u s, i}}}}) + \frac{1}{3} \sum_{i = 1}^{2} (\frac{1}{Z_{M, i} + \frac{1}{\frac{1}{Z_{c a v i t y, i}} + \frac{1}{Z_{f i b r o u s, i}}}})

(16)

therefore, the transfer matrix becomes as follows.

T_{3} = [\begin{array}{l} 1 & 0 \\ Z_{3} & 1 \end{array}]

(17)

the reflection coefficient is then calculated as:

R = \frac{Z_{i} - Z_{0}}{Z_{i} + Z_{0}}

(18)

where

Z_{0}

is the characteristic impedance of air. Finally, the sound absorption coefficient is computed as:

α = 1 - {| R |}^{2}

(19)

It was observed that the orifice diameter (O_max = 2.0 mm) < wavelength at 6.3 kHz (λ = 54 mm), validating the subwavelength and incompressible conditions. The viscous boundary-layer thickness varies from 0.22 mm (100 Hz) to 0.03 mm (6.3 kHz), comparable to orifice radius (r = O/2) to indicating that orifice impedance is governed primarily by viscous–thermal effects. The computed lattice spacing for perforation ratios (0.5–4.5%) and orifice diameters results in centre-to-centre pitches (p) of 4–25 mm and found to ≥ ∼4×O. Thereby, hole coupling effect is limited which promoted homogenised surface impedance model for square lattice under the influence of change in orifice diameter (Figure 10).

The Figure 13 presents a PP absorber made from jute composite materials and the left image shows the back of the absorber, revealing its tessellated framework with sections filled with jute fleece as a natural filler, while others are covered with a black composite layer. The right image displays the final tessellated polyform PP structure with a uniform perforated surface, where black dots represent the perforations essential for sound absorption.

Figure 13.

Photograph showing back of the absorber with filler jute fleece (left) and final tessellated polyform PP panel absorber (Right) with black dots.

These flow visualisations provide qualitative support for the enhanced viscous interaction expected near the geometric discontinuities of the tessellated configuration.

Experimental validation of tessellated perforated polyform structure

To evaluate whether the broadband absorption behaviour arises solely from the combination of multiple cavity depths or whether the tessellated polyform topology contributes additional acoustic effects, a controlled comparison configuration was considered. In this configuration, a flat multi-depth microperforated panel (MPP) arrangement was prepared using the same perforation parameters and cavity depths employed in the tessellated polyform structure. This comparison allows isolation of the influence of geometric topology from the well-known broadband effect of multiple resonant cavities.

The control structure consisted of a flat perforated panel fabricated from the same jute-reinforced composite material used in the tessellated structure. The perforation parameters were kept identical, including the orifice diameter (1 mm), perforation ratio, and panel thickness. The backing cavity was divided into multiple compartments with depths corresponding to those used in the tessellated polyform configuration (10, 20, 30, 40, 50, and 60 mm). In this way, both systems contained equivalent acoustic resonators, while the only difference between them was the geometric arrangement of the panel segments.

Figure 14 presents the comparative noise absorption coefficient (NAC) curves obtained for the flat multi-depth configuration and the tessellated polyform structure. Both configurations exhibit broadband absorption behaviour resulting from the superposition of multiple cavity resonances. However, the tessellated polyform structure demonstrates a smoother absorption profile and consistently higher absorption levels in the mid-to-high frequency region.

Figure 14.

Plots of estimated values of NAC of (i) tessellated PP estimated using modified Maa model (―), (ii) tessellated PP backed by jute fleece estimated using modified Maa model (…), actually measured NAC values for (iii) 60 mm thick breaker card jute fibre fleece (─ ─), (iv) tessellated PP (O), (v) tessellated PP filled with jute fibre (▬▬●▬▬), (vi) flat multi-depth MPP configuration ( $\times$ ) and (vii) NAC demand for recording room (▬▬).

