Multifunctional acoustic and mechanical metamaterials prepared from continuous CFRP composites

Abstract

The imperative advance towards achieving “carbon neutrality” necessitates the development of porous structures possessing dual acoustic and mechanical properties in order to mitigate energy consumption. Nevertheless, enhancing various functionalities often leads to an increase in the structural weight, which limits the feasibility of using such structures in weight-sensitive applications. In accordance with the outlined specifications, a novel structural design incorporating carbon fiber reinforced polymer (CFRP) composites alongside mechanical and acoustic metamaterials has been introduced for the first time. This innovative construction exhibits a lightweight composition with excellent mechanical and acoustic characteristics. Experimental findings demonstrate that with meticulous planning and fabrication, CFRP composite structures can achieve a balance of lightweight construction, high strength, exceptional energy absorption, and remarkable resilience. By introducing membrane and reasonable cavity design, the structure can produce low broadband noise reduction performance by a local resonance effect and impedance matching mechanism of metamaterials. The structural sound insulation capability breaks traditional mass law, resulting in an exceptionally broadband sound insulation peak (bandwidth of nearly 1000 Hz). Furthermore, the sound absorption characteristic of the structure surpasses that of the melamine sponge at frequencies below 300 Hz, demonstrating superior low-frequency sound absorption properties. The proposed structure provides new approaches for the design of multifunctional lightweight superstructures.

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New concepts

The simultaneous optimization of lightweight, high load-bearing capacity, robustness, and low-frequency noise reduction in acoustic-mechanical metamaterials presents a challenging multi-physics problem. Achieving this requires a comprehensive understanding of acoustic and mechanical metamaterial driving mechanisms, design principles, and base material properties. This study proposes a novel design approach for acoustic-mechanical metamaterials, enhancing structural robustness while maintaining light weight, high strength, and effective low-frequency noise reduction through material improvements. By integrating 2D/3D mechanical metamaterials with labyrinth-type cavity, membrane-type acoustic metamaterial, local resonance is achieved to enhance sound insulation and absorption performance. Experimental results demonstrate an exceptional sound insulation capability with a wide peak bandwidth (approximately 1000 Hz) that defies traditional mass law. Additionally, the metamaterial exhibits impressive mechanical response characteristics, with a deformation recovery rate of up to 98% and the ability to withstand external loads nearly 800 times its own weight. These findings present innovative avenues for the development of multifunctional metamaterial designs.

1. Introduction

Acoustic metamaterials are gradually being used in vibration and noise control due to their extraordinary properties that surpass those of natural materials. Common acoustic metamaterials include membrane-type acoustic metamaterials,¹ plate-type acoustic metamaterials,² and Helmholtz resonators.³ These structures absorb or reflect noise by the impedance matching method⁴ and dissipate sound energy by the local resonance mechanism.⁵ Based on this, it is possible to achieve low broadband sound absorption or insulation through structural design. Concerning membrane-type acoustic metamaterials (MAMs), their sound absorption and insulation capabilities are influenced by membrane vibration, which stems mainly from the action of membrane tension.⁶ This parameter is notoriously challenging to control and prone to diminishing the desired effects due to stress relaxation. To harness the noise-reducing benefits of MAMs while overcoming their inherent mechanical limitations, scholars have integrated plates, Helmholtz cavities, and other components with membranes to develop composite sandwich structures⁷ for bearing significant loads.

For these novel sandwich structures with integrated multifunctions, combining different components gives them excellent designability and their acoustic performance can also be enhanced in several ways. The first way is to design the membrane-cavity coupling structure by increasing the number of membranes to improve the amplitude of sound transmission loss (STL).^8,9 Meanwhile, this form can also control the sound isolation frequency band by adding gas pressure.¹⁰ The second way is to combine porous materials with plate-type acoustic metamaterials,¹¹ where the composite structure can generate multiple STL peaks at low frequencies and improve low-frequency sound isolation performance. The third way is to combine perforated plates, MAMs, and cavities to form a honeycomb structure¹² that can provide both excellent sound insulation and absorption within 1000 Hz. The sound absorption performance of sandwich structures can also be enhanced by Helmholtz resonators. According to the impedance matching mechanism, the sound absorption performance of the resonant cavity is generated by the thermal effect caused by the frictional resistance between the hole and the gas,^13,14 as well as the gas resonance effect inside the hole and the cavity. Meanwhile, the sound absorption frequency band of the resonant cavity will be affected by the aperture, cavity volume, temperature¹⁵ and other factors. By strategically combining Helmholtz resonators with varying apertures and cavity volumes, it is possible to achieve a wide range of absorption peaks across different frequencies.^16–18 However, due to the effect of the volume constraint of the Helmholtz cavity on the low-frequency sound absorption, the researchers have subjected the cavity to a curling process, thereby augmenting the cavity volume while maintaining consistent thickness. The innovative folded cavity design not only increases the sound propagation path but also amplifies thermal loss caused by gas-cavity wall friction, thereby augmenting sound energy dissipation.¹⁹ This structural modification facilitates the absorption band frequencies towards lower ranges. Meanwhile, the high-frequency sound absorption coefficient (SAC) can be enhanced by incorporating porous materials into the structure.^20–22 Similar to the behavior of sound energy dissipation by gas resonance in a cavity, the sound-absorbing effect is also produced when the frequency of the sound wave is close to the natural frequency of the local resonance type metamaterial.^1,23 In structural design, to break through the independent relationship between sound absorption and insulation, a variety of resonance and anti-resonance forms must be considered to accomplish noise reduction design.^24,25

