A causally optimal broadband acoustic metamaterial sound absorber design method and sound absorber

Abstract

This invention provides a method for designing a causally optimal broadband acoustic metamaterial sound absorber and introduces a novel method for achieving causally optimal broadband absorption (COBA) by designing and manufacturing a metamaterial sound absorber. The method involves three key steps: (1) calculating the COBA spectrum by solving an optimization problem based on causal constraints; (2) designing a resonator array such that the mode density and resonance intensity match the COBA spectrum; and (3) manufacturing the sound absorber using a large-scale production method such as a mold molding process. The resulting acoustic metamaterial sound absorber exhibits superior broadband absorption performance compared to conventional porous sound absorbers, particularly in the low-frequency range, within a given thickness limitation. This invention represents a significant advance in the development of high-performance and space-saving noise control solutions.

Description

[Technical Field]

[0001] The present invention belongs to the technical field of sound-absorbing materials, and more particularly to a method for designing a causally optimal broadband acoustic metamaterial sound absorber and the sound absorber itself. [Background technology]

[0002] Noise pollution remains a deeply rooted problem in modern society, impacting people's health, productivity, and quality of life. Conventional porous sound-absorbing materials such as sponges and fibers have been widely used for noise reduction, but they have limitations in low-frequency absorption and performance in confined spaces. Because these materials absorb sound energy by relying on high dissipation, they are ineffective at low frequencies, and thicker structures are required to achieve sufficient absorption.

[0003] In recent years, acoustic metamaterials have become a promising alternative to conventional sound-absorbing materials. These artificially designed structures possess unique properties, such as superior absorption capabilities not found in natural materials, due to their sub-wavelength characteristics. Acoustic metamaterials can increase energy density by utilizing local resonance, improving absorption characteristics even at low frequencies. However, typical designs of acoustic metamaterial sound absorbers exhibit narrowband absorption characteristics, limiting their effectiveness in real-world applications often related to broadband noise.

[0004] To address this problem, researchers have explored various strategies for broadening the absorption bandwidth of acoustic metamaterials. One approach involves integrating multiple resonators with different resonant frequencies into a single structure. While this method can broaden the absorption bandwidth, without appropriate design objectives, it can lead to complex designs, increased thickness, and potentially unsuitability for applications in confined spaces.

[0005] Recent research has also revealed that there is a fundamental limit to the maximum absorption achievable within a given thickness, known as a causal constraint. This limit stems from the causal principle in wave propagation, where the system's response cannot precede its excitation. Causal constraints provide a theoretical framework for understanding the trade-off between the absorption bandwidth and structural thickness of acoustic metamaterials, guiding the design of optimal sound absorbers.

[0006] Despite these advances, there is still a need for a systematic method for designing and manufacturing acoustic metamaterial sound absorbers that achieve optimal broadband absorption within a given thickness. Such a method should utilize causal constraints to determine a theoretically optimal absorption spectrum and provide practical means to realize that spectrum. Furthermore, this method should be compatible with efficient large-scale production techniques for widespread adoption in real-world applications. [Overview of the project] [Problems that the invention aims to solve]

[0007] The object of the present invention is to provide a method for designing a causally optimal broadband acoustic metamaterial sound absorber and a sound absorber that satisfies these requirements. The present invention introduces a novel method for achieving causally optimal broadband absorption (COBA) by designing and manufacturing a metamaterial sound absorber, which includes the integration of optimization techniques, resonator array design, and large-scale production methods. The present invention represents a significant advance in the development of high-performance and space-saving noise control solutions. [Means for solving the problem]

[0008] The technical means of the present invention are as follows:

[0009] JPEG2026509389000002.jpg74125

[0010] Furthermore, in the above design method, the resonator is a quarter-wavelength tube.

[0011] Furthermore, in the above design method, the resonator is either a linear structure or a compact structure formed by bending without changing its length and cross-sectional area.

[0012] Furthermore, in the design method described above, step (b) further includes achieving a desired mode density and resonator strength by adjusting the number, dimensions, and spacing parameters of the resonators.