A quantitative comparison between the two configurations indicates that the tessellated polyform structure provides a higher mean noise absorption coefficient across the investigated frequency band. The average NAC over the frequency range of 400–6300 Hz increased from 0.71 for the flat multi-depth configuration to 0.82 for the tessellated polyform structure, corresponding to an improvement of approximately 15.5% in broadband absorption performance.

Furthermore, the effective absorption bandwidth, defined as the frequency range where NAC ≥0.8, is noticeably wider for the tessellated configuration. This observation indicates that the tessellated arrangement enhances the overlap of individual resonance peaks, resulting in more uniform broadband absorption.

From an acoustic perspective, the improvement observed in the tessellated configuration can be attributed to the increased number of geometric discontinuities introduced by the interlocking L-tromino topology. These discontinuities create additional edge regions where local velocity gradients are intensified, thereby increasing viscous shear interaction between the oscillating air particles and the panel surface. As a result, the tessellated geometry promotes enhanced energy dissipation compared with a flat multi-depth configuration where the perforated surface remains continuous.

These results suggest that while broadband absorption is primarily achieved through the combination of multiple cavity depths, the tessellated polyform topology further enhances acoustic performance by introducing additional geometric discontinuities that promote local airflow redistribution and increased viscous interaction near panel edges.

Figure 14 compares the NAC of developed polyform structure across different frequencies (63-6300 Hz). The grey circles represent the measured NAC without jute fleece, showing relatively low absorption at lower frequencies, which gradually increases as the frequency rises. In contrast, the black dots (tessellation with jute fleece) exhibit significantly improved absorption, particularly in the mid-to-high-frequency range, where values reach as high as NAC = 0.9, indicating near-total sound absorption.

The dashed curve (theoretical NAC with jute fleece) closely aligns with the calculated NAC derived from RT 60, displaying a steep rise around 1000 Hz, confirming that the addition of jute fleece enhances acoustic absorption by increasing viscous losses (equation (16)), Transfer matrix T₂).

The demand of noise absorption level for a recording room (black straight line) was compared in relation to the calculated NAC of tessellated polyform structure tested in reverberation room with and without jute fleece at back cavity (Figure 14). The figure indicated that without jute fleece, the system struggles to meet the required absorption levels. However, with the inclusion of jute fleece, it surpasses the necessary absorption levels, making it highly effective for acoustic treatment applications.

Mechanical and fire response of jute cloth reinforced composite panel

Mechanical and fire response of the jute cloth reinforced composite panel as presented in Table 3 were found be effective for its application in making PPs and tessellated polyform structure as per the protocol lined for natural fibre composite in various non-structural applications.^41–43 The composite exhibited sufficient load-bearing capacity (tensile modulus, 6.1 GPa) and stiffness (flexural modulus, 8.1) for non-structural acoustic panels. Its Limiting Oxygen Index (LOI) of 28.1 indicates good flame resistance, enhancing its suitability for use in fire-sensitive environments. The competitive mechanical and fire response helped in integrated design and realisation of a tessellated polyform structure.

Table 3.

Mechanical and fire response of jute cloth reinforced composite panel.

Parameters	Values
Tensile strength (MPa)	103
Tensile modulus (GPa)	6.1
Flexural strength (MPa)	167
Flexural modulus (MPa)	8.1
LOI	28.1

Performance comparison of leading broadband perforated panel absorber configurations

The performance comparison of broadband perforated panel absorbers, as shown in.

Table 4, highlights significant improvements in uniform and high sound absorption across 250-2000 Hz. Notably, the N-MH MPP with interpolated straight tube achieves >0.9 absorption over 78.2% of the band, while multi-chamber and multilayer designs provide broad coverage with absorption generally above 0.8. Peak absorption values near 0.98 are reported for advanced coiled cavity and dual-gradient multilayer configurations.

Table 4.

Performance comparison of leading broadband perforated panel absorber configurations based on experimental and theoretical studies, highlighting absorption efficacy over the 250-2000 Hz frequency band.