Prior research predominantly examined the acoustic characteristics of sandwich structures to elucidate the mechanisms contributing to their exceptional sound absorption and insulation abilities, neglecting a comprehensive investigation and enhancement of their mechanical properties.^26,27 Therefore, it is particularly important to weigh the acoustic and mechanical advantages of structures to create multi-functional metamaterials. The negative Poisson's ratio structures have been widely studied by researchers owing to their exceptional deformation and energy dissipation properties.²⁸ However, the good auxetic properties lead to a loss of strength and stiffness, limiting the application of the structures in engineering. Therefore, in order to increase the bearing capacity without sacrificing the structure lightweight, fiber reinforced polymer (FRP) composites are used as the base material to prepare metamaterials. There are currently three main ways to prepare metamaterial structures using FRP composites. The first is the most popular, 3D printing technology. However, due to the relatively small amount of fibers in the matrix, the performance of the structure is greatly reduced.²⁹ The second common way is to use computer numerical control (CNC) milling machine to cut laminates, and assemble them into complex metamaterials through interlocking assembly.^30,31 However, due to the inconsistency between the fiber direction and the deformation mode of the structure, the energy absorption characteristics of the structure are significantly reduced. The third way is to use the corrugated plates to make a metamaterial structure via stacking and bonding. In this method, the design of the structure and its deformation mode are carefully considered, making the direction of continuous fibers consistent with the structure deformation direction.^32,33 Although this method can maintain good auxetic properties of the structure even under large deformation, the catastrophic stress drop caused by structural failure is still disastrous. And because it is necessary to consider multiple situations comprehensively, only a limited number of simple structures can be prepared using this method.^33–36 Therefore, this research focuses on the use of prepreg with high fiber content, comprehensive consideration of fiber direction, structural design and preparation process. The goal is to propose a metamaterial with light weight, high strength, high energy absorption, no cliff-like stress reduction, and good sound absorption and sound insulation properties.

This work involves material modification³⁷ at a microscale level or the adoption of conventional honeycomb architectures at a macroscale level to provide structural reinforcement, coupled with the integration of foam within the framework to optimize acoustic functionality.³⁸ Meanwhile, several investigations have employed cavity and labyrinth structures with inherent load-bearing capacities. Based on this, optimization of material properties and structural designs for sound and energy absorption capabilities has been performed.³⁹ In consideration of the aforementioned conditions, the cavity may be substituted with a lattice structure to achieve a diminished weight and enhance the acoustic and mechanical equilibrium.^16,40–42 Supported by the theoretical foundations and design experience of acoustic metamaterials and negative Poisson's ratio structures, this paper focuses on obtaining an acoustic-mechanical multifunctional structure with both load-carrying and noise-reducing capabilities through material and structural redesign.

2. Results and discussion

2.1. Coupling design of acoustic-mechanical metamaterials

The CFRP composite-based metamaterials exhibit favorable mechanical characteristics such as lightweight, high specific strength, and high specific stiffness, while also enabling large deformations.³² Despite these advantages, the abrupt stress drop observed during fiber failure on the stress–strain curve significantly diminishes the energy absorption capacity of the structure.⁴³ To address this issue, an innovative petal-like structural design by integrating multi-stage deformation capabilities with composite materials is proposed in this study as shown in Fig. 1. The design parameters of the petal-like structure are delineated in Fig. 2(a). In light of the preparation process for composite materials, a platform segment with a length of l_h has been devised to enhance the bonding area of the structure. In the compression process, the presence of small chamfers often leads to stress concentration and subsequent initial fracture. To avoid this problem, a semicircular cross-section with a radius of R has been implemented. This design aims to enable the components to sustain the load post fiber failure at the corner, consequently mitigating stress fluctuations and endowing the structure with favorable energy absorption properties. It is worth noting that in order to enhance acoustic designability, 2D/3D gradient petal-like structures constructed with three layers by adjusting the angle parameter are adopted, and their parameters are shown in Table 1.

Fig. 1 Design of multi-functional acoustic and mechanical metamaterials. (a) Design based on 2D mechanical metamaterials: (i) labyrinth-type resonator;²⁴ (ii) gradient design and punching position; (iii) design of channels and cavities; (iv) physical display. (b) Design based on 3D mechanical metamaterials: (i) membrane-type resonator combined with vibrator;²⁷ (ii) combined with gradient sandwich structure with good mechanical properties; (iii) combined with 3D gradient petal-like structure; (iv) physical display.

Fig. 2 Manufacturing process overview. (a) Preparation process and configuration parameters of the composite petal-like structure. (b) Preparation process and cutting configuration of the carbon fiber plates. (c) Assembly of the 2D acoustic-mechanical metamaterials, the design of the holes and the location of the membranes. (d) Stacking process of 3D acoustic-mechanical metamaterials, assembly aids, hole design and membrane location.

Table 1 Values of geometric parameters used

t (mm)	l 1 (mm)	l 2 (mm)	l 3 (mm)	l h (mm)	R (mm)	r (mm)	b 1 (mm)	b 2 (mm)	θ (°)
0.5	6	8	29	3	2	0.55	21	3	30, 45 or 60

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The labyrinth-type resonator²⁴ and membrane-type resonator bound to vibrators²⁷ are combined with the designed 2D/3D composite gradient petal-like structures to improve mechanical properties, along with the cavity size and the length ratio of the sound channel influenced by the changes of the angle parameter for each layer. The utilization of a space-coiling strategy in the design of the labyrinth-type resonator serves to effectively dissipate sound energy through viscous effects. Moreover, the integration of the labyrinth-type resonator with a gradient design of a 2D composite petal-like structure allows for manipulation of the length of the coiled channel. Given the heightened sensitivity of composite materials to defects, it becomes imperative to strike a balance between mechanical and acoustic properties during the drilling of the structure and design of the coiled channel. Previous research conducted by some researchers has systematically investigated composite auxetic structures with defects, revealing that defects located in the middle position of 2D structures do not significantly impact the mechanical and auxetic properties of the structure.²⁸ Consequently, the decision to place the hole in the middle position of the structure was made. To visually highlight the position of the punch, some red cylinders were embedded at the corresponding location, as depicted in Fig. 1(a)(ii). Fig. 1(a)(iii) showcases the design of six cavities and four sound channels for optimal acoustic performance. In the development of the membrane-type resonator, conventional methods of adding vibrators to the membrane are eschewed in favor of utilizing the contact interface of a 3D structure to facilitate multiple vibrations, thereby enhancing sound energy dissipation. This innovative approach seeks to achieve the integration of acoustic-mechanical metamaterials by strategically merging the gradient design of the sandwich structure and membrane-type metamaterials from a mechanical perspective. At the end, the structure with superior acoustic and mechanical characteristics can be achieved.