[0013] Furthermore, in the design method described above, step (c) optimizes the structure of the resonator array in step (b) so that the resonator array satisfies the requirements of a mass production method while maintaining predetermined noise spectral absorption characteristics. Preferably, the mass production method is a mold process method, that is, a method of producing sound absorbers by demolding them from a mold while ensuring acoustic characteristics, or by assembling the demolded parts at a later stage.

[0014] One technical means of the present invention further provides a causally optimal broadband acoustic metamaterial sound absorber obtained by the design method described above.

[0015] JPEG2026509389000003.jpg30125

[0016] Furthermore, in the above-described acoustic metamaterial sound absorber, the sound absorber includes a set of quarter-wavelength tube resonator arrays, (a) Each quarter-wavelength tube has the same aperture area, JPEG2026509389000004.jpg15125

[0017] JPEG2026509389000005.jpg33125

[0018] Furthermore, in the design method described above, the quarter-wavelength tube is either a straight structure or a compact structure formed by bending without changing its length and cross-sectional area.

[0019] Furthermore, the above acoustic metamaterial sound absorber is manufactured by a molding process.

[0020] Furthermore, the manufacturing method of the above acoustic metamaterial sound absorber is (a) a step of designing a sound absorber by the above design method of the causal optimal broadband acoustic metamaterial sound absorber; (b) a step of replicating and manufacturing the designed sound absorber using a mass production method.

[0021] Furthermore, in the manufacturing method of the above acoustic metamaterial sound absorber, the step of using the mass production method is a step of adopting a molding process method, that is, while ensuring acoustic characteristics, the sound absorber is produced by being released from the mold or produced by assembling parts released from the mold later.

[0022] Furthermore, in the manufacturing method of the above acoustic metamaterial sound absorber, raw materials suitable for mold production in mass production are used, and the raw materials include plastics, metals, papers, gypsum, and ceramics.

[0023] The present invention provides another technical solution, that is, a noise control system including one or more of the above causal optimal broadband acoustic metamaterial sound absorbers or acoustic metamaterial sound absorbers designed by the above method

[0024] Furthermore, the applications of the above noise control system are used in advanced manufacturing, aerospace, construction, highway and railway transportation, military defense, acoustics, medical, energy, environmental protection, entertainment, education, culture and sports, office, household appliances, IT fields or other fields where effective noise reduction is required in space-limited areas.

[0025] Specifically, these fields include automotive manufacturing, consumer electronics, audio equipment, sound equipment, recording equipment, home appliance manufacturing, data center facilities, office equipment, industrial machinery, shipbuilding, medical equipment, energy equipment, environmental protection equipment, sporting goods, musical instrument manufacturing, toy manufacturing, furniture manufacturing, stage design, music and film production, virtual reality (VR), augmented reality (AR), gaming equipment, educational equipment, and cultural and creative products. [Effects of the Invention]

[0026] Compared to the prior art, the advantages of the present invention are as follows: 1. The present invention provides a causally optimal broadband sound absorber that achieves a predetermined noise spectrum within a limited thickness by employing a novel design method that adjusts the mode density and resonance intensity distribution of a resonator array to match a theoretically optimal absorption curve derived from causal constraints. This overcomes the limitations of conventional porous sound-absorbing materials, which lack the freedom to customize the absorption spectrum and have difficulty absorbing low-frequency sounds, as well as the limitations of typical acoustic metamaterials that exhibit narrowband absorption characteristics. 2. The sound absorber of the present invention can be manufactured using large-scale production methods such as mold molding processes, making it more suitable for practical applications. 3. The present invention has broad applicability in multiple industries where effective noise control in confined spaces is required, such as transportation, construction, and manufacturing. The present invention represents a significant advance in the field of noise absorption technology by providing a framework for designing and manufacturing acoustic metamaterial sound absorbers with optimal performance. [Brief explanation of the drawing]

