A method for constructing bound states in a continuum and a sound absorption structure

Abstract

The application relates to a bound state in the continuum construction method and a sound absorption structure in a continuum, and the method comprises the following steps: setting a bridge pipe in a two-state system composed of two asymmetric cavities; a Hamilton matrix of the two-state system is constructed, and a calculation formula of two characteristic values is derived; by adjusting the near-field coupling contribution in the Hamilton matrix, the changes of the real part and the imaginary part of the two characteristic values and the radiation quality factor are observed until a Friedrich-Wintgen (FW) BICs structure is constructed; a time coupling mode theory is used to calculate the sound absorption coefficient of the two-state system, the position of the bridge pipe is adjusted, the condition of deviating from the BICs is used to obtain a quasi-BICs, so that the low radiation loss of the quasi-BICs just compensates for the inherent loss, and the critical coupling condition of perfect absorption is reached. Compared with the prior art, the application opens up a way to study the FW BICs with a bridge type near-field coupling in an asymmetric system, and provides an opportunity for developing an acoustic device with a high quality factor and asymmetric wave control.

Description

Technical Field

[0001] This invention relates to the field of acoustic devices, and in particular to a method for constructing bound states in a continuum and a sound-absorbing structure. Background Technology

[0002] In recent years, bound states in the continuum have attracted increasing interest due to their intriguing physical properties, such as infinitely high quality factors (Q factors) and enhanced wave-matter interactions.

[0003] Bound states in a continuum are completely isolated modes without radiation, yet they exist in the continuum spectrum of radiative, optical, elastic, and acoustic systems. Bound states in a continuum offer many intriguing physical properties, such as infinitely high quality factors and enhanced wave-matter interactions. When deviating from bound states in a pure continuum, so-called bound states in a quasi-continuum can be realized, possessing extremely large Q-factors and allowing interaction between the quasi-continuum bound states and their external environment. Bound states in a continuum have various physical formation mechanisms, such as bound states in a symmetry-protected continuum induced by geometric symmetry properties, bound states in a random continuum based on wavefield distribution modulation, and bound states in the Friedrich-Wintgen and Fabry-Pérot continuums achieved by adjusting far-field and / or near-field coupling between resonances. Different formation mechanisms and various modulation techniques facilitate the effective manipulation of the properties of bound states in both continuum and quasi-continuum, resulting in a variety of high-performance and tunable lasers, sensors, and nonlinear generators.

[0004] In recent years, bound states in acoustic continuums have received increasing attention. Since the discovery of bound states in symmetric-protected continuums in waveguide systems in the 1960s, much research has focused on this area, resulting in significant progress in the physical formation mechanisms and applications of bound states in acoustic continuums. For example, bound states in acoustically symmetric-protected continuums, bound states in Friedrich-Wintergen continuums, and bound states in so-called "mirror-induced" continuums have been realized in Helmholtz resonators placed on one side of an acoustic waveguide. Bound states in acoustic Fabry-Perot continuums are constructed by modulating radiative interference between two identical resonators at a certain distance in the waveguide system. Bound states in acoustic Friedrich-Wintergen continuums are achieved by placing two identical resonators close to each other at the waveguide ends, where far-field radiative interference between the two resonators largely contributes to the formation of bound states in the continuum. However, despite the great importance and potential of near-field coupling in determining the quality of bound states in a continuum, previous studies have rarely explored bridging near-field coupling in the construction of bound states in the acoustic Friedrich-Wintergen continuum experimentally. Summary of the Invention

[0005] The purpose of this invention is to overcome the defects of the prior art by providing a method for constructing bound states in a continuum and a sound-absorbing structure, thus opening up a way to study bound states in an acoustic Friedrich-Wintergen continuum with bridging near-field coupling in asymmetric systems.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A method for constructing bound states in a continuum includes the following steps:

[0008] A bridge pipe is installed to connect the two asymmetric cavities in a two-state system consisting of two asymmetric cavities;

[0009] Construct the Hamiltonian matrix of the two-state system and derive the formulas for calculating the two eigenvalues ​​of the Hamiltonian matrix;

[0010] By adjusting the near-field coupling contribution in the Hamiltonian matrix, the changes in the real and imaginary parts of the two eigenvalues ​​and the radiation quality factor are observed until the bound state structure in the Friedrich-Wintergen continuum is constructed.