2.2. Preparation process

The fabrication of 2D/3D novel petal-like structures involves the fabrication of both continuous CFRP petal-like plates and carbon fiber laminate plates. The CFRP petal-like plates were manufactured utilizing a hot molding process as depicted in Fig. 2(a), with the same mechanical properties of the composite laminates as in previous studies by Li et al.²⁹ Following cleaning of the mold with alcohol and application of a release agent, two layers of single layer 0.25 mm woven carbon fiber/epoxy prepreg (T300/epoxy composite, High Gain Industrial Ltd, Hong Kong) were placed on the mold. Subsequently, the mold was subjected to heating in an autoclave at 80 °C for 30 minutes, then further heated to 130 °C for 90 minutes before final curing. Upon demolding, a computer numerical control (CNC) milling machine is employed to cut the fabricated sheet into petal-like strips with the required specific dimensions. The cut petal-like strips are then joined into a 2D or 3D auxetic structure through the application of a two-component adhesive (2216 A and B, Minnesota Mining and Manufacturing, US) and assembly aids. Carbon fiber laminates with a combined thickness of 0.5 mm are produced via the process illustrated in Fig. 2(b), employing identical materials as for the petal-like sheets. To produce the acoustic cavities and carbon fiber plates mentioned in Fig. 1, they are cut into different shapes (the key manufacturing steps are shown in Part S1, ESI†). Finally, petal-like plates, carbon fiber plates of different shapes, membranes and external frames prepared by 3D printing (Part S2, ESI†) are assembled and bonded, as shown in Fig. 2(c) and (d).

2.3. Resilience and deformation mechanism

This section investigates the mechanical behavior and deformation mechanism of 2D/3D composite petal-like structures through cyclic loading experiments. In order to ensure the reproducibility of the preparation method, three samples of each structural configuration were fabricated for cyclic loading assessments. Fig. 3(a) and (b) present stress–strain curves depicting the mechanical behavior of two distinct structures throughout five consecutive cyclic loading processes, alongside the experimental deformation modes observed specifically during the initial loading cycle. Both structures displayed consistent reproducibility in general. The relative densities of the 2D and 3D petal-like structures are 0.11 and 7.07 × 10⁻⁴, respectively, emphasizing the lightweight characteristics of both structures. The study reveals that the structures exhibit good energy absorption capabilities without significant stress reduction during the compression process. Notably, the two structures demonstrate energy absorption properties of 24.69 J and 4.03 J during the first compression cycle for 2D and 3D structures, with specific energy absorption (SEA) values of 0.35 J g⁻¹ and 0.14 J g⁻¹, respectively. Furthermore, the higher energy absorption capacity of the structures is attributed to the utilization of CFRP composites. While the initial maximum compressive strength of the structure shows a decrease beginning with the second cycle, subsequent cycles exhibit a moderate decline in compressive strength. To further elucidate the issue and offer a reference for future research endeavors, a thorough examination of the deformation and failure mechanisms occurring during the initial loading cycle was conducted using finite element analysis (Part S3, ESI†).

Fig. 3 The mechanical properties of 2D/3D CFRP composite petal-like structures. (a) Cyclic loading curve and failure process of the 2D structure. (b) Cyclic loading curve and failure process of the 3D structure. (c) Poisson's ratio and modulus. (d) Picture showing a 2D petal-like structure that can support 800 times its own weight and remain intact after loading. (e) Comparison of 2D/3D metamaterials with other lattice metamaterials: (i) the relationship between recoverability and compressive strength; (ii) the relationship between compressive strength and density; (iii) the relationship between energy absorption characteristics and density.

The comparisons of modulus and Poisson ratio of the two structures under small deformation are illustrated in Fig. 3(c). The error bar illustrates the effect of repeated experiments on structural properties. It can be observed that the influence of 2D and 3D configuration changes on Poisson's ratio is negligible during the first cyclic loading. Specifically, in the 2D structure, the deformation of the middle layer cells was constrained by the presence of a carbon fiber plate. On the other hand, in 3D structures, the intermediate layer cells displayed reduced auxetic characteristics due to the presence of membranes on both upper and lower layers, impacting their deformation capabilities. Interestingly, during the subsequent cyclic loading process, the auxetic properties of the structure are not constant. Specifically, the deformability of the unit-cell with an angle parameter of 60 degrees saw a significant decrease, mainly due to structural failure during the compression process. Additionally, for the 2D-45 structure, the deformation of the structure during compression led to the failure of the carbon fiber laminate, weakening the inhibitory effect of deformation. Subsequently, an anomalous increase in the auxetic properties of the 2D-45 structure was observed during the cyclic loading process. In addition to the structure's Poisson's ratio, the equivalent compression modulus of the structure under cyclic loading was also studied. Although the failure of the unit-cell led to a decrease in the overall compression modulus of the structure, after the fifth cycle of compression, the maximum compression modulus of the 2D and 3D structures still approached 0.4 MPa and 0.1 MPa respectively. Considering that out-of-plane compression is the primary loading mode for 2D structures in practical applications, the equivalent compression modulus under such loading conditions was also determined. The results indicated that the 3D structure exhibited the lowest equivalent compression modulus at 0.35 MPa, whereas the 2D structure demonstrated the highest out-of-plane compressive modulus at 7.08 MPa, approximately two times greater than the in-plane compression modulus of 3.30 MPa. In light of the correlation between the mass and load-bearing capacity of the structure, it is evident that the 2D framework exhibits remarkable resilience, supporting a load approximately 800 times its own mass (55 kg/0.07 kg) with minimal deformation, as illustrated in Fig. 3(d).

