Metamaterial based on metasurface of Cradinib pattern and optimization design method thereof

Abstract

The metasurface metamaterial is characterized in that a through hole is formed in the middle of one face of a hollow disc, resonant cavity partition plates are symmetrically arranged in the hollow disc, semi-elliptical arc-shaped plates are arranged in cavities separated by the resonant cavity partition plates and close to the side wall of the hollow disc, and slit openings are formed in the middles of the semi-elliptical arc-shaped plates; through holes are formed in the other surface of the hollow disc and positioned at two ends of one group of resonant cavity partition plates; the invention provides a novel metasurface metamaterial structure, broadband noise reduction can be realized, multiple limitations of a traditional sound barrier are solved, parameters are optimized and analyzed through the particle swarm optimization, optimal configuration of structure parameters is obtained, and after optimization, the effective sound insulation frequency range above 30dB is expanded.

Description

Technical Field

[0001] The present invention relates to the technical field of noise pollution control, and in particular to a Chladni pattern-based metasurface metamaterial and an optimization design method thereof. Background Art

[0002] Traditional sound barriers have numerous limitations. Their noise reduction capabilities are often limited to a narrow frequency band, preventing them from achieving broadband coverage. Their structural designs often utilize traditional materials such as metal and concrete, limiting the realization of specialized acoustic properties. Their design methods often lack flexibility, making them difficult to adapt to complex and changing acoustic environments. Furthermore, achieving effective noise reduction often requires a large space. While existing research on metamaterials has shown potential, their sound insulation performance still needs to be further improved, and their structural design can be simplified. Therefore, this paper proposes a metamaterial based on a Chladni pattern metasurface and its optimization design method to address these existing challenges. Summary of the Invention

[0003] In response to the above problems, the purpose of the present invention is to propose a metamaterial based on a Chladni pattern metasurface and an optimization design method thereof. The metamaterial based on the Chladni pattern metasurface and the optimization design method thereof proposes a new metamaterial structure of the metasurface, which can achieve broadband noise reduction and solve many limitations of traditional sound barriers. At the same time, through the particle swarm algorithm to optimize the parameters and analyze them, the optimal configuration of the structural parameters is obtained. After optimization, the effective sound insulation frequency range above 30dB is expanded.

[0004] To achieve the objectives of the present invention, the present invention is implemented through the following technical solutions: a metamaterial based on a Chladni figure metasurface, including a CPM unit cell structure, wherein the CPM unit cell structure includes a hollow disk, a through hole, a resonant cavity partition plate and a semi-elliptical arc plate, a through hole is opened in the middle of one side of the hollow disk, the resonant cavity partition plate is symmetrically arranged in the hollow disk, a semi-elliptical arc plate is provided near the side wall of the hollow disk in the cavity separated by the resonant cavity partition plate, a slit opening is provided in the middle of the semi-elliptical arc plate, and the other side of the hollow disk is provided with through openings at both ends of one group of resonant cavity partition plates.

[0005] Further improvements are: the diameter of the hollow disk is 100 mm, the diameter of the through hole is 20 mm, the height of the hollow disk is 30 mm, the thickness of the outer wall of the hollow disk is 1 mm, and the thickness of the upper and lower side walls is 3 mm.

[0006] Further improvements are: the thickness of the resonance cavity partition plate is 1 mm, the major axis diameter of the semi-elliptical arc plate is 39 mm, the slit opening width is 3 mm, and the minor axis diameter of the semi-elliptical arc plate is 24.5 mm.

[0007] An optimization design method for a Chladni pattern metasurface metamaterial comprises the following steps:

[0008] Step 1: Design parameter analysis: denote the hollow disk diameter as D, the through-hole diameter as S, the hollow disk height as H, the upper and lower sidewall thicknesses as T, the hollow disk outer wall thickness and the resonance cavity partition plate thickness as t, the semi-elliptical arc plate major axis diameter as A, the slit opening width as d, and the semi-elliptical arc plate minor axis diameter as B. Then, use the control variable method to analyze the effects of t, A, B, and d on transmission loss and band gap range.