Configuration	Performance over 250-2000 Hz band	Reference
N-MH MPP with interpolated straight tube	78.2% of frequency band achieves >0.9 absorption coefficient	44
Multi-chamber MPPA (MC-MPPA)	>0.8 absorption in dual ranges [397-1000] & [698-1895] Hz	45
MPPU with U-shaped cavities	69% average absorption in 300-1200 Hz, 89% in 600-1200 Hz octave	46
PCD-MPP (parallel coiled cavities)	Average 0.91 and maximum 0.98 absorption in 400-1600 Hz	47
Dual-gradient multilayer Ultra-MPP	>0.98 absorption coefficient over 2-20 kHz range	48
Multilayer MPP (broadband design)	Constant high absorption in 400-2000 Hz frequency range	49
Three-chamber optimized (8.6 octaves)	Continuous >0.8 absorption across 1591 Hz bandwidth (8.6 octaves)	50
Meta-MPP (ultrabroadband)	>100% improvement over traditional MPPs, 0.37-10 kHz range	51
Composite MPP + porous metal (low-freq)	62.96% (30 mm) & 73.59% (50 mm) average absorption in 100-1800 Hz	52
Jute-rUPR composite based tessellated perforated polyform panels with jute fibre filled back cavity	NAC approaching 0.9 across 400–6300 Hz	Current study

The current study’s jute-rUPR composite-based panels demonstrate noise absorption with >0.9 coefficients over the entire frequency band, reinforcing the potential of sustainable composites in acoustic materials. These advancements confirm the importance of optimizing geometries, materials, and cavity designs to enhance broadband sound attenuation effectively.

Conclusion

This study presents a systematic and innovative methodology for developing high-performance acoustic perforated panels. The perforated panels (PPs) were developed from jute cloth reinforced recycled PET composite panel of 3 mm thickness, followed by precision drilling to achieve perforation ratios of 0.5%, 1.5%, 3%, and 4.5%, with orifice diameters of 1 mm, 1.5 mm, and 2 mm. The acoustic performance of these perforated panels was subsequently optimised through impedance tube testing, using the transfer matrix method to evaluate their noise absorption coefficient (NAC).

The optimised PPs were then tessellated and assembled into a single, cohesive polyform structure supported by jute-reinforced composite frame, with cavity depths varying between 10 and 60 mm.

Fibre fraying at the rear of the PPs caused irregularities in the orifice geometry, which FEM analysis confirmed to increase viscous and inertial interaction within the structure. To address these effects, the transfer matrix of the classical Maa model was adapted to incorporate ‘the modification’ in orifice shape (transfer matrix T₁) as the model underestimate NAC. However, NAC curve indicated that the noise absorption reached 90% over a narrow frequency range, which is not effective for a suitable application. Further modification (transfer matrix T₂) was achieved by filling the cavity with jute fleece. This fleece improved viscous resistance and altered the internal air pathways, increasing the internal friction due to the presence of jute fleece, thereby resisting airflow and generating additional viscous dissipation and inertial effect. The combined effect changes the complexity of the orifice and cavity filling necessitated further adjustments of the transfer matrix.

CFD analysis provided qualitative insight into the influence of tessellated geometry on local airflow behaviour and highlighted the presence of flow separation near L-tromino edges. However, the acoustic performance of the developed polyform absorber was ultimately validated through experimental measurements.

The performance of the final polyform structure was validated through reverberation room testing, simulating real-world conditions. The results confirmed that a single product could reliably achieve a NAC ≥0.9 over the frequency range of 400 to 6300 Hz.

A controlled comparison with an equivalent flat multi-depth MPP configuration confirmed that although broadband absorption originates from the combination of multiple cavity depths, the tessellated polyform topology provides additional enhancement in absorption uniformity and broadband efficiency.