In addition to the well-documented auxetic properties, the structural behavior also exhibits a buckling phenomenon under compression. The buckling of the 2D carbon fiber flat plate is primarily attributed to its large slenderness ratio. This buckling of the carbon fiber plate further induces buckling in the overall 2D composite petal-like structure. With the escalation of compression displacement, the carbon fiber plate utilized for partitioning the cavity experiences initial failure in response to significant deformation. However, because the petal-like structure prepared with continuous CFRP composite did not fail, the structure still had a good load bearing capacity, and there was no obvious stress reduction process on the stress–strain curve. Subsequent to the increasing compression displacement, the inward shrinking of the bending-dominated petal-like structure persisted, resulting in pronounced stress concentration at the small corner, leading to initial failure at this site. It is noted that the auxetic characteristics were influenced by the angle parameter, with the primary failure site identified as the 60° cell layer under 0.3 compressive strain. Furthermore, as the number of cyclic loading cycles increased, there was a corresponding rise in the instances of failure at small corners, thereby limiting the load-bearing capacity of the petal-like structures and consequently reducing both strength and energy absorption performance during subsequent cyclic loading events. In the analysis of the 3D composite petal-like structure, the compression process reveals phenomena such as debonding between carbon fiber and film components, fiber failure at the small corner, and fluctuations in the stress–strain curve. Additionally, as compression displacement advances, buckling behavior becomes evident. Comparable to 2D structures, prolonged loading times lead to increased instances of rod failure, impacting overall structural strength and energy absorption capacity.

Finally, in order to further demonstrate the mechanical advantages of the proposed structure in this study, Fig. 3(e) uses three Ashby plots to illustrate the three most important sets of mechanical properties of the metamaterial: the relationship between strength and resilience (whether the structure has high robustness); the relationship between density and strength (whether it is lightweight and has high strength); and the relationship between density and energy absorption (whether the structure has excellent energy absorption characteristics). The CFRP petal-like metamaterials are compared to some previously reported lattice metamaterials.^44–52 Contrary to traditional views, the research results challenge the view that lightweight, material strength, high-energy-absorbing structures, and recoverability are incompatible, as these structures exhibit over 90% recoverability, lightweight, high strength, and excellent energy absorption characteristics in multiple loading cycles without a relaxation period. In addition, by manipulating dimensions (2D/3D), the petal-shaped CFRP structure has the design capability for a robust strength of 0.2–3 MPa while maintaining sufficient elasticity. It is posited that augmenting the number of layers and refining the layer optimization process will yield further enhancements in strength and broaden the scope of potential applications for this structure.

2.4. Sound absorption and insulation performance

The sound insulation and absorption capabilities of 3D and 2D multifunctional structures are achieved through the local resonance mechanism and the creation of sound channels, respectively. The structures are analyzed and optimized by combining theory, simulation, and experiment (theory and simulation can be found in Part S4 and S5, ESI†). The study firstly focuses on the 3D structure as the subject of analysis and establishes the numerical model as shown in Fig. 4(a). Subsequently, a comparison of the STL is made between the proposed structure and an equivalent plate with identical surface density following the mass law as shown in Fig. 4(b). Using a petal-like core layer in 3D multifunctional structures, instead of an additional block, synergizes the membrane to undergo multiple anti-resonances, generating a broadband STL peak within 560–1510 Hz. This novel approach showcases the potential for enhanced performance in acoustic metamaterials by manipulating structural components. It has been found that 3D structures exhibit superior sound isolation capabilities in the very low-frequency band below 125 Hz and in a wide frequency band from 745–1525 Hz when compared to plates adhering to the mass law.

Fig. 4 The sound absorption and insulation properties of the 2D/3D all CFRP composite petal-like structures. (a) Numerical modeling of the 3D structure. (b) Comparison of sound insulation advantages and structural vibration deformation nephograms. (Comparison with a plate of the same surface density.) The STL of the equivalent structure based on the mass law is given by: . Here, ρ_m and D are the density and thickness of the equivalent plate, respectively. (c) Dynamic parameter analysis and the vibration deformation nephogram of the membrane. (d) Numerical modeling of the 2D structure. (e) Relationship between SAC and acoustic resistance and reactance. (f) Energy density dissipation nephogram and sound pressure and velocity distribution nephogram. In addition, the sound energy dissipation nephogram corresponding to acoustic resistance and the sound pressure–velocity distribution nephogram corresponding to acoustic reactance are shown at specific frequency positions.

In order to provide a more in-depth examination of the sound insulation benefits associated with the 3D multifunctional structure, this study employs a combined analysis of the vibrational deformations exhibited by the metamaterial and the dynamic characteristics of the membranes. As illustrated in Fig. 4(b), six specific peak frequencies of the STL curve are chosen for analysis, and their vibrational deformations have been observed. A is located in the structural stiffness control section, and the sound insulation effect of 3D structures is mainly affected by the stiffness. The comprehensive analysis indicates that the overall structure exhibits a downward vibration pattern, with the deformation of the petal-like core layer increasing layer by layer. Owing to the high stiffness of the 30 degree core layer in direct contact with the gas, the impedance mismatch causes a portion of the sound wave to be reflected. The structural displacement exhibits minimal magnitude in its entirety, and the rigidity of the metamaterial is expressed, leading to exhibition of sound isolation properties at this specific frequency. The central region of the upper plate at location B exhibits a noticeable downward deflection, counteracted by an upward displacement in the first-layer membrane, leading to anti-resonant behavior and contraction of the 30 degree core layer. The upper side demonstrates superior structural stiffness, resulting in a portion of the sound wave being reflected and the transmission of the remaining portion to the 45 degree core layer via the hole position of the membrane. Since the second-layer membrane is intact, the petal-like core layer and the membrane produce a synergistic vibration phenomenon under the action of sound waves. Nevertheless, the displacement of membranes in opposite directions effectively nullifies each other, leading to a diminished out-of-plane average displacement of the membrane, which is an order of magnitude smaller than the displacement of the 30 degree core layer. At this point, the flexible membrane also behaves as an approximate rigidity, reflecting a large number of radiated sound waves, thereby yielding a construct endowed with superior sound attenuation properties within this specific frequency range.