[0011] Furthermore, the method adjusts the near-field coupling contribution in the Hamiltonian matrix by modulating the diameter and position of the bridge connector.

[0012] Furthermore, the expression for the Hamiltonian matrix is:

[0013]

[0014] In the formula, H is the calculated value of the Hamiltonian matrix, and ω j and γ j denoted as the resonant angular frequency and radiation attenuation rate of the cavity, respectively; j is the cavity index, with a value of 1 or 2, representing different cavities; κ is the near-field coupling contribution of cavity 1 and cavity 2; and i is the imaginary unit.

[0015] Furthermore, the expressions for calculating the two eigenvalues ​​of the Hamiltonian matrix are as follows:

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023] In the formula, σ1 is one of the eigenvalues, σ2 is another eigenvalue, and ω A Let ω be the resonant angular frequency of a cavity. R γ is the resonant angular frequency of another cavity. A γ is the radiation attenuation rate of a cavity. B The radiation attenuation rate of the other cavity.

[0024] Furthermore, the value of the radiation quality factor is log 10 (Q rad1 ) or log 10 (Q rad2 ), where Q rad1 =Re{σ1} / (2Im{σ1}), where Re{σ1} is the real part of σ1 and Im{σ1} is the imaginary part of σ1.

[0025] Furthermore, when there are eigenvalues ​​with zero imaginary part and infinitely high radiation quality factor, the bound state structure in the Friedrich-Wintergen continuum is constructed.

[0026] Furthermore, the method also includes using time-coupled mode theory to calculate the sound absorption coefficient of the two-state system and evaluate the sound absorption effect of the two-state system.

[0027] Furthermore, the expression for calculating the sound absorption coefficient is as follows:

[0028]

[0029]

[0030] α = 1 - |r| 2

[0031] In the formula, For cavity j, the resonance mode is... Γ represents the incident wave. m(n) This represents the intrinsic decay rate of cavity m or n. Indicates resonance The resulting re-radiation, m and n are cavity indices, m=1, n=2, r is the reflection coefficient of the entire system, and α is the sound absorption coefficient.

[0032] Furthermore, the expression for calculating the inherent decay rate is as follows:

[0033]

[0034] In the formula, r0 is the reflection coefficient of the system when it resonates under normal incidence.

[0035] Furthermore, the method also includes adjusting the position of the bridging pipe to deviate from the conditions of the bound state in the continuum to obtain the bound state in the quasi-continuum, so that the low radiation loss of the quasi-bound state just compensates for the intrinsic loss, achieving the critical coupling condition for perfect absorption.

[0036] The present invention also provides a method for constructing a bound state in a continuum as described above to obtain a sound-absorbing structure in a quasi-continuum, including a first sound-absorbing sub-cavity, a second sound-absorbing sub-cavity and a bridging pipe, wherein the two ends of the bridging pipe are respectively connected to the first sound-absorbing sub-cavity and the second sound-absorbing sub-cavity;

[0037] The cross-sectional area and cavity depth of the first and second sound-absorbing sub-cavities are different;

[0038] The different diameters and positions of the bridge pipe correspond to different sound absorption effects of the bound sound-absorbing structure in the quasi-continuum;

[0039] The wall thickness of the first sound-absorbing sub-cavity, the second sound-absorbing sub-cavity, and the bridge pipe is all within the range of 4mm to 5.5mm.

[0040] Furthermore, the cross-sectional shape of the bridge pipe is circular.