Overall, this integrated approach—combining natural fibre composites of competitive mechanical and fire response made in modern manufacturing techniques (SMC route), CFD-based optimisation and geometry driven acoustic modulation demonstrates the potential for producing sustainable, high-performance acoustic solutions suitable for low aerodynamic condition like recording studios, industrial enclosures, or private offices, architectural and industrial noise control applications.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by Department of Science and Technology & Bio-Technology, Government of West Bengal, India; Sanction No. 35(Sanc.)-ST/P/S&T/6G-5/2018, dated 3

ORCID iDs

Devarun Nath

Mallika Datta

Debasish Das

Data Availability Statement

The data that support the findings of this study may be available on request from the corresponding author.*

References

King

. Here, there, and everywhere: how the SDGs must include noise pollution in their development challenges. Environment 2022; 64: 17–32. https://doi.org/10.1080/00139157.2022.2046456

UNESCO Institute for Statistics . SDG 11 synthesis report: tracking progress towards inclusive. In: Safe, resilient and sustainable cities and human settlements, 2018. United Nations.

Basu

Datta

Sengupta

, et al. Jute felt for noise reduction: understanding effect of pore size distribution. J Nat Fibers 2022; 19: 6482–6496. https://doi.org/10.1080/15440478.2021.1921663

Fink

. A new definition of noise: noise is unwanted And/or harmful sound. Noise is the new ‘secondhand smoke. Proc Meet Acoust 2020; 39: 050002.

Datta

Das

Nath

. Textiles for noise control. In: Kumar

(ed). Textiles for Functional Applications. IntechOpen, 2021. Epub ahead of print 22. https://doi.org/10.5772/intechopen.99274

Surfaces

. Soundproofing vs sound absorbing – explaining the difference | ASI. Acoustical Surfaces 2024. https://www.acousticalsurfaces.com/blog/soundproofing/soundproofing-vs-sound-absorbing/ (accessed 18 May 2025).

Mago

Sunali

, et al. Sound insulation: key concepts and technologies. In: Garg

Gautam

Rab

, et al. (eds). Handbook of Vibroacoustics, Noise and Harshness. Singapore: Springer Nature Singapore, pp. 1–44.

Garg

Gautam

Devi

. Airborne sound absorption characteristics of acoustical materials for noise control applications. In: Garg

Gautam

Rab

, et al. (eds). Handbook of Vibroacoustics, Noise and Harshness. Singapore: Springer Nature, pp. 1–30.

Medved

. Building acoustics and noise control in buildings. Building Physics. Cham: Springer International Publishing, pp. 331–406.

10.

American National Standards Institute & Acoustical Society of America . American national standard acoustical performance criteria, design requirements, and guidelines for schools, part 1: permanent schools. Acoustical Society of America.

11.

Berg

Blair

Benson

. Classroom acoustics: the problem, impact, and solution. Lang Speech Hear Serv Sch 1996; 27: 16–20. https://doi.org/10.1044/0161-1461.2701.16

12.

Nober

. Auditory discrimination of learning disabled children in quiet and classroom noise. J Learn Disabil 1975; 8: 656–659. https://doi.org/10.1177/002221947500801010

13.

Smaldino

Crandell

. Classroom acoustics. Semin Hear 2004; 25: 115. https://doi.org/10.1055/s-2004-828662

14.

Bradley

Sato

Picard

. On the importance of early reflections for speech in rooms. J Acoust Soc Am 2003; 113: 3233–3244. https://doi.org/10.1121/1.1570439

15.

Rakerd

Hunter

Berardi

, et al. Assessing the acoustic characteristics of rooms: a tutorial with examples. Perspect ASHA Spec Interest Groups 2018; 3: 8–24. https://doi.org/10.1044/persp3.SIG19.8

16.

Nowicka

. The acoustical assessment of the commercial spaces and buildings. Appl Acoust 2020; 169: 107491. https://doi.org/10.1016/j.apacoust.2020.107491

17.

SheikhMozafari

. Enhancing sound absorption in micro-perforated panel and porous material composite in low frequencies: a numerical study using FEM. Sound Vib 2024; 58: 81–100. https://doi.org/10.32604/sv.2024.048897

18.