The structural top and bottom plates at location C exhibit reduced displacement, contrasting with the higher displacement observed in the core layers in contact with the two-layer membranes. The core layer in contact with the two membranes essentially pulls the membrane to either side, causing the core layer to interact with the membrane. The out-of-plane average displacement of the flexible membrane is also small relative to the rigid core layer, resulting in an overall rigid structure that is difficult to be excited by sound waves, and the radiated sound waves are heavily reflected. The D position is similar to C in that the plate remains essentially rigid, and the membrane can also be considered rigid under the action of the petal-like core layer in contact with it. Unlike position C, the petal-like core layer no longer exhibits overall out-of-plane stretching, and the torsion phenomenon occurs in each core layer. Both membranes move partially upward and partially downward reflecting the effect of multiple petal-like metamaterials interacting with the membrane, which can broaden the sound insulation bandwidth. Regarding position E, analogous to position B, the tensile expansion exhibited by the 30 degree core layer causes the plate and membrane in contact with it to vibrate to either side. Concurrently, a downward movement of the plate on both sides of the metamaterial is observed, accompanied by an upward displacement of the first-layer membrane, resulting in an anti-resonance phenomenon between the membrane and plate. The superior auxetic property of the metamaterial results in a high rigidity in its upper portion, leading to significant reflection of incident sound waves. Furthermore, the second-layer membrane and the bottom plate impede the transmission of sound waves to the lower side. At location F, the structure exhibits minor out-of-plane average displacements of the top plate, bottom plate, and both membranes due to the act of the petal-like core layer. This phenomenon makes the sound waves difficult to pass through the structure, resulting in the generation of the STL peak.

After analyzing the sound insulation phenomenon of the structure from the perspective of vibration deformation, it is observed that certain minor deformations may not be visually expressed. Based on this, the reason for the excellent noise reduction property of the metamaterial can be synergistically analyzed through the dynamic mass and dynamic stiffness of the membrane. The dynamic parameter curves of each membrane are acquired separately, allowing for the elucidation of the sound insulation mechanism. This is accomplished by analyzing the extreme value jump phenomenon and zero-value transition phenomenon exhibited in the curves.

Several extreme-value jump points and zero-value transition points are picked up in the curves for detailed analysis, and the curves and displacement nephograms are shown in Fig. 4(c). Modes A, C, D, F, and G are located at zero-valued transition points, while the remaining modes are positioned at extreme jump value points. Using modes A and F as illustrative cases, the petal-like core layer induces a layer-by-layer torsional effect at 165 Hz. Moreover, the core layer facilitates the transmission of vibrations to the connected membrane, resulting in non-uniform downward deformation. The equivalent mass and stiffness of the membrane at this frequency are close to zero. The longitudinal displacement of the structure demonstrates a relative maximum, resulting in a complete loss of rigidity. This phenomenon renders the structure vulnerable to sound excitation, allowing for the direct transmission of sound radiation through the metamaterial. As a consequence, the structural sound isolation value approaches zero due to the resonance effect. In Modes C and D, the upper membrane experiences upward vibrational deformation due to the pulling force exerted by the 30 degree petal-like core layer. Despite being influenced by a downward pulling force from the 45 degree core layer, the out-of-plane average displacement remains consistently upward and greater in magnitude. Currently, the equivalent mass and stiffness of the upper membrane is approximately 0, making it susceptible to excitation by sound waves and resonance with it. This results in the transmission of sound through the upper membrane to the underlying 45 degree core layer. At the same frequencies, the lower membrane demonstrates certain equivalent mass and stiffness properties that facilitate the partial isolation of residual sound waves on the lower aspect of the structure. Nevertheless, the small magnitude of the equivalent parameters of the lower membrane leads to STL dips at these frequencies within the metamaterial. At the frequency position of Mode G, the upper membrane produces an upward vibrational deformation with certain equivalent mass and stiffness properties. This deformation allows sound waves to pass through holes in the membrane and enter the 45 degree core layer. Simultaneously, the lower membrane experiences a significant out-of-plane displacement, facilitating the easy penetration of sound radiation to the lower side of the structure, leading to the STL dip.

In opposition to the zero-value transition phenomenon, membranes display a significant increase in equivalent mass and stiffness at extreme value jump points, rendering the structure resistant to excitation by sound waves, such as Modes E, H, and I. At the three specified frequency points, the out-of-plane average displacement of the upper or lower membrane is negligible, allowing the structure to be considered quasi-rigid in its reflection of sound waves, thereby contributing to the superior sound isolation properties exhibited by metamaterials. It is worth noting that the extreme value jump phenomenon of the upper membrane only partially addresses the problem of sound transmission. Furthermore, even if the upper membrane exhibits rigidity, sound waves are still able to propagate to the lower side of the structure through the hole position of the membrane. Similar to Mode B, if the upper side structure exhibits a significant stiffness and the lower side membrane fails to effectively reflect sound waves, the resulting structure also does not achieve optimal levels of sound insulation.

In the research of the 2D petal-like structure, the cavities are interconnected through the excavation of holes along the carbon fiber's sidewalls. This modification augments the volume of the cavities and establishes a channel for sound waves, thereby enabling an exploration of the structure's sound absorption capabilities. The numerical model of the 2D petal-like structure and the boundary conditions for sound absorption simulation are shown in Fig. 4(d). The sound absorption efficacy of 2D petal-like structures primarily hinges on the dissipation of sound energy achieved through the impedance matching process. The dissipation is attributed to the thermal effect arising from the frictional phenomena caused by gas viscosity within narrow regions and the roughness of the material surface. Furthermore, the gas resonance between various cavities plays a significant role in enhancing the dissipation process. The visualization of acoustic resistance depicts the consumption of sound energy resulting from the thermal effect induced by frictional resistance. The acoustic reactance can be defined as the potential energy interactions between gas particles within cavities and the particles' kinetic energy, which is the sum of mechanical energy. When the particles resonate and the acoustic reactance reaches 0, the sound energy is converted into mechanical energy dissipation, as illustrated in Fig. 4(e). This work focuses on the selection of four specific frequencies to investigate the dissipation of sound energy and the distribution of sound pressure–velocity within a structure, to elucidate the underlying mechanism of sound absorption, as illustrated in Fig. 4(f).