[0041] Furthermore, both the first and second sound-absorbing sub-cavities are cuboid structures.

[0042] Furthermore, the dimensions of the first sound-absorbing sub-cavity are 48mm*48mm*189mm; the dimensions of the second sound-absorbing sub-cavity are 15mm*28mm*160mm; the cross-sectional shape of the bridge pipe is circular with a diameter of 27mm; the distance from the center of the bridge pipe to the front surface of both the first and second sound-absorbing sub-cavities is 50mm; the thickness of the bridge pipe, the sidewall thickness of the first sound-absorbing sub-cavity, and the sidewall thickness of the second sound-absorbing sub-cavity are all 5.5mm.

[0043] Furthermore, the material of the bound-state sound-absorbing structure in the quasi-continuum is a photosensitive resin.

[0044] Furthermore, the bound-state sound-absorbing structure in the quasi-continuum is an integrally molded structure.

[0045] Furthermore, the bound-state sound-absorbing structure in the quasi-continuum has a perfect sound-absorbing effect with a narrow bandwidth.

[0046] Compared with the prior art, the present invention has the following advantages:

[0047] (1) This invention proposes a dual-state system consisting of two asymmetric cavities and a bridging tube. By adjusting the diameter and position of the bridging tube, the near-field coupling effect of the proposed system can be effectively adjusted, realizing the bound state in the Friedrich-Wintergen continuum. This opens up a way to study the bound state in the acoustic Friedrich-Wintergen continuum with bridging near-field coupling in asymmetric systems. This enriches the field of bound states in acoustic continuum and provides an opportunity to develop acoustic devices with high Q factor and asymmetric wave control.

[0048] (2) This invention proposes modulating a two-state system into a bound state deviating from the continuum. This provides a bound state in a quasi-continuum. When the bound state in the quasi-continuum supports the system's radiation loss and intrinsic loss to reach the critical coupling condition, high-Q perfect absorption can be achieved. Experimental results verify the theoretical and simulation results, proving the existence of the bound state in the continuum and the perfect absorption based on the bound state in the quasi-continuum.

[0049] (3) The bound state sound-absorbing structure in the quasi-continuum of the present invention has the advantages of simple structure, low manufacturing cost and high adjustability. Attached Figure Description

[0050] Figure 1a A schematic diagram illustrating the near-field and far-field interactions between two resonant modes;

[0051] Figure 1b A schematic diagram of the interaction between two acoustic resonators connected by a bridge and sharing the same radiation field.

[0052] Figure 1c For the radiation quality factor log 10 (Q rad1 The diagram illustrates the concept of κ and ω2 / ω1 variations in the proposed two-state system. In the analysis, the parameters are set as γ1 = 0.2ω1 and γ2 = 0.04ω2.

[0053] Figure 1d For the radiation quality factor log 10 (Q rad1 A schematic diagram illustrating the concept of κ and γ2 / γ1 variations in the proposed two-state system is shown; in the analysis, the parameters are set to ω1 = 1Hz and ω2 = 1.2Hz.

[0054] Figure 2a A schematic diagram of the real parts of the eigenvalues ​​of a two-state system;

[0055] Figure 2b A schematic diagram of the imaginary part of the eigenvalues ​​of a two-state system;

[0056] Figure 2c The diagram illustrates the radiation quality factor of the two-state system as κ changes, with parameters set to ω2 / ω1 = 1.2 and γ2 / γ1 = 0.24.

[0057] Figure 3a This is a schematic diagram of the experimental sample, with the wall thickness set to 5.5 mm;

[0058] Figure 3b For a dual-cavity system with d a A schematic diagram of the reflection amplitude (|r|) varying with ω / 2π, and the distance l between the tubes. h Fixed at 146 mm;

[0059] Figure 3c For dual-cavity systems with l h A schematic diagram of the reflection amplitude (|r|) varying with ω / 2π, with tube diameter d. a Fixed at 27mm;

[0060] Figure 3d For d a =27mm and l h A schematic diagram of the simulation results for the characteristic frequency, pressure field (represented by color), and sound intensity field (represented by green arrows) of a dual-cavity system with a diameter of 146 mm.