[0027] [Figure 1] This diagram compares the typical structural dimensions of a metamaterial sound absorber with those of a conventional porous material. [Figure 2]In the optimization example in the embodiment, the noise spectrum S(λ) and effective thickness limit d are predetermined COBA spectrum ACOBA(λ). Here, a is the spectrum of the predetermined noise spectrum S(λ), and b is the COBA spectrum ACOBA(λ). [Figure 3] The embodiment is a metamaterial sound absorber having a quarter-wavelength tube array of the same diameter, where a is a straight-structured quarter-wavelength tube and b is a compact-form quarter-wavelength tube formed by folding the tube. [Figure 4] The embodiment is a metamaterial sound absorber having a quarter-wavelength tube array with different diameters but uniformly distributed resonant frequencies. [Figure 5] The absorption spectra of a custom-made metamaterial silencer and a conventional porous material compared in an example for noise from a power transformer. Here, a is the noise spectrum of a large transformer measured within a 1 / 3 octave band, and b is the actual absorption spectrum of the metamaterial silencer and the conventional porous material, and the corresponding metamaterial silencer. [Modes for carrying out the invention]

[0028] Twenty years have passed since the emergence of the field of acoustic metamaterials, and two distinctly different trends have emerged. One points to the continuous pursuit of new phenomena, mainly through topological structures, and the other points to practical application problems that are difficult to solve by conventional means, with commercialization as the ultimate goal. This invention aims to solve the latter problem, namely the problem in the field of sound absorption. Noise remains a widespread problem in the 21st century, especially low-frequency noise generated from machinery, traffic, railways, aircraft, etc. While these noises can be absorbed by conventional sound-absorbing materials, their use is impractical due to the volume of material required. This presents an opportunity for metamaterial sound absorbers. Can metamaterials outperform low-cost conventional acoustic materials (e.g., foam, rock wool, glass fiber, etc.)? In recent years, the answer to this question has been affirmative. This specification demonstrates the customizability of metamaterials to achieve the maximum absorption permissible by causal relationship for any particular noise with the minimum thickness of the sound absorber. Within the constraints of a limited space, the mechanical noise absorption performance is generally far superior to that of conventional sound absorbers. On the other hand, due to their unique structural scale, acoustic metamaterials can be mass-produced using mold molding processes, and a wide variety of materials can be selected, including metals used in high-temperature applications, plastics and paper used in lightweight applications, and ceramics used in applications requiring high hardness.

[0029] Conventional porous materials such as foam, rock wool, and glass fiber absorb sound through the friction of air molecules in the interface layer between the air and the solid framework (called the viscous boundary layer). The displacement velocity of air molecules in this layer exhibits a monotonic gradient field, and its length scale is given below. JPEG2026509389000006.jpg6125 Here, v = 1.5 × 10 -5 m 2 / s is the kinematic viscosity of air, and f is the frequency of the sound. Therefore, a common way to improve sound absorption efficiency is to increase the surface area of ​​the solid-air interface and thus increase the dissipation efficiency per unit volume. Efficient porous materials tend to have a porosity close to 1. The average pore size l is on the order of approximately δ [the light gray area in Figure 1] in order to maximize absorption within a given volume. Porous sound absorbers are inherently characterized by a low quality factor and a broad absorption spectrum. However, care must be taken to ensure that the dissipation coefficient of the porous sound absorber is not too high. Otherwise, an impedance mismatch may occur at the interface between the air and the sound absorber, potentially preventing sound waves from entering the material. Therefore, impedance mismatch is always a limiting factor for the performance of porous sound absorbers. Since impedance is an important parameter of sound absorbers, its definition and meaning will be explained in detail in the following theory section.