At frequency A, a notable increase in thermal dissipation is observed specifically at the holes in the plates and membranes. Simultaneously, a certain level of thermal energy dissipation is observed at the sites of the holes in the lateral walls and the central baffle plates in the 45 degree petal-like cavities. One of the factors to consider is the thermal energy dissipation within the holes, which is attributable to frictional losses caused by the viscosity of the gas present. This form of thermal loss decreases layer by layer with the decrease of the sound speed. The thermal loss near baffle plates can be attributed to the accumulation of gas particles resulting from sound pressure differentials between the two sides of the cavity. Friction between these particles and the cavity wall further contributes to thermal loss. Corresponding to this phenomenon, the acoustic resistance at this frequency starts to increase. Moreover, the gas particles within the cavity exhibit compression at frequency A, leading to downward movement. The resonance among the particles results in an acoustic reactance approaching 0, thereby endowing the structure with specific sound absorption traits at this frequency.

The thermal loss at frequency B is observed analogously with A, particularly in the vicinity of the hole and baffle positions, where the acoustic resistance of the structure surpasses that of the A frequency. This indicates an amplification of sound energy conversion into thermal energy dissipation at this specific frequency. In contrast to frequency A, the gas particles within the smaller petal-like cavity operating at frequency B exhibit compression and a downward trajectory, whereas the gas particles within the larger petal-shaped cavity demonstrate expansion and an upward trajectory. Despite ongoing resonance of the gas particles at frequency B, the resonance effect is less pronounced compared to that at A. Correspondingly, the acoustic reactance is farther away from the value of 0 than that at A. The acoustic resistance serves as a measure of actual energy loss, while acoustic reactance represents the virtual loss of energy, thus showing the superior sound absorption capabilities of the B frequency.

Both the acoustic resistance of frequencies C and D exhibit higher magnitudes than that of B, with a noticeable gradual transition of thermal losses from the hole and baffle locations to the entire cavity sidewall. Among them, the structural acoustic resistance of frequency D is in proximity to unity, while the SAC showcases a maximum value within the designated frequency range. Moreover, the vibrational characteristics of gas particles within the cavities located at positions C and D exhibit significant complexity, manifesting as compression, expansion, and equilibrium states across various cavities. The study examines the vibration response of a resonant cavity at higher-order natural frequencies, focusing on the collaborative acoustic reactance curve to assess the overall impact of particle vibration. The analysis reveals that the acoustic reactance of frequency D approaches zero, indicating a pronounced resonance effect of gas particles at this specific frequency.

Next, a parametric analysis of the sound absorption and insulation performance of 2D/3D petal-like structures is conducted separately. As the 3D petal-like structure is mainly used for sound insulation research, the distribution relationship is changed between layers of the structure according to the layer classification method in Fig. 1. It is worth noting that the order and perforation positions of the plate and membrane are not adjusted, only the angle of the petal-like core layer is changed, and the relationship between the structural layers is shown in Fig. 5(a). Meanwhile, in the process of revealing the sound absorption mechanism, it is found that the sound wave transmission paths inside the cavities on both sides of the baffle plate are consistent through the study of the sound wave transmission path. Under the condition that the cavity volume and perforation diameter are the same, the resonance frequency of the gas is the same, and even if the number of such channels is increased, the sound absorption bandwidth cannot be widened. The perforation positions and hole sizes of each layer are adjusted in the 2D petal-like structure in Fig. 1 to verify the above conclusion and optimize the structure, and the aperture arrangement method is shown in Fig. 5(b). It is worth mentioning that in Fig. 5(b) and (d), the four holes and six holes refer to the number of perforations in each layer of the plate or membrane. The four holes refer to the original structure used for analysis in Fig. 4, and the six holes refer to the case where perforations are made together in the corresponding positions of the six cavities. The gradient arrangement of holes refers to the secondary design of hole diameter for each layer of plate or membrane based on the corresponding cavity size. The hole radii on the side with smaller cavity volumes are 0.6–0.9 mm respectively, while the hole radii on the side with larger cavity volumes are 1.35–1.65 mm.

Fig. 5 The parameterized analysis of 2D/3D CFRP composite petal-like structures. (a) 3D petal-like structure interlayer arrangement. (b) 2D petal-like structure aperture arrangement and sound transmission path in parametric analysis. Where the hole radius is designed as r₁ = 0.6 mm, r₂ = 0.75 mm, r₃ = 0.9 mm, r₄ = 1.35 mm, r₅ = 1.5 mm, and r₆ = 1.65 mm. (c) Calculating the STL by rearranging the 3D petal-like structure in each layer. (d) Calculating the SAC for the 2D structure by varying the location of holes and aperture. (e) A comparison of the sound isolation bandwidth and the position where the frequency band occurs. Among them, MLAM+ is G. Sal-Anglada's structure,⁵³ SSCRAM is Lin's structure,¹² SSAM is Liu's structure,⁵⁴ and CEMAM is Li's structure.⁵⁵ (f) A comparison of the band dominance of the first absorption peak occurrence and SAC. The frequency scale factors are obtained by the following formula: FSF = (1200 Hz − f_n)/1200 Hz, where f_n is the first sound absorption peak frequency of the structures. Among them, MPS is Pan's structure,²³ ALPM is Zhang's structure,¹⁵ SSM is Sun's structure,⁵⁶ and MLCRAM is Liu's structure.¹⁸ (g) Multi-performance comparison of 2D and 3D petal-like multifunctional structures. Reference data: Advanced structures.^12,54,55 Multifunctional structures.^16,38,57