[0061] Figure 3e For diameter d a Schematic diagrams of the reflection amplitude (|r|) for experimental and simulation results of dual-cavity systems with diameters of 2.2 mm, 8.4 mm, and 27 mm, and the distance between the tubes is l. h Fixed at 146 mm;

[0062] Figure 3f Pipe spacing l h This is a schematic diagram of the reflection amplitude (|r|) for experimental and simulation results of dual-cavity systems with diameters of 50mm, 90mm, and 146mm, where the tube diameter is d. a Fixed at 27 mm;

[0063] Figure 4a For in d a =27mm and l h A schematic diagram of the simulation results for the characteristic frequency, pressure field (represented by color), and sound intensity field (represented by green arrows) of a dual-cavity system with a diameter of 50 mm.

[0064] Figure 4b For in d a =27mm and l h A schematic diagram of the theoretical, experimental, and simulation absorption coefficients at 50 mm. The theoretical results were calculated using time-coupled mode theory.

[0065] Figure 5 This is a flowchart illustrating a method for constructing bound states in a continuum according to an embodiment of the present invention;

[0066] Figure 6 This is a front view schematic diagram of a bound-state sound-absorbing structure in a quasi-continuum provided in an embodiment of the present invention;

[0067] Figure 7 This is a left-side schematic diagram of a bound-state sound-absorbing structure in a quasi-continuum provided in an embodiment of the present invention;

[0068] Figure 8 This is a top view schematic diagram of a bound-state sound-absorbing structure in a quasi-continuum provided in an embodiment of the present invention;

[0069] In the diagram, 1 is the first sound-absorbing sub-cavity, 2 is the second sound-absorbing sub-cavity, 3 is the bridging pipe, and 4 is the side wall. Detailed Implementation

[0070] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0071] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0072] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0073] Example 1

[0074] like Figure 5 As shown, this embodiment provides a method for constructing bound states in a continuum, including the following steps:

[0075] S1: A bridge pipe is installed to connect the two asymmetric cavities in a two-state system consisting of two asymmetric cavities;

[0076] S2: Construct the Hamiltonian matrix of the two-state system and derive the formulas for calculating the two eigenvalues ​​of the Hamiltonian matrix;

[0077] S3: By adjusting the near-field coupling contribution in the Hamiltonian matrix, observe the changes in the real and imaginary parts of the two eigenvalues ​​and the radiation quality factor until the bound state structure in the Friedrich-Wintergen continuum is constructed.

[0078] As a preferred embodiment, the above method further includes S4: using time-coupled mode theory to calculate the sound absorption coefficient of the two-state system and evaluate the sound absorption effect of the two-state system;

[0079] By adjusting the position of the bridging pipe, the conditions of the bound states in the continuum are deviated from those in the continuum to obtain the bound states in the quasi-continuum. This allows the low radiation loss of the bound states in the quasi-continuum to just compensate for the intrinsic loss, thus achieving the critical coupling condition for perfect absorption.

[0080] This embodiment introduces bridging near-field coupling in a two-state acoustic system and realizes bound states in an acoustic Friedrich-Wintergen continuum with a highly asymmetric structure. The bridging near-field coupling is provided by a bridging tube between two air cavities with different cross-sectional areas and different cavity depths. It can be tuned by changing the bridging near-field coupling, which allows for the effective construction of bound states in both continuums and quasi-continuums with tunable characteristics.