[0009] Step 2: Define the parameter optimization problem. Optimize the parameters t, A, B, and d using the particle swarm algorithm. The optimization problem is represented by M, and the average transmission loss TL on F = [fl, fu] is defined as

[0010]

[0011] Where f represents the frequency, f l and f u are set to 0Hz and 5000Hz respectively, thus the parameter optimization problem is defined as finding the maximum value of M;

[0012] Step 3: Output the optimization results. Using the formula in step 2, we can determine that when M reaches its maximum value, the outer wall thickness of the hollow disk and the resonance cavity partition plate are 1 mm, the major axis diameter of the semi-elliptical arc plate is 39 mm, the slit opening width is 3 mm, and the minor axis diameter of the semi-elliptical arc plate is 24.5 mm.

[0013] A further improvement is that the control variable method in step 1 specifically keeps the parameters D, S, H and T at fixed values, and evaluates the impact of each of the parameters t, A, B and d on the band gap range and transmission loss curve by changing one of the parameters t, A, B and d separately and keeping the other parameters unchanged.

[0014] A further improvement is that the optimization ranges of the parameters t, A, B and d in step 2 are set to t∈[1-1.8mm], A∈[30-39mm], B∈[16-25mm] and d∈[2-3mm].

[0015] The beneficial effects of the present invention are as follows: the present invention proposes a new metasurface metamaterial structure, which can achieve broadband noise reduction and solve many limitations of traditional sound barriers. At the same time, through the particle swarm algorithm to optimize the parameters and analyze them, the optimal configuration of the structural parameters is obtained. After optimization, the effective sound insulation frequency range above 30dB is expanded. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is the CPM unit cell structure diagram of the present invention.

[0017] Figure 2 This is a model diagram of the CPM unit cell structure experimental device of the present invention.

[0018] Figure 3 This is a transmission loss curve diagram of the CPM unit cell structure experiment of the present invention.

[0019] Figure 4 Figure 2 is the sound pressure distribution and local velocity streamline diagram at four representative frequencies of the present invention.

[0020] Figure 5 This is a comparison chart of the numerical simulation and experimental results of the transmission loss of the four-cavity CPM unit cell structure of the present invention.

[0021] Figure 6 This is a numerical simulation curve diagram of the transmission loss of the present invention.

[0022] Figure 7 This is a flow chart of the structural parameter optimization design based on the PSO algorithm of the present invention.

[0023] Figure 8 This is the PSO convergence curve of the present invention and the TL comparison curve before and after CPM optimization.

[0024] Figure 9 These are four variant derivative structural diagrams of CPM in Example 3 of the present invention.

[0025] Figure 10 This is a transmission loss diagram of different CPM structures in Example 3 of the present invention.

[0026] Among them: 1. Hollow disk; 2. Through hole; 3. Resonance cavity partition plate; 4. Semi-elliptical arc plate; 5. Slit opening; 6. Through port. DETAILED DESCRIPTION

[0027] In order to deepen the understanding of the present invention, the present invention will be further described in detail below with reference to the examples. The examples are only used to explain the present invention and do not constitute a limitation on the scope of protection of the present invention.

[0028] With the accelerated development of industrialization and urbanization, the impact of noise pollution on living environments and workplaces is increasing, and the use of sound barriers is becoming increasingly widespread. However, traditional sound barriers have many limitations. Their noise reduction capabilities are often limited to a narrow frequency band, failing to achieve broadband coverage. Structural designs often utilize traditional materials such as metal and concrete, limiting the realization of specialized acoustic properties. Design methods often lack flexibility and are difficult to adapt to complex and changing acoustic environments. Furthermore, achieving effective noise reduction often requires a large space.