Ning

Ren

Zhao

. Acoustic properties of micro-perforated panel absorber having arbitrary cross-sectional perforations. Appl Acoust 2016; 111: 135–142. https://doi.org/10.1016/j.apacoust.2016.04.012

19.

Wang

Bennett

. Multi-chamber micro-perforated panel absorbers optimised for high amplitude broadband absorption using a two-point impedance method. J Sound Vib 2023; 547: 117527. https://doi.org/10.1016/j.jsv.2022.117527

20.

Lin

Yao

, et al. Low-frequency broadband sound absorption of the metastructure with extended tube resonators and porous materials. Appl Acoust 2024; 217: 109827. https://doi.org/10.1016/j.apacoust.2023.109827

21.

Cobo

. Modelling of microperforated panel absorbers with circular and slit hole geometries. Acoustics 2021; 3: 665–678. https://doi.org/10.3390/acoustics3040042

22.

Carbajo

Poveda-Martínez

Godinho

, et al. Tunable perforated panel sound absorbers for variable acoustics room design. Appl Sci 2024; 14: 2094. https://doi.org/10.3390/app14052094

23.

Mei

Yang

Ding

, et al. Ultra-broadband sound absorption via a parallel composite structure consisting of perforated panel resonators with tube bundles and porous material. Appl Acoust 2024; 222: 110071. https://doi.org/10.1016/j.apacoust.2024.110071

24.

Afsharfard

Jafari

Rad

, et al. Modifying vibratory behavior of the car seat to decrease the neck injury. J Vib Eng Technol 2023; 11: 1115–1126. https://doi.org/10.1007/s42417-022-00627-4

25.

Afsharfard

Farshidianfar

. An efficient method to solve the strongly coupled nonlinear differential equations of impact dampers. Arch Appl Mech 2012; 82: 977–984. https://doi.org/10.1007/s00419-011-0605-1

26.

Jafari

Afsharfard

. Metamaterial Bi-stable vibration absorbers for railway tracks: experimental study of flexural wave control. Epub ahead of print 23 2025. https://doi.org/10.48550/arXiv.2506.18801

27.

Nath

Das

Chattopadhyay

, et al. Using polyethylene terephthalate bottle waste as a viable precursor for the synthesis of unsaturated polyester resin in fabrication of jute fibre reinforced composites. Polym Polym Compos 2024; 32: 09673911241233171. https://doi.org/10.1177/09673911241233171

28.

Datta

Basu

Nath

, et al. Non-destructive reverberant testing of natural fibrous samples in a diffused acoustic field environment. Textil Res J 2024; 94: 1724–1736. https://doi.org/10.1177/00405175241235396

29.

Helmholtz

Hvon

. On the sensations of tone as a physiological basis for the theory of music. Longmans, Green 1885.

30.

Phong

Papamoschou

. Acoustic transmission loss of perforated plates. In: 18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference). American Institute of Aeronautics and Astronautics, 2012, pp. 2012–2071. Epub ahead of print. https://doi.org/10.2514/6

31.

Randeberg

. Perforated panel absorbers with viscous energy dissipation enhanced by orifice design. Norwegian University of Science and Technology, 2000. Doctoral Thesis: https://ntnuopen.ntnu.no/ntnu-xmlui/bitstream/handle/11250/249798/125365_FULLTEXT01.pdf?sequence/1/text/The/20main/20part/20of/20thetwo/20plates/20to/20be/20varied

32.

Maa

. Theory and design of microperforated panel sound-absorbing constructions. Sci China Press Co Ltd 1975; 18: 55–71.

33.

Zwikker

Cand KCW

. Sound absorbing materials. Elsevier Publishing Company, 1949.

34.

Maa

D-Y

. Potential of microperforated panel absorber. J Acoust Soc Am 1998; 104: 2861–2866. https://doi.org/10.1121/1.423870

35.

Mathur

. Acoustic metamaterial architectured composite layers, methods of manufacturing the same, and methods for noise control using the same. US9390702B2. https://patents.google.com/patent/US9390702B2/en (2016), (accessed 6 May 2025).

36.