[0081] To demonstrate the above concepts, this embodiment first designs the proposed system to realize bound states in the Friedrich-Wintergen continuum. This is theoretically verified by the pure eigenvalues ​​of the modes and experimentally demonstrated by the vanishing linewidth of the reflection curve. Furthermore, by altering the position of the bridging tube, we deviate from the conditions of bound states in the continuum, establishing a quasi-continuum bound state whose radiation loss precisely compensates for the inherent losses of the proposed system, resulting in perfect absorption. Compared to previous studies on realizing bound states in the acoustic continuum based on radiation coupling, this scheme demonstrates greater freedom in bound state modulation techniques and provides opportunities for more asymmetric bound state support systems in the continuum by introducing bridging near-field coupling. Our work proposes a new theoretical design and application platform for bound states in the acoustic continuum, which will pave the way for the development of high-Q and asymmetric acoustic devices.

[0082] The above scheme will be described in detail below.

[0083] I. The concept of bound states in the Friedrich-Wintergen continuum with bridging near-field coupling

[0084] Bound states in the Friedrich-Wintergen continuum are a unique phenomenon arising from the disruptive interference of multiple radiation modes within a structure. In time-coupled-mode theory, when two resonances are located in the same cavity and coupled to the same radiation channel, a Hamiltonian matrix for the system can be obtained:

[0085]

[0086] here The resonant mode of the cavity is represented by j, where j is the cavity index (j = 1, 2), and ω j and γ j κ and κ represent the resonant angular frequency and radiation attenuation rate of the cavity, respectively. Let represent the near-field and far-field couplings of cavity 1 and cavity 2, respectively. Through mathematical calculations based on formula (1), the conditions for bound states in the Friedrich-Wintergen continuum can be obtained, where the imaginary part of one eigenvalue of the Hamiltonian matrix is ​​equal to 0, as follows:

[0087]

[0088] As shown in Equation (2), when γ1≈γ2 or κ≈0, the bound states in the Friedrich-Wintergen continuum exist in ω1≈ω2. In previous studies, such bound states in the Friedrich-Wintergen continuum have been observed in two symmetrical cavities. However, for asymmetric acoustic systems with ω1≠ω2 and γ1≠γ2, we need to adjust the value of κ to construct a bound state in the continuum. In this study, we introduce a bridging tube to modulate near-field coupling in a two-state system consisting of two asymmetric cavities, as shown in Equation (2). Figures 1a-1b As shown. We effectively modulate the bridge proximity field coupling of the two cavities by modulating the diameter and position of the bridge nozzle, so that the two-state system satisfies the condition of Equation (2) and results in a bound state in the continuum.

[0089] II. Constructing bound states in the Friedrich-Wintergen continuum with bridging near-field coupling

[0090] In the following section, this embodiment will theoretically demonstrate how bound states in the Friedrich-Wintergen continuum can be constructed in the proposed system by adjusting the bridging near-field coupling. Then, the two eigenvalues ​​of the Hamiltonian matrix H shown in Equation (1) can be derived as follows:

[0091]

[0092]

[0093] here As a conceptual proof of the near-field coupling κ contribution, we first consider a two-state system with varying ω2 / ω1 values, where γ1 = 0.2ω1 and γ2 = 0.04ω2. Figure 1c As shown, for an asymmetric two-state system with varying ω2 / ω1, bound states in the Friedrich-Wintergen continuum can be realized by appropriately adjusting the value of κ. Here, Q rad1 =Re{σ1} / (2Im{σ1}), where Re{σ1} and Im{σ1} are the real and imaginary parts of σ1, respectively. Furthermore, for asymmetric two-state systems with varying γ2 / γ1 (ω1 = 1 Hz, ω2 = 1.2 Hz), bound states in the Friedrich-Wintergen continuum can also be realized by appropriately adjusting the value of κ, such as... Figure 1d As shown.