[0029] Acoustic metamaterials overcome the limitations of traditional sound barriers through unit cell design, structural construction, and parameter tuning, demonstrating significant advantages in broadband noise reduction, achieving specialized acoustic properties, and space-saving designs. They exhibit unusual acoustic behaviors, including negative material properties and capabilities such as anomalous refraction, subwavelength imaging, invisibility, and unidirectional transmission, as well as negative parameter properties such as Young's modulus, Poisson's ratio, density, and bulk modulus. These properties, derived from arrays of unit acoustic systems such as Helmholtz resonators, offer new approaches to noise control.

[0030] Prior art has proposed a compact acoustic metamaterial that, by utilizing the principle of Fano-like interference, achieves over 90% attenuation of incident sound energy within a broadband frequency range of 571Hz to 1043Hz. A new type of Helmholtz acoustic metamaterial (HAM) in prior art has been proposed, demonstrating that a double-layer HAM can achieve near-perfect sound absorption at approximately 687Hz, with transmission loss exceeding 10dB within the range of 661 to 1074Hz. This method of achieving broadband, low-frequency sound absorption by stacking multiple units and optimizing internal parameters provides a new strategy for the application of acoustic metamaterials in low-frequency noise control.

[0031] Existing technology also coils a quarter-wavelength resonator into a spiral and combines it with a flat cylinder to form a new metamaterial structure. It is shown that factors such as the resonator's entrance diameter, internal wall thickness, total height, and material properties significantly affect its sound absorption performance. Even if the resonator's maximum external dimension is only 1 / 18 of the target sound wavelength, it can still exhibit excellent sound insulation performance under plane wave and diffuse sound field excitation. Although these metamaterials show potential for application, their sound insulation performance still needs to be further improved, and the structural design can be further simplified.

[0032] To achieve the above objectives, the present invention proposes an acoustic metasurface metamaterial (Chladni Patterns Metamaterial—CPM) based on Chladni patterns.

[0033] Example 1

[0034] according to Figure 1-Figure 5As shown, this embodiment provides a metamaterial based on a Chladni figure metasurface, including a CPM unit cell structure. The CPM unit cell structure includes a hollow disk 1, a through hole 2, a resonance cavity partition plate 3 and a semi-elliptical arc plate 4. The hollow disk is circular, and a through hole 2 is provided in the middle of one side of the hollow disk 1. The resonance cavity partition plates 3 are symmetrically provided in the hollow disk 1. The resonance cavity partition plates are symmetrically provided in four groups. The through holes connect the four cavities separated by the resonance cavity partition plates. A semi-elliptical arc plate 4 is provided near the side wall of the hollow disk 1 in the cavity separated by the resonance cavity partition plate 3. The long axis diameter side of the semi-elliptical arc plate is fixedly connected to the side wall of the hollow disk. A slit opening 5 is provided in the middle of the semi-elliptical arc plate 4. The other side of the hollow disk 1 is provided with through openings 6 at both ends of one group of resonance cavity partition plates 3.

[0035] The diameter of the hollow disk 1 is 100 mm, the diameter of the through hole 2 is 20 mm, the height of the hollow disk 1 is 30 mm, the outer wall thickness of the hollow disk 1 is 1 mm, and the upper and lower side walls are 3 mm thick.

[0036] The thickness of the resonance cavity partition plate 3 is 1 mm, the major axis diameter of the semi-elliptical arc plate 4 is 39 mm, the width of the slit opening 5 is 3 mm, and the minor axis diameter of the semi-elliptical arc plate 4 is 24.5 mm.

[0037] Use the pressure acoustics module of COMSOL Multiphysics to build a circular four-cavity KGM three-dimensional finite element model diagram, as shown in the attached manual. Figure 2 The design parameters are shown in Table 1. The CPM was placed at the center of a 1000 mm long cylindrical waveguide to simulate its effect in an impedance tube and calculate its transmission loss. Considering the significant impedance difference between air and the structural solid material, all inner and outer walls were set as rigid boundaries. The inlet and outlet of the waveguide were defined as circular port boundaries. A vertically incident plane wave with an amplitude characteristic value of 1 Pa was applied at the inlet. The wave transmitted through the structure was captured at the outlet. The transmission loss was calculated as the ratio of the incident acoustic wave energy to the transmitted acoustic wave energy.