[0030] Increasing the dissipation coefficient is not the only way to increase absorption. Since the energy absorption density is the product of the material's dissipation coefficient and the local sound energy density, the higher the energy density, the greater the absorption. Metamaterial sound absorbers essentially employ this alternative path. By designing local resonances to increase local energy density, metamaterial sound absorbers require only a weaker material dissipation coefficient and a structural scale of l≫δ, thus enabling the absorber to achieve impedance matching with air and nearly 100% absorption. On the other hand, the local resonance structure of metamaterial sound absorbers is typically sub-wavelength (where l<λ=c / f, c=343 m / s is the speed of sound in air), so the structural scale falls into the dark gray shaded region in Figure 1. Due to the low dissipation and sub-wavelength characteristics of metamaterial sound absorbers, their absorption always manifests as a high-quality coefficient with sparse and narrow frequency peaks. Narrowband absorption is meaningful in special cases, but most practical applications still require broadband noise absorption capability. To compensate for this inherent drawback of metamaterial sound absorbers, it is essential to pursue a strategy of integrating multiple units. Each unit resonates at a different frequency, resulting in a broader absorption spectrum. It has been found that an optimal integration solution can realize a sound absorber with a wide frequency and tunable absorption spectrum, whose performance can surpass that of conventional acoustic sound absorbers in certain applications. In other words, by designing a metamaterial sound absorber in reverse and combining it with the minimum sample thickness according to natural laws, a specific absorption spectrum matching the target noise can be achieved. In commercialization, this high degree of customizability will bring about a paradigm shift in many acoustic application fields. Below, we will describe this design solution in detail, starting with the fundamental limitations imposed on wave absorption by causal relationships.

[0031] Time progresses in only one direction, toward the future. According to causality, what happens to a sound absorber at a given point in time is determined solely by what happened before that point in time, and not by what will happen in the future. Mathematically, the Fourier transform shows that time and frequency are conjugate variables. The reinforcement of causality in the time domain, i.e., time asymmetry, greatly affects the properties of materials in the frequency domain. Especially in the case of electromagnetic waves, the dielectric function is usually a function of frequency and has a real part and an imaginary part. In the 1920s, two physicists, Hans Kramers and Ralf Kronig, independently derived the famous Kramers-Kronig relation relating the real and imaginary parts of the dielectric function. In similar research, there is the Bode-Fano limit used in network matching. Recent studies have also shown limits on absorption spectra and minimum sample thickness τ, which can be expressed by the following inequality. TIFF2026509389000007.tif655 Here, d is the thickness of the sample and A is the ratio of absorbed energy to the normal incident energy. An important conclusion from equation (3) is that perfect absorption does not exist, since A=1 causes the integral to diverge in any finite bandwidth. This causal inequality also highlights the importance of sample thickness as a “resource” for wave absorption. Typically, for a given τ, enhancing absorption in one frequency band comes at the expense of absorption in other frequency bands; in other words, absorption cannot be increased without cost. Therefore, for a particular signal energy spectrum S(λ), all excess absorption outside the signal frequency range is wasted, and its maximum absorption should correspond to a material-independent absorption spectrum A(λ) determined independently by the thickness of the absorber. This spectrum is called the causally optimal broadband absorption (COBA) of the incident signal and represents the upper limit of energy absorption allowed by causality. JPEG2026509389000008.jpg13125

[0032] To find the solution to this optimization problem, we introduce the Lagrangian multiplier μ and form a Lagrangian function. JPEG2026509389000009.jpg10125

[0033] JPEG2026509389000010.jpg30125

[0034] JPEG2026509389000011.jpg27125

[0035] JPEG2026509389000012.jpg17125

[0036] This can be done by substituting the solution to equation (5a) into the integral of equation (5b). For a given d and a known incident spectrum S(λ), the maximum absorption can be explicitly evaluated.

[0037] According to equation (5), for a given thickness d, each noise signal S(λ) has a unique COBA (Causal Optimal Broadband Absorption). Achieving or designing for COBA means achieving optimal performance of the sound absorber at the minimum thickness. In Figure 2, the Gaussian noise signal S(λ) with a center frequency of 100 Hz (i.e., a center wavelength of 3.14 meters) is given by exp[-(λ-3.14)]. 2 The example given is: When the thickness of the absorber is limited to 15 cm, the corresponding A COBA This corresponds to the solid line in Figure 2, and the total absorption efficiency is as follows. JPEG2026509389000013.jpg6125 Under the constraint of the same thickness, all absorption spectra that deviate from the solid line will have a lower absorption efficiency for that S(λ). For example, the dotted absorption spectrum in Figure 2 has a higher absorption efficiency at the center frequency within the same 15 cm thickness, but the overall absorption efficiency drops to 80.7%.