Zhao

Fan

. Enhancing low frequency sound absorption of micro-perforated panel absorbers by using mechanical impedance plates. Appl Acoust 2015; 88: 123–128. https://doi.org/10.1016/j.apacoust.2014.08.015

37.

Bravo

Maury

. Sound attenuation and absorption by micro-perforated panels backed by anisotropic fibrous materials: theoretical and experimental study. J Sound Vib 2018; 425: 189–207. https://doi.org/10.1016/j.jsv.2018.04.006

38.

Song

Bolton

. A transfer-matrix approach for estimating the characteristic impedance and wave numbers of limp and rigid porous materials. J Acoust Soc Am 2000; 107: 1131–1152. https://doi.org/10.1121/1.428404

39.

Yang

Mei

Yang

, et al. Membrane-type acoustic metamaterial with negative dynamic mass. Phys Rev Lett 2008; 101: 204301. https://doi.org/10.1103/PhysRevLett.101.204301

40.

Shaid Sujon

Islam

Nadimpalli

. Damping and sound absorption properties of polymer matrix composites: a review. Polym Test 2021; 104: 107388. https://doi.org/10.1016/j.polymertesting.2021.107388

41.

Ichim

Muresan

Codau

. Natural-fiber-reinforced polymer composites for furniture applications. Polymers 2024; 16: 3113. https://doi.org/10.3390/polym16223113

42.

Pickering

Efendy

MGA

. A review of recent developments in natural fibre composites and their mechanical performance. Compos Part Appl Sci Manuf 2016; 83: 98–112. https://doi.org/10.1016/j.compositesa.2015.08.038

43.

Addcomposites . What are natural fiber composites? Basics applications and future potentials. https://www.addcomposites.com/post/what-are-natural-fiber-composites-basics-applications-and-future-potentials (2024), (accessed 19 May 2025).

44.

Mao

, et al. Optimization design and analysis of the broadband acoustic absorber of the microperforated panel with an interpolated straight tube. J Vib Control 2024; 30: 5110–5121. https://doi.org/10.1177/10775463231217780

45.

Wang

Bennett

. Ultra-broadband sound absorption in a compact multi-chamber micro-perforated panel absorber with varying depths. AIP Adv 2024; 14: 015009. https://doi.org/10.1063/5.0187328

46.

Lechner

Angle

Palczewski

, et al. Oxide dissolution and oxygen diffusion scenarios in niobium and implications on the bean–livingston barrier in superconducting cavities. J Appl Phys 2024; 135: 133902. https://doi.org/10.1063/5.0191234

47.

Min

Lou

Zhao

. Optimization of parallel coiled cavities of different depths in microperforated panel sound absorbers. Sci Rep 2025; 15: 1401. https://doi.org/10.1038/s41598-025-85171-3

48.

Qian

Zhang

. Dual-gradient multilayer ultra-microperforated panel composite for ultra-broadband and quasi-perfect sound absorption. Appl Phys Lett 2025; 126: 131702. https://doi.org/10.1063/5.0257704

49.

Yang

Bai

Shen

, et al. Optimal design and experimental validation of sound absorbing multilayer microperforated panel with constraint conditions. Appl Acoust 2019; 146: 334–344. https://doi.org/10.1016/j.apacoust.2018.11.032

50.

Wang

Liang

Mei

. Optimization design of a micro-perforated panel absorber with 8.6 octave bands. ArXiv. 2023; 2305.18298 [eess.AS]. https://doi.org/10.48550/arXiv.2305.18298

51.

Shi

Luo

Liu

, et al. Metamaterial sound absorbers based on microperforated panels: an approach toward enhanced flexibility and near-limit broadband performance. ArXiv . 2025; 2501.07012 [physics.app-ph]. https://doi.org/10.48550/arXiv.2501.07012

52.

Shen

Bai

Yang

, et al. Low frequency sound absorption by optimal combination structure of porous metal and microperforated panel. Appl Sci 2019; 9: 1507. https://doi.org/10.3390/app9071507