[0038] Transmission loss (TL) is calculated from the ratio of incident sound energy to transmitted sound energy:

[0039]

[0040] Where W in and W out are the input and output powers of the incident wave, respectively.

[0041] As the instruction manual Figure 3As shown in the figure, within the effective frequency range of 0-3500 Hz, the sound insulation performance of the CPM at different frequencies can be observed. Before 673 Hz, the TL is minimum, ranging from approximately 0–10 dB. This is likely due to the longer wavelengths of low-frequency sound waves, which easily bypass gaps in the structure or penetrate through resonant modes. Between 673 and 1338 Hz, the TL increases from 10 dB to 80 dB. A TL peak of 105 dB is observed at 1340 Hz, marking the first resonance. Within the 1340-1775 Hz range, the TL gradually decreases back to 10 dB after the resonance ends. A brief drop below 10 dB is observed between 1775 and 1801 Hz. Subsequently, starting at 1801 Hz, the TL gradually increases, reaching a second peak of 88 dB at 2998 Hz, where another resonance occurs. Sound insulation performance exceeding 10 dB is then exhibited until 3500 Hz.

[0042] Numerical simulation of sound insulation mechanism

[0043] Fano-like interference, also known as Fano resonance, results from the interaction of multiple waves in both continuous and discrete states. This phenomenon manifests as constructive and destructive interference near the resonant frequencies associated with the discrete-state waves, resulting in an asymmetric profile in the transmission spectrum. When discrete-state waves exhibit two resonant frequencies, transmission loss increases between these two frequencies. When the external sound wave frequency falls within the band of increased transmission loss, significant energy is lost during the interference process, resulting in transmission loss. This effectively suppresses sound wave propagation, thereby reducing noise.

[0044] In order to more intuitively demonstrate the noise reduction effect of the CPM of this application, the pressure and local velocity streamline distribution on the z-axis cross section are studied. Four representative frequencies are selected: 1000, 1700, 2400 and 3050 Hz, located on both sides of the first and second peaks respectively, and the sound pressure field and local velocity streamline distribution of the cross section at each frequency are obtained through numerical simulation, as shown in the attached manual. Figure 4 As shown. At 1000Hz, the sound pressure distribution is uneven, the sound waves are reflected, refracted and interfered, and the local velocity streamlines are directional. At this time, the sound insulation is achieved by changing the sound wave path through the structure, which consumes energy and does not reach the optimal resonance. At 1700Hz, the sound pressure distribution and streamline morphology change. At this time, the first resonance state has just passed, the coupling with the sound wave is weakened, and the energy dissipation is reduced. At 2400Hz, the sound pressure inside the CPM decreases, and the streamlines show a new trend. At this time, they are preparing for the second resonance state, accumulating energy dissipation, and improving the sound insulation effect. At 3050Hz, the sound pressure distribution is uniform and the streamlines are scattered. At this time, the second resonance state has passed, the effective coupling is weakened, and the sound insulation is significantly reduced. These observations show that the interaction between the sound barrier structure and the sound waves varies with frequency, and through mechanisms such as resonance and interference, it achieves absorption and blocking of sound waves of different frequencies.

[0045] Experimental verification of numerical simulations

[0046] The sound insulation performance of the super unit sample is tested based on the four-microphone transfer function method. The test principle diagram is attached to the manual. Figure 2 As shown in Figure d, the KGM superunit sample was fabricated using photosensitive resin using three-dimensional (3D) printing technology. The metamaterial's D is 100 mm, S is 20 mm, and its height H is 30 mm. The upper and lower circular plates have a thickness T of 3 mm and a wall thickness t of 1.4 mm. The major axis A of the ellipse in the resonant cavity is 32 mm, the minor axis B is 21 mm, and the slit opening width d is 2.2 mm. The test equipment used was the SW4201 circular impedance tube measurement system. The internal side length of the test tube is 100 mm, and the test frequency range is 50 to 1600 Hz. The SW series impedance tube is a new type of impedance tube designed by Beijing Shengwang Company based on the transfer function method and complies with GB / T 18696.2, GB / J 88, ISO 10534-2, ASTM E1050-12, and ASTM E2611-17 standards.