[0038] The absorption rate (A) of a metamaterial sound absorber is given by the formula A = 1 - |(Z - ρc) / (Z + ρc)| 2 It can be calculated as follows: Here, ρ = 1.2 kg / m 3is the air density, and c is the speed of sound in air. JPEG2026509389000014.jpg36125

[0039] Here, β is the attenuation coefficient, and r n and ω n are the resonance intensity and frequency of the n-th resonator, respectively. N represents the total number of resonators, and the surface porosity φ is the ratio of the total opening area of the resonators to the area exposed to the incident sound. For simplicity and generality, the higher-order modes of the resonators are ignored here. This can be corrected by a more accurate treatment for a specific resonator type.

[0040] In the first term of the sum of the above Lorentz functions, since it changes from negative to positive near each resonance frequency, the sum of all modes tends to cancel each other out, and as a result, the net result can be ignored. On the other hand, the second term in the sum is always positive, so the contributions of all modes are cumulatively added and become relatively large. Therefore, the following mode density N d (ω) is defined, and its sum can be converted to an integral to approximate the impedance in the form of a real integral. JPEG2026509389000015.jpg14125 <匡

[0041] Here, ω1(ω N ) is the first (N-th) resonance frequency. As mentioned above, since the metamaterial essentially has a high quality factor, β becomes very small. That is, the impedance can be further simplified as follows. JPEG2026509389000016.jpg10125

[0042] Equation (6) conveys an important message. That is, the metamaterial sound absorber can adjust the impedance by adjusting the product N d (ω)r(ω) of the mode density and the intensity function, thereby achieving customized absorption. JPEG2026509389000017.jpg20125

[0043] JPEG2026509389000018.jpg20125

[0044] A suitable resonator array is obtained according to the constraints of the above equation, and then an absorber is constructed from the suitable resonator array.

[0045] To intuitively illustrate the effect of COBA, we will consider the noise of a power transformer as an example. Figure 5(a) shows the noise of a large transformer measured in a 1 / 3 octave band, where 99% of the energy is concentrated in the frequency range of 110 Hz to 560 Hz. Limiting the thickness of the sound absorber to τ=10, equation (5) gives the COBA solution shown by the dashed line in Figure 5(b). JPEG2026509389000019.jpg11125 On the other hand, conventional acoustic sponges can only achieve 56% efficiency (3.6 dB of reflection loss) for the same 10 cm thickness because their absorption capabilities at lower and higher frequencies are wasted (as shown by the dashed line in Figure 5(b)).

[0046] To test the effectiveness of the above design and implementation, a 10 cm thick acoustic metamaterial sound absorber was designed to achieve customized causally optimal broadband absorption (COBA) for transformer noise. A Fabry-Perot (FP) resonator, which is a quarter-wave tube, was used as the basic unit, and the distribution of resonant frequencies was designed by adjusting its length, while the resonance intensity was designed by adjusting the aperture area.

[0047] When higher-order resonances are considered, if an array of M FP resonators is arranged in a row and pointed towards a sound wave, its surface impedance is given by the following equation. JPEG2026509389000020.jpg29125

[0048] Here, L m and ω m θ is the length of the m-th FP tube and the first harmonic frequency, respectively, where q is the order of the harmonic, and φ mThis is the ratio of the opening area to the total area of ​​the m-th FP tube. The imaginary part of the Dirac function is the result of the Kramers-Kronig relation. d By introducing (x)dx to represent the number of FP resonators having the first harmonic resonant frequency x within the frequency range dx, the initial sum in equation (7) can be rewritten as an integral, and by an approximation similar to that described above, the imaginary part of Z(ω) is ignored. JPEG2026509389000021.jpg26125

[0049] JPEG2026509389000022.jpg23125

[0050] JPEG2026509389000023.jpg25125

[0051] JPEG2026509389000024.jpg20125

[0052] JPEG2026509389000025.jpg13125

[0053] As shown in Figure 3, the designed sound absorber includes a quarter-wavelength tube resonator array, where, (a) Each quarter-wavelength tube has the same aperture area, (b) The distribution of tube lengths is the density at the frequency of the first resonant mode for all quarter-wave tubes. TIFF2026509389000026.tif37 is such that it satisfies equation (2). JPEG2026509389000027.jpg11125

[0054] The quarter-wavelength tubes used here may be straight (Figure 3(a)) or they may be compact structures formed by bending the tubes while maintaining their length and cross-sectional area (Figure 3(b)).