[0094] The results shown in Figure 1 correspond to a two-state system with variations in the geometry of the coupled resonators and the bridging connection. In the following analysis, a system with fixed resonators but varying bridging connections will be discussed. In this embodiment, the parameters of the two resonators are set as ω2 / ω1 = 1.2, γ2 / γ1 = 0.24, ω1 = 1Hz, and γ1 = 0.2ω2, and as follows... Figures 2a-2cAs shown, when κ approaches -0.129, it reaches a bound state in the Friedrich-Wintergen continuum, witnessing the zero imaginary part of σ1 and an infinitely high Q. rad The results in Figure 1-2 show that efficient modulation of κ provides a feasible approach for constructing bound states in the Friedrich-Wintergen continuum in asymmetric two-state systems.

[0095] III. Observing the bound states and bridging near-field coupling in the Friedrich-Wintergen continuum

[0096] This embodiment proposes a practical dual-cavity system with a bridging nozzle to experimentally verify the existence of bound states in a Friedrich-Wintergen continuum with bridging proximity field coupling. For example... Figure 3a As shown, the two cavities are configured with different cross-sectional areas and different cavity depths (lengths). Cavity 1 has a width (W1) of 48 mm, a height (H1) of 48 mm, and a length (l1) of 189 mm. Cavity 2 has a width (W2) of 15 mm, a height (H2) of 28 mm, and a length (l2) of 160 mm. The characteristic values ​​of cavities 1 and 2 are 437.36 + 83.83i Hz and 516.85 + 17.54i Hz, respectively, which means ω2 / ω1 = 1.18 and γ2 / γ1 = 0.21. To introduce κ, a bridging pipe is added between the two cavities, which can adjust the diameter of the pipe (d). a ) or the distance between pipes (l h This is used to adjust the bridging near-field coupling between the two cavities. h It is the distance from the center of the tube to the front surface of the dual-cavity system.

[0097] Since the bound states in a continuum are completely isolated modes and do not interact with the incident waves from the outside, both theoretically and experimentally, the disappearance of the resonance peaks and the disappearance of the linewidths of the reflection, absorption, and transmission curves of the bound states in the continuum can be observed. This indicates that the bound state-supported system in the continuum cannot be excited and has an infinitely high Q coefficient. Figure 3b and Figure 3c As shown, by changing the diameter or position of the bridge tube in the simulation, when d a =27mm and l h When the linewidth is 146 mm, the disappearance of the reflection amplitude linewidth can be observed. This embodiment also calculates the characteristic frequency of the proposed system at the disappearance linewidth, showing a pure true characteristic frequency of 1074.7 Hz, verifying the existence of bound states in the Friedrich-Wintergen continuum, such as... Figure 3d As shown. Furthermore, Figure 3dThe pressure and sound intensity fields shown indicate that no sound waves radiate to the far field of the two-cavity system, demonstrating the characteristics of bound states in the Friedrich-Wintergen continuum. In the experiment, the reflection amplitude (|r|) of the two-cavity system was measured at different tube diameters or spacings to examine the vanishing of resonance peaks and linewidth. First, the tube spacing was fixed at 146 mm, and the tube diameters were varied. Figure 3e As shown, when d a =2.2mm and d a At d = 8.4 mm, the dual-cavity system supports leakage mode, which leads to the resonance peak in the reflection curve. However, when d a At 27 mm, the dual-cavity system supports bound states in a pure Friedrich-Wintergen continuum, thus exhibiting a flat profile near 1074.7 Hz, indicating the disappearance of the resonance peak and linewidth. Similarly, the evolution of bound states in the Friedrich-Wintergen continuum of leakage modes can be tracked by fixing the tube diameter and varying the tube spacing, as shown... Figure 3f As shown. Therefore, by analyzing the reflection coefficient and characteristic frequency of the proposed dual-cavity system, we comprehensively demonstrate the observation of bound states in the acoustic Friedrich-Wintergen continuum with bridging near-field coupling.