[0047] The SW series impedance tube system is compatible with the four-microphone transfer function method. A single test can determine the material's normal sound absorption coefficient and acoustic impedance across the full measurement frequency range. Compared to standing wave tubes designed based on the standing wave ratio method, this significantly improves the efficiency of testing material acoustic properties.

[0048] In the experiment, the 3D printed CPM sample was fixed on the sample holder in the middle of the impedance tube. The speaker at the starting end of the impedance tube emitted a broadband sound wave, which propagated along the axis of the sound source tube to the test sample. Due to the small diameter of the tube, the sound wave can be approximated as a plane wave. The sound wave is incident vertically on the surface of the test sample, part of which is absorbed, another part is reflected, and the rest is transmitted through the sample to the receiving tube on the other side. The end of the receiving tube is made of sound-absorbing material. By testing the sound pressure values of the four sound pressure sensors in the sound source tube and the receiving tube, the transmission loss of the test sample can be calculated, as shown in the attached manual. Figure 5 shown.

[0049] As can be seen from the figure, in the low-frequency range below 400Hz, the simulated and experimental values are quite close, with relatively low transmission loss values and a relatively gradual change. However, in the mid-frequency range of approximately 600-1200Hz, some discrepancies between the two values occur within the 1000-1200Hz range. This discrepancy may be due to a variety of factors during the actual measurement process. First, the impedance tube's inherent sound insulation capacity has an upper limit, which limits the actual measured value of the test sample at high sound insulation performance, resulting in the experimental value not accurately reflecting the true sound insulation performance of the CPM in this frequency range. Second, the signal-to-noise ratio also affects the measurement results. In actual testing environments, various noise interferences are inevitable. When the signal-to-noise ratio is not ideal, the measurement accuracy will be affected, causing the test value to deviate from the simulation value. Furthermore, reflections from the metamaterial structure may also cause discrepancies. Due to the complexity of the actual structure, the CPM structure may reflect sound waves, which may not be fully accounted for in the simulation, thus affecting the measurement results.

[0050] Despite this, the test peak is about 48dB, which can achieve good sound insulation effect in practical applications; in the high frequency band above 1200Hz, the simulation value shows an obvious peak, and the test value also has an upward trend, and finally tends to be flat, and the transmission loss is above 20dB.

[0051] Example 2

[0052] according to Figure 2 、 6 As shown in FIG. 8 , this embodiment provides an optimization design method for a metamaterial based on a Chladni pattern metasurface, comprising the following steps:

[0053] Step 1: The diameter of the hollow disk 1 is recorded as D, the diameter of the through hole 2 is recorded as S, the height of the hollow disk 1 is recorded as H, the thickness of the upper and lower side walls is recorded as T, the thickness of the outer wall of the hollow disk 1 and the thickness of the resonance cavity partition plate 3 are recorded as t, the major axis diameter of the semi-elliptical arc plate 4 is recorded as A, the width of the slit opening 5 is recorded as d, and the minor axis diameter of the semi-elliptical arc plate 4 is recorded as B, as shown in the attached manual. Figure 2 As shown in a and b, a is a three-dimensional structure diagram and b is a front cross-sectional view. Then, the influence of t, A, B and d parameters on transmission loss and band gap range is analyzed by the control variable method.

[0054] The controlled variable method specifically keeps the parameters D, S, H, and T fixed, and evaluates the impact of each parameter t, A, B, and d on the band gap range and transmission loss curve by changing one of the parameters t, A, B, and d separately while keeping the other parameters unchanged, as shown in Table 1 below.