[0055] Another simple example is the case where all resonant frequencies are equally spaced δ and uniformly distributed. Therefore, M d= 1 / δ is a constant, and the cross-sectional area of ​​each FP tube should be designed to satisfy the following equation. JPEG2026509389000028.jpg5125 Furthermore, considering the higher harmonics of the FP tube, in order to ensure that all resonant frequencies are evenly distributed, the frequency interval of their first harmonics must be an integer fraction of the lowest harmonic frequency.

[0056] As shown in Figure 4, the sound absorber also includes a set of quarter-wavelength tube resonator arrays, where, (a) Since the resonant frequencies of all resonators are evenly distributed with a spacing δ, the density M at the frequency of the first resonant mode of each resonator d It is a constant and equal to 1 / δ. JPEG2026509389000029.jpg10125(c) The first harmonic interval between resonators is an integer fraction of the lowest resonant frequency.

[0057] Continuing with the example of transformer noise, we use the first strategy where the FP tube array has the same aperture area. As shown in Figure 5(b), 9 × 9 × 10 cm 3By producing 60 folded FP tubes within a space using a mold process, a labyrinthine, compact structure is formed as a functional unit for the metamaterial sound absorber. Laboratory impedance tube measurements show the absorption spectrum, indicated by the solid line in Figure 5(b). The experimental results, although highly unstable, closely followed the ideal COBA result within the frequency range of 110–560 Hz where noise energy is concentrated. The total internal reflection loss was 11.5 dB, only 0.6 dB lower than COBA and much higher than conventional acoustic sponges. The difference from COBA is mainly due to the absorption of sounds above 560 Hz by the inevitable higher-order modes of the FP tubes. However, high-frequency absorption contributes little to the causal constraint integral in equation (3). In practical applications, a large number of such metamaterial sound absorbers can be combined to form sound-absorbing panels, soundproof walls, or soundproof covers to provide system noise reduction for target machinery. Furthermore, these various metamaterial sound absorbers can be individually customized for different noise spectra in various areas of mechanical equipment and used in corresponding locations to create a more efficient overall solution.

[0058] The above example demonstrates that customized COBA (Causally Optimal Broadband Absorption) absorption performance is typically far superior to conventional porous materials, especially when noise has large low-frequency components. This advantage forms the basis for the commercialization of acoustic metamaterials. However, the complex structure of metamaterial absorbers poses a challenge in large-scale production. While 3D printing is an ideal choice for prototype design and testing due to its flexibility, existing 3D printing technologies still face challenges in production efficiency and volume for large-scale production. Fortunately, as shown in Figure 1, for audible sound (20 Hz to 20,000 Hz), the wavelength of sound waves is not so small, and the structural scale of acoustic metamaterials is typically on the order of millimeters to centimeters. This is precisely within the range of conventional mold production processes, which are more efficient, reliable, and better suited for large-scale production. The inset in the upper right of Figure 1 shows a COBA metamaterial absorber produced by mold injection molding. The layered structure in the inset in Figure 5(b) is a structural optimization performed on the mold production method. This allows metamaterial sound absorbers to be produced by demolding from a mold, or by assembling parts that have been demolded from the mold, while ensuring acoustic performance. Furthermore, in mass production methods using molds, other raw materials suitable for mold production, such as metal, paper, plaster, and ceramics, can be used in addition to plastic injection molding.

[0059] The present invention further provides another example of an acoustic metamaterial sound absorber designed by the above method, or a noise control system using one or more of the above acoustic metamaterial sound absorbers.