[0098] IV. Perfect Acoustic Absorption Based on Bound States in Quasi-continuum

[0099] By deviating from the conditions of bound states in a continuum, a completely isolated bound state in a continuum can be transformed into a bound state in a quasi-continuum, capable of interacting with external incident waves while also possessing a high radiation quality factor. Bound states in a quasi-continuum provide an ideal way to achieve frequency-selective ultra-narrowband acoustic absorption. As shown in Figures 1-3, the radiation loss of the proposed dual-cavity system can be effectively modulated by adjusting the bridging connector. Perfect acoustic absorption can be achieved when the radiation loss and intrinsic loss reach the critical coupling condition. Compared to conventional acoustic systems that utilize relatively high intrinsic losses to achieve perfect absorption, the bound state system in a quasi-continuum can achieve perfect absorption with considerably low intrinsic losses, resulting in an extremely narrow operating bandwidth.

[0100] To achieve perfect acoustic absorption in a dual-cavity system, we can use time-coupled mode theory to evaluate the absorption coefficient of the coupled system:

[0101]

[0102] in Γ represents the incident wave. m(n) This indicates the inherent decay rate of the cavity. Indicates resonance The resulting re-radiation. It can be used... To calculate Γ based on the relationshipm(n) The value of is given by , where r0 is the reflection coefficient of the system under normal incident resonance, and m and n are cavity indices (m = 1, n = 2). Therefore, the reflection coefficient of the entire system is:

[0103]

[0104] The sound absorption coefficient can then be calculated based on the following relationship:

[0105] α = 1 - |r| 2

[0106] like Figure 4a As shown, a bound-state support system in a quasi-continuum was designed, with the same geometric parameters as the two cavities in Figure 3, and the bridge tube was set to d. a =27mm, l h =50mm. The characteristic frequency of the bound states in the quasi-continuum supported by this system is 732.94 + 4.68i Hz. Without inherent (thermoviscous) losses, the pressure and acoustic fields of the bound states in this quasi-continuum exhibit leakage characteristics. Figure 4a ), which differs from the location characteristics of bound states in a continuum ( Figure 3d In practical quasi-continuum bound-state supported systems, intrinsic losses completely compensate for radiation losses, and then perfect absorption with a narrow bandwidth can be observed both theoretically and experimentally. Figure 4b This proves the correctness of the theoretical results.

[0107] The above results demonstrate the capability of bound states in the Friedrich-Wintergen continuum with tunable bridging near-field coupling in targeted narrowband acoustic absorption. More importantly, these results validate that bridging near-field coupling can serve as an effective tool for tuning the system's radiation quality factor, which will facilitate the application of bound states in the acoustic continuum to improve tunability.

[0108] V. Bound-state sound-absorbing structures in quasi-continuum

[0109] This embodiment also obtains a bound-state sound-absorbing structure in a quasi-continuum based on the above-described method for constructing bound states in a continuum, such as... Figure 6-8 As shown, it includes a first sound-absorbing sub-cavity 1, a second sound-absorbing sub-cavity 2, and a bridging pipe 3, with the two ends of the bridging pipe 3 connected to the first sound-absorbing sub-cavity 1 and the second sound-absorbing sub-cavity 2, respectively.

[0110] The first sound-absorbing cavity 1 and the second sound-absorbing cavity 2 have different cross-sectional areas and cavity depths, and are two cavities with asymmetrical heights.

[0111] Different diameters and positions of the bridge pipe 3 correspond to different sound absorption effects of the bound state sound-absorbing structure in the quasi-continuum.

[0112] The first sound-absorbing cavity 1 and the second sound-absorbing cavity 2 are also structures whose dimensions can be pre-adjusted.

[0113] The cross-sectional shape of the bridge pipe 3 can be circular, polygonal, irregular, etc., but is preferably circular.

[0114] The wall thickness of the first sound-absorbing cavity 1, the second sound-absorbing cavity 2, and the bridging pipe 3 is preferably within the range of 4mm to 5.5mm.