[0055] Table 1 Design parameters of the four test groups (unit: mm)

[0056]

[0057]

[0058] As the instruction manual Figure 6 Figure 2 shows the TL calculation results for four test groups using the COMSOL Multiphysics Pressure Acoustics Module. Figure (a) shows the results for test group 1, demonstrating the effect of wall thickness t on TL. As t increases, the cutoff frequency of the first band gap and the starting frequency of the second band gap remain unchanged, while the width of the first band gap narrows and the width of the second band gap increases. Figure (b) illustrates the effect of the ellipse's major axis, A, on the TL of test group 2. Increasing parameter A does not cause the TL curve of the first band gap to shift in a single direction, but it shifts the cutoff frequency of the second band gap to the right and increases the band gap width. Figure (c) shows the TL data for test group 3, illustrating the impact of the ellipse's minor axis, B, on the CPM acoustic performance. Increasing B shifts the TL curve to the left overall, with a clear gradient change in the cutoff frequency of the second band gap. Figure (d) illustrates the effect of the ellipse's slit opening width, d, on the TL of test group 4. As parameter d increases, the cutoff frequency of the first band gap shifts to the right, its width increases, and the width of the second band gap decreases, while the overall band gap width remains unchanged.

[0059] Step 2: In order to obtain the complete first and second band gaps and maximize the noise reduction performance of the CPM sound barrier in the frequency range of 0-5000 Hz, the parameters t, A, B and d are optimized by the particle swarm algorithm (PSO). Taking into account the limitations of the actual manufacturing process, the optimization ranges of the parameters t, A, B and d are set to t∈[1-1.8mm], A∈[30-39mm], B∈[16-25mm] and d∈[2-3mm]. The optimization problem is expressed as M, and the average transmission loss TL on F=[fl,fu] is defined as follows:

[0060]

[0061] Where f represents the frequency, f l and f u They are set to 0Hz and 5000Hz respectively, and the parameter optimization problem is defined as finding the maximum value of M, that is, maximizing M can obtain the optimal design size parameters of the CPM metamaterial.

[0062] This optimization algorithm is implemented through a Matlab script that calls COMSOL Multiphysics to calculate the corresponding value of TL. The main process is as shown in the attached manual. Figure 7 shown.

[0063] Step 3: As the instruction manual Figure 8As shown in Figure a, it shows the convergence curve during the PSO algorithm optimization process. The optimal parameters when M reaches the maximum value are obtained by the formula in step 2: the outer wall thickness of the hollow disk 1 and the thickness of the resonance cavity partition plate 3 are 1 mm, the major axis diameter of the semi-elliptical arc plate 4 is 39 mm, the width of the slit opening 5 is 3 mm, and the minor axis diameter of the semi-elliptical arc plate 4 is 24.5 mm.

[0064] The TL comparison before and after CPM optimization is shown in the attached manual. Figure 8 As shown in Figure (b), observing the effective frequency range before 3500Hz, the optimized CPM achieves an ultra-wide frequency band TL exceeding 10dB from 673Hz to 3500Hz. Local peaks of 48.5dB, 88dB, and 102dB are reached at 1780Hz, 2000Hz, and 3365Hz, respectively, showing an overall upward trend. The frequency band above 30dB has been widened from 986–1659Hz and 1950–3440Hz before optimization to a complete continuous band of 1068–3440Hz, a 9.7% increase. The average TL has increased from 36.7dB before optimization to 45.8dB, a 24.8% increase. These results demonstrate that the PSO-based optimization design algorithm significantly improves the noise reduction performance of CPM.

[0065] Example 3

[0066] according to Figure 9 and Figure 10 As shown, this embodiment provides four deformed derivative structures based on the Chladni pattern metasurface metamaterial and compares them with the TL of the original benchmark unit cell circular four-cavity CPM, including a hollow disk 1, a through hole 2, a resonance cavity partition plate 3 and a semi-elliptical arc plate 4. A through hole 2 is provided in the middle of one side of the hollow disk 1, and the resonance cavity partition plates 3 are symmetrically provided in the hollow disk 1. The through hole connects the cavities separated by the resonance cavity partition plates. A semi-elliptical arc plate 4 is provided near the side wall of the hollow disk 1 in the cavity separated by the resonance cavity partition plates 3, and a slit opening 5 is provided in the middle of the semi-elliptical arc plate 4. A through hole 6 is provided at both ends of one group of resonance cavity partition plates 3 on the other side of the hollow disk 1.