[0060] Noise control systems are used in advanced manufacturing, aerospace, construction, highway and rail transport, military and defense, acoustics, medical, energy, environmental protection, entertainment, education, culture and sports, office, consumer electronics, IT, or other fields where effective noise reduction is required due to space limitations.

[0061] Specifically, these fields include automotive manufacturing, consumer electronics, audio equipment, sound equipment, recording equipment, home appliance manufacturing, data center facilities, office equipment, industrial machinery, shipbuilding, medical equipment, energy equipment, environmental protection equipment, sporting goods, musical instrument manufacturing, toy manufacturing, furniture manufacturing, stage design, music and film production, virtual reality (VR), augmented reality (AR), gaming equipment, educational equipment, and cultural and creative products.

Claims

1. A causally optimal broadband acoustic metamaterial sound absorber design method, applicable to a sound absorber having a predetermined noise spectrum S(λ) and effective thickness limit d, where λ is the wavelength of sound in air. (c) The step of optimizing the structure of the resonator array in step (b), and then configuring the resonator array to constitute a causally optimal broadband acoustic metamaterial sound absorber, A method for designing a causally optimal broadband acoustic metamaterial sound absorber, characterized by including the following:

2. The design method according to claim 1, characterized in that the resonator is a quarter-wavelength tube.

3. The design method according to claim 1 or 2, characterized in that the resonator is a linear structure or a compact structure formed by bending without changing its length and cross-sectional area.

4. The design method according to claim 1, further comprising step (b) adjusting the number, dimensions, and spacing parameters of the resonators to achieve a desired mode density and resonator strength.

5. The design method according to claim 1, characterized in that step (c) optimizes the structure of the resonator array in step (b) so that the resonator array satisfies the requirements of a mass production method while maintaining predetermined noise spectral absorption characteristics.

6. A causally optimal broadband acoustic metamaterial sound absorber, A causally optimal broadband acoustic metamaterial sound absorber, characterized in that it is a causally optimal broadband acoustic metamaterial sound absorber obtained by the design method of claim 1.

7.

8. The sound absorber includes a set of quarter-wavelength tube resonator arrays. (a) Each quarter-wavelength tube has the same aperture area,

9. The sound absorber includes a set of quarter-wavelength tube resonator arrays. (a) The resonant frequencies of all resonators are uniformly distributed, and the interval between the resonant frequencies is δ, thereby the density M at the frequency of the first resonant mode of each resonator. ｄ is a constant and is equal to 1 / δ, (c) The acoustic metamaterial sound absorber according to claim 7, characterized in that the first harmonic interval between resonators is an integer fraction of the lowest resonant frequency.

10. The acoustic metamaterial sound absorber according to claim 7, 8, or 9, characterized in that the quarter-wavelength tube has a straight structure or a compact structure formed by bending without changing its length and cross-sectional area.

11. The sound absorber is manufactured by a mold process, as described in claim 6.

12. The method for manufacturing the aforementioned acoustic metamaterial sound absorber is as follows: (a) the step of designing a sound absorber by the method of claim 1, (b) A method for manufacturing an acoustic metamaterial sound absorber according to claim 6, comprising the step of replicating and manufacturing a designed sound absorber using a mass production method.

13. The method for manufacturing an acoustic metamaterial sound absorber according to claim 12, characterized in that the step of using the mass production method is the step of employing a mold process method.

14. A method for manufacturing an acoustic metamaterial sound absorber according to claim 12, characterized in that raw materials suitable for mold production are used in mass production, and the raw materials include plastic, metal, paper, gypsum, and ceramic.

15. A noise control system, A noise control system characterized by comprising one or more acoustic metamaterial sound absorbers designed by the method described in claim 1, or causally optimal broadband acoustic metamaterial sound absorbers described in claim 6.

16. Applications of the noise control system according to claim 15, characterized in that it is used in advanced manufacturing, aerospace, construction, highway and rail transport, military defense, acoustics, medical, energy, environmental protection, entertainment, education, culture and sports, office, consumer electronics, IT fields, or other fields where effective noise reduction is required due to space limitations.

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