From Fig. 5(c), it can be seen that the arrangement of petal-like core layers has little impact on the resonance and anti-resonance frequency bands of the structure. Due to the holes of the membrane and plate only existing in the top two layers, different core layer angles correspond to different cavity heights, which will lead to differences in sound dissipation. This difference will cause variations in the peak and dip values of the STL, such as when layer 3 is moved to the first layer, the increase in the first layer cavity volume reduces the resonance frequency between the gas inside the cavity and the gas inside the hole, resulting in a decrease in sound insulation within the range of 665–965 Hz on the STL curve. At the same time, through the comparison curve in Fig. 5(d), it can be found that the structure of 6 holes in each layer confirms our conclusion and the sound absorption performance is basically consistent with the structure of 4 holes in each layer. Besides, according to the method of setting gradient holes matched to the cavities, the low-frequency absorption band can also be expanded to a certain degree. In light of the superior broadband sound insulation and low-frequency sound absorption advantages exhibited by 2D and 3D petal-like multifunctional structures, a comprehensive performance comparison of various advanced structures within the sound insulation and absorption domain has been conducted. The comparison results are shown in Fig. 5(e) and (f). Fig. 5(e) depicts the distribution of sound isolation bands across various structures, presenting their respective bandwidths. The comparative analysis highlights the 3D petal-like multifunctional structure as possessing the broadest sound isolation band, prominently manifesting in the sub-1500 Hz frequency range. This feature underscores the structure's role of low and broadband noise isolation on the sub-wavelength scale. The study elucidates the sound isolation phenomenon achieved through the organic combination of acoustic-mechanical metamaterials. The enhanced interaction between the additional mass and the membrane is facilitated by the substitution of traditional additional blocks with a petal-like core layer. Furthermore, the deformation recoverable property of the structure is enhanced, leading to increased potential for practical application of the overall system. Fig. 5(f) illustrates a comparison of the first sound absorption peak frequency and the SAC across various structures. The analysis shows that the 2D petal-like multifunctional structure exhibits the lowest sound absorption frequency, while the SAC is higher at this particular frequency. This suggests a balanced sound absorption performance of the structure when considering these two perspectives. Simultaneously, the observed sound absorption phenomenon is a result of the intricate design of sound channels. By fine-tuning the perforation aperture, enhanced sound absorption capabilities at low frequencies can be achieved without compromising the structural load-bearing capacity. This can exemplify the acoustic characteristics exhibited by the gradient aperture depicted in Fig. 5(d), showcasing superior design flexibility. Ultimately, a detailed analysis is conducted to compare the mechanical, acoustic, and application characteristics of multifunctional structures in relation to conventional plates governed by the mass law. Additionally, a comparison is made with advanced porous materials featuring broadband sound absorption properties, as well as advanced structures that have significantly impacted their respective fields. This work also explores the various attributes of multifunctional structures, highlighting the performance advantages of petal-like acoustic-mechanical multifunctional structures and the research breadth in several fields as shown in Fig. 5(g).

Specifically, they can be used as sandwich structures inside the shells of cars, trains, airplanes, and even submarines, significantly reducing noise damage to the human body while ensuring load-bearing (Part S6, ESI†). Additionally, the hot molding process and automatic dispensing process have become quite mature, making large-scale preparation of the structure feasible, thereby greatly reducing the production cost. Furthermore, the demand for technology will also drive the development of new industries. For instance, as 3D printing technology addresses the issue of continuous fiber reinforced composite materials being unable to print complex configurations,²⁹ automation and lower costs will promote the commercialization of structures.

In order to investigate the exploration of analytical results derived from the numerical model, two configurations are randomly chosen for impedance tube experiments within the scope of parametric analysis. Following the expressive method presented in Fig. 1, the study focuses on the characterization of a 3D petal-like structure arranged with layer 2-layer 1-layer 3, alongside a 2D petal-like structure featuring perforations within chambers I, III, IV, and VI. The samples, experimental device, and the sound absorption and insulation curves obtained are shown in Fig. 6.

Fig. 6 The sound absorption and insulation performance of 2D/3D CFRP composite petal-like structures. (a) 2D/3D structure of vaseline application. (b) Specimen stuffed into a tube. (c) Impedance tube for sound absorption and the model of sound transmission. (d) Impedance tube for sound insulation and the model of sound transmission. (e) Sound insulation and absorption performance comparison of 2D metamaterials. (f) Sound insulation and absorption performance comparison of 3D metamaterials. (g) Comparison of the experimental and simulated STL of the 3D metamaterial. (h) Comparison of the experimental and simulated SAC of the 2D metamaterial.

Vaseline is administered externally to the petal-like structure with a length of 101 mm and subsequently positioned within an impedance tube. A plane wave is emitted by the microphone to engage with the object, inducing the formation of a standing wave pattern. This experimental setup and resulting wave phenomena are illustrated in Fig. 6(a)–(d). The STL and SAC of the specimen are determined through the utilization of the transfer function method. The corresponding values are illustrated in Fig. 6(e) and (f). To validate the efficacy of the simulation technique utilized, the sound absorption and insulation characteristics of the multi-scale petal-like structure are computed individually and subsequently compared against experimental data. The comparative curves are presented in Fig. 6(g)–(h) for assessment and discussion.

The experimental findings depicted in Fig. 6(e) demonstrate that the 2D petal-like structure exhibits significant sound absorption capabilities within the ranges of 165–420 Hz and 650–1135 Hz. The remarkable sound absorption phenomenon observed can be attributed to dual underlying factors: firstly, the thermal effect caused by friction between the gas and the structure under the influence of sound waves is attributed to the viscosity of the gas and the surface roughness of the material. The conversion of sound energy into thermal energy dissipates, facilitating the structure to realize absorption of sound waves. Furthermore, the phenomenon of resonance occurs between gas particles within the cavity when the frequency of the incident plane wave closely aligns with the natural frequency of the system. This resonance leads to the absorption of sound radiation by the structure. While in the sound insulation band (such as at 815–1500 Hz) of the 2D petal-like structure, it is noted that the structural equivalent stiffness is heightened, leading to a significant reflection of sound waves from the structural surface. Consequently, only a minor fraction of the sound energy passes through the structure, thereby contributing to the substantial sound insulation of the structure, with the peak value exceeding 47 dB. Meanwhile, as illustrated in Fig. 6(f), the 3D petal-like structure manifests two distinct absorption peaks within 500 Hz. The structural configuration demonstrates exceptional sound isolation capabilities across a broad frequency band of 560–1510 Hz, achieving a peak sound isolation of 53 dB within this specific frequency interval. It is noted that the structure only has poor sound insulation performance in the frequency band with excellent sound absorption performance due to the contradictory relationship between resonance and anti-resonance phenomenon.