[0067] The diameter of the hollow disk 1 is 100 mm, the diameter of the through hole 2 is 20 mm, the height of the hollow disk 1 is 30 mm, the outer wall thickness of the hollow disk 1 is 1.4 mm, and the upper and lower side wall thicknesses are 3 mm.

[0068] The thickness of the resonance cavity partition plate 3 is 1 mm, the major axis diameter of the semi-elliptical arc plate 4 is 39 mm, the width of the slit opening 5 is 3 mm, and the minor axis diameter of the semi-elliptical arc plate 4 is 24.5 mm.

[0069] As the instruction manual Figure 9 As shown in a, the hollow disk is circular, and six groups of resonance cavity partition plates are symmetrically arranged. The long axis diameter side of the semi-elliptical arc plate is fixedly connected to the side wall of the hollow disk.

[0070] As the instruction manual Figure 9 As shown in b, the hollow disk is circular, and four groups of resonance cavity partition plates are symmetrically arranged. The short axis diameter side of the semi-elliptical arc plate is fixedly connected to the side wall of the hollow disk.

[0071] As the instruction manual Figure 9 As shown in middle c, the hollow disk is circular, and the resonance cavity partition plates are symmetrically arranged in four groups with a ventilation tube structure at the center. Through holes are symmetrically arranged on one side of the hollow disk outside the ventilation tube to connect the four cavities separated by the resonance cavity partition plates, and the long axis diameter side of the semi-elliptical arc plate is fixedly connected to the side wall of the hollow disk.

[0072] As the instruction manual Figure 9 As shown in middle d, the hollow disk is square, and four groups of resonance cavity partition plates are symmetrically arranged. The long axis diameter side of the semi-elliptical arc plate is fixedly connected to the side wall of the hollow disk.

[0073] As the instruction manual Figure 10 As shown, under the same structural parameters, Figure 9 The six-cavity CPM in Figure a has a more continuous, broadband first absorption bandgap, achieving effective sound absorption exceeding 30dB in the frequency range of 1182-2433Hz and a TL peak of 101Hz at a high frequency of 2147Hz. In contrast, the first bandgap of the original four-cavity CPM exhibits more favorable sound insulation performance in the low-frequency range.

[0074] Figure 9 The expanded elliptical CPM (b) is derived by swapping the values of the major axis (A) and minor axis (B) of the original CPM. When axis A is smaller than axis B, the first and second band gaps narrow, while the third band gap widens. This weakens lower-frequency sound insulation and enhances high-frequency sound insulation.

[0075] Considering both noise reduction and ventilation performance, a circular hollow ventilation opening with the same diameter of 24mm was opened in the center of the original CPM. Figure 9 Compared with the original sound-absorbing CPM, the ventilated CPM exhibits a more uniform sound absorption band gap and an average TL of approximately 20 dB, which is lower than that of the sound-absorbing CPM. However, compared with the ASVM proposed in the prior art, it exhibits superior sound absorption performance.

[0076] Figure 9 The effect of the cavity shape on the sound insulation performance of CPM was further studied in Figure d. In the 0-3500 Hz range, the circular CPM with a diameter of 100 mm showed more uniform sound absorption and a higher TL peak than the square CPM with a side length of 100 mm.

[0077] In summary, CPMs of different structural forms have different TL curve characteristics and different frequency bands in which they exert their primary noise reduction functions. Among them, the six-cavity CPM has the best overall sound insulation performance, namely the widest band gap and the largest average TL, indicating that increasing the number of cavities can effectively improve the sound insulation performance of the CPM. The ventilated CPM sacrifices the resonance cavity space, and its TL decreases significantly. The elliptical expanded CPM has enhanced high-frequency sound insulation performance and weakened low-frequency sound insulation performance. The square CPM has multiple TL peaks in the 0-3500Hz range, and its overall sound insulation performance is reduced compared to the original CPM.

[0078] In actual application, CPMs with different structural forms can be selected according to specific application scenarios. For example, in high-frequency noise scenarios, elliptical extended CPMs can be used, which have enhanced high-frequency sound insulation performance and weakened low-frequency sound insulation performance. Alternatively, six-cavity CPMs with the best comprehensive sound insulation performance can be selected.

[0079] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A metamaterial based on a Chladni pattern metasurface, characterized by: The invention comprises a CPM unit cell structure, wherein the CPM unit cell structure comprises a hollow disk (1), a through hole (2), a resonance cavity partition plate (3) and a semi-elliptical arc plate (4); a through hole (2) is provided in the middle of one side of the hollow disk (1); the resonance cavity partition plate (3) is symmetrically provided in the hollow disk (1); a semi-elliptical arc plate (4) is provided in the cavity separated by the resonance cavity partition plate (3) and close to the side wall of the hollow disk (1); a slit opening (5) is provided in the middle of the semi-elliptical arc plate (4); and through openings (6) are provided at both ends of one group of the resonance cavity partition plates (3) on the other side of the hollow disk (1).

2. The Chladni pattern-based metasurface metamaterial according to claim 1, characterized in that: The diameter of the hollow disk (1) is 100 mm, the diameter of the through hole (2) is 20 mm, the height of the hollow disk (1) is 30 mm, the outer wall thickness of the hollow disk (1) is 1 mm, and the upper and lower side wall thicknesses are 3 mm.

3. The Chladni pattern-based metasurface metamaterial according to claim 1, characterized in that: The thickness of the resonance cavity partition plate (3) is 1 mm, the major axis diameter of the semi-elliptical arc plate (4) is 39 mm, the width of the slit opening (5) is 3 mm, and the minor axis diameter of the semi-elliptical arc plate (4) is 24.5 mm.

4. The optimization design method of a Chladni pattern metasurface metamaterial according to claim 1, wherein: The following steps are involved: Step 1: Design parameter analysis: the diameter of the hollow disk (1) is recorded as D, the diameter of the through hole (2) is recorded as S, the height of the hollow disk (1) is recorded as H, the thickness of the upper and lower side walls is recorded as T, the thickness of the outer wall of the hollow disk (1) and the thickness of the resonance cavity partition plate (3) are recorded as t, the major axis diameter of the semi-elliptical arc plate (4) is recorded as A, the width of the slit opening (5) is recorded as d, and the minor axis diameter of the semi-elliptical arc plate (4) is recorded as B. Then, the transmission loss and band gap range influence of the parameters t, A, B and d are analyzed by the control variable method; Step 2: Define the parameter optimization problem. Optimize the parameters t, A, B, and d using the particle swarm algorithm. The optimization problem is represented by M, and the average transmission loss TL on F = [fl, fu] is defined as Where f represents the frequency, f l and f u are set to 0Hz and 5000Hz respectively, thus the parameter optimization problem is defined as finding the maximum value of M; Step 3: Output the optimization results. The formula in step 2 is used to determine that when M reaches its maximum value, the outer wall thickness of the hollow disk (1) and the thickness of the resonance cavity partition plate (3) are 1 mm, the major axis diameter of the semi-elliptical arc plate (4) is 39 mm, the width of the slit opening (5) is 3 mm, and the minor axis diameter of the semi-elliptical arc plate (4) is 24.5 mm.

5. The optimization design method of a Chladni pattern metasurface metamaterial according to claim 4, characterized in that: The control variable method in step 1 specifically keeps the parameters D, S, H, and T at fixed values, and evaluates the effect of each of the parameters t, A, B, and d on the band gap range and the transmission loss curve by changing one of the parameters t, A, B, and d separately while keeping the other parameters unchanged.

6. The optimization design method of a Chladni pattern metasurface metamaterial according to claim 4, characterized in that: The optimization ranges of the parameters t, A, B and d in step 2 are set to t∈[1-1.8mm], A∈[30-39mm], B∈[16-25mm] and d∈[2-3mm].

Images