Upon comparing the data depicted in Fig. 6(g) and (h), it becomes evident that the trends exhibited by the STL and SAC curves derived from experimental and simulation are largely aligned. The distinctions between the two primarily manifest in the following ways: Initially, the structural sound insulation performance is assessed through a comparison of experimental and simulation results across various frequency bands. It is observed that both sets of data exhibited a consistent trend throughout the full frequency range. However, a relatively obvious discrepancy is identified in the low frequency band below 500 Hz, where the peak value difference ranged from 12 to 24 dB. Furthermore, the divergence in broadband sound insulation peaks is relatively pronounced after 500 Hz, with a difference of approximately 65 Hz observed in the frequency band. Besides, when analyzing the structural sound absorption performance, significant discrepancies are observed between the experimental and simulation results at the first-order resonance frequency, characterized by a substantial peak error. Moreover, a band error of approximately 150 Hz is identified at the second-order resonance frequency. As a result of the application of thread seal tape and Vaseline to the exterior of the structure in order to prevent sound leakage, the boundary constraints present a high level of complexity and exert a significant constraint effect. Consequently, achieving an exact match with the simplified ideal boundary conditions proves challenging. Therefore, the numerical model demonstrates a greater degree of flexibility in comparison to the actual environment, leading to a decrease in the overall stiffness of the structural system. The sound insulation performance of the structure is primarily influenced by its stiffness, particularly before reaching the first-order natural frequency. A decrease in equivalent stiffness can lead to a reduction in sound insulation effectiveness. This discrepancy in sound insulation performance at lower frequencies between experimental and simulation results thus arises. The frequency band discrepancy is primarily attributed to the influence of membrane tension, as stress relaxation may occur during bonding and curing processes, resulting in a reduction in the membrane's equivalent stiffness. Consequently, the intrinsic frequency of the membrane decreases, causing a shift in resonance towards a lower frequency range. The differences between experimental and simulation data for sound absorption in the 2D petal-like multifunctional structure are mainly related to the following aspects: Firstly, the sound absorption effect requires very high precision of structure preparation, with particular emphasis on the manual fabrication of 2D petal-like core layers comprised of carbon fiber composites. The creation of sound channels and perforations presents considerable challenges in achieving the same level of precision as that obtained through 3D printing technology, potentially leading to discrepancies in the frequency band relative to the simulated results. Secondly, the numerical model employed in this study solely accounts for thermal viscosity at the specific locations of the holes in the plate and membrane. This results in the exclusion of thermal viscosity effects in certain narrow areas of the sound channels, consequently leading to some narrow bandwidths of the absorption peaks or low peak values. Finally, due to the high stiffness of the 2D petal-like core layer, placing it in a softer polyurethane frame may appear as a squeezing phenomenon on the soft material, which will lead to the volume change of the resonance cavity and result in the difference of the sound absorption frequency.

3. Summary

In conclusion, a novel design methodology that integrates sound-mechanical metamaterials with lightweight, high-strength continuous CFRP composites is proposed to achieve a harmonious balance between the mechanical and acoustic performance of the structure. Through a comprehensive analysis of both experimental and analytical data, it is evident that the newly developed CFRP composite petal-like structures exhibit favorable equivalent compression modulus, distinct auxetic characteristics, outstanding energy absorption capabilities, and robust deformation resilience. These desirable characteristics can be attributed to the optimized configuration and layup design of the continuous CFRP utilized in the construction of the structures. Moreover, by manipulating the stacking mode of the structure (2D/3D), the novel CFRP composite petal-like structures exhibit favorable acoustic properties in terms of sound absorption and sound insulation. In terms of noise reduction, perforations have been strategically introduced into the lateral boundaries of the 2D petal-like structure to establish sound channels. It has been demonstrated that this method effectively extends the propagation channel of sound waves in confined spaces, reducing resonance frequency among gases within the cavity to a significantly low range, specifically below 300 Hz, and enhancing the overall structure's absorption efficiency for low frequency sound waves. Simultaneously, the petal-like core layer of the 3D structure is both a foundational support component and a means of replacing additional mass to facilitate the generation of multiple anti-resonance effects within the MAM. This culminates in highly effective sound isolation with a 1000 Hz bandwidth. This solves the problem of the low carrying capacity of conventional acoustic metamaterials and has wide application potential in transportation and other fields.

4. Experimental work

4.1 Mechanical part

Prior to conducting the structural failure experiment, a strain rate of less than 10⁻³ s⁻¹ was meticulously maintained, with the structure being compressed to a strain level of 0.05. The deformation process of the structure was meticulously analyzed utilizing digital image correlation (DIC) software (measurement methodology can be found in Part S7, ESI†). The 2D/3D composite petal-like structures, as described in the preceding section, underwent cyclic compression experiments using an Instron 5566 universal testing machine. The specimen was positioned at the center of the platen, with the rigid platen above it compressed longitudinally to complete each cycle. The failure pattern of the structure was captured by high-resolution cameras for further analysis.

4.2 Acoustic part

The SAC and STL of the 2D/3D composite petal-like structures were measured by an F100 impedance tube device provided by Beijing Shengwang Acoustic-Electric Technology Co., LTD. Using a square tube with an inner diameter of 102 × 102 mm, the effective operating frequency range is 45 Hz to 1600 Hz. The outer frame of the sample is printed square to ensure a tight fit with the impedance tube. The evaluation of the sound absorption and insulation performance of the structure was conducted using the sound source tube and specimen combination, as well as the sound source tube, receiver tube, and specimen combination. Meanwhile, experimental data obtained using VA-Lab can be analyzed through the resolution of the transfer function.

Author contributions

Zhen-Yu Li: conceptualization, methodology, formal analysis, investigation, writing – original draft preparation, visualization. Hong-Ze Li: methodology, formal analysis, writing – original draft preparation, visualization. Jin-Shui Yang: resources, supervision, writing – review & editing, funding acquisition. Li Ma: validation, writing – review & editing. Xin-Tao Wang: validation, writing – review & editing. Yuan-Yuan Gao: methodology, formal analysis. Bin-Gang Xu: methodology, formal analysis. Jian Xiong: validation, writing – review & editing. Hong Hu: term, validation, data curation, resources, supervision, writing – review & editing, funding acquisition.

Data availability

The data supporting this article have been included as part of the ESI.†

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the Research Grants Council of Hong Kong Special Administrative Region Government for the NSFC/RGC Joint Research Scheme (Grant Nos: N_PolyU516/20 and No. 12061160461) and the National Natural Science Foundation of China under grant No. 12172098.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4mh01173b

‡ Both authors contributed equally to this article

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