[0115] Both the first sound-absorbing cavity 1 and the second sound-absorbing cavity 2 can be cubic, spherical, irregular, or other structures, with a cuboid structure being preferred.

[0116] This solution provides a preferred bound-state sound-absorbing structure in a quasi-continuum with the following dimensions: the first sound-absorbing sub-cavity 1 has dimensions of 48mm*48mm*189mm; the second sound-absorbing sub-cavity 2 has dimensions of 15mm*28mm*160mm; the bridging pipe 3 has a circular cross-sectional shape with a diameter of 27mm; the distance from the center of the bridging pipe 3 to the front surface of both the first and second sound-absorbing sub-cavities 1 and 2 is 50mm; the thickness of the bridging pipe 3, the thickness of the sidewall 4 of the first sound-absorbing sub-cavity 1, and the thickness of the sidewall 4 of the second sound-absorbing sub-cavity 2 are all 5.5mm.

[0117] The material of the bound-state sound-absorbing structure in the quasi-continuum is photosensitive resin, and the whole structure is a one-piece molded structure.

[0118] Experiments were conducted on the dimensions of the bound-state sound-absorbing structure in the preferred quasi-continuum described above, and the corresponding sound absorption characteristic curves were obtained as follows: Figure 4b As shown, it achieves near-perfect and perfect sound absorption in the 720-740Hz range.

[0119] VI. Conclusion

[0120] This embodiment demonstrates the effect of bridging near-field coupling in a two-state acoustic system on the bound states in the constructed acoustic Friedrich-Wintergen continuum. A further two-cavity system is proposed to verify the theoretical results. This two-cavity system consists of two highly asymmetric cavities and a bridging tube. By adjusting the diameter and position of the bridging tube, the bridging near-field coupling can be effectively tuned. By studying the reflection characteristics and eigenvalues ​​of the tuned two-cavity system, the disappearance of resonance peaks, linewidth loss, and purely real eigenvalues ​​of the bound states in the Friedrich-Wintergen continuum are observed theoretically and experimentally.

[0121] Furthermore, this embodiment, by adjusting the position of the bridging pipe, deviates from the conditions for bound states in a continuum to obtain bound states in a quasi-continuum, allowing for perfect absorption. In this designed bound-state-support system in a quasi-continuum, although the intrinsic loss is small, the low radiation loss of the bound states in the quasi-continuum precisely compensates for the intrinsic loss, thus achieving the critical coupling condition for perfect absorption. Experimental, simulation, and theoretical results are in good agreement, demonstrating the reliability of the theoretical analysis.

[0122] The field of bound states in acoustic continuums continues to develop rapidly, with a wealth of modulation techniques anticipated to advance the framework and applications of bound states in acoustic continuums. This embodiment provides an in-depth study of bound states in acoustic Friedrich-Wintergen continuums with bridging near-field coupling in asymmetric systems, which will contribute to the framework and applications of bound states in acoustic continuums.

[0123] VII. Experimental Section

[0124] Numerical simulation: The simulation (numerical calculation) was performed using the commercial finite element software COMSOL Multiphysics, with the preset "Pressure Acoustics, Frequency Domain" module. The material in the domain was air, set to a static air density ρ = 1.21 kg / m³. 3 The speed of sound is c = 343 m / s. The dynamic viscosity of air is μ = 1.81 × 10⁻⁶. -5 N·S / m 2 The preset ambient temperature was T = 293.15 K (20℃). An "acoustic hard boundary" condition was set in the simulation, meaning the structural boundary has perfect reflection and no wave transmission. The characteristic frequencies and characteristic fields of the proposed dual-cavity system can be calculated through characteristic frequency simulation. The reflection and absorption coefficients can be calculated through frequency domain simulation. In the frequency domain simulation, the "thermoviscous boundary layer impedance" is used to calculate the thermoviscous loss of the proposed dual-cavity system.

[0125] Manufacturing: The experimental samples were manufactured using 3D printing technology with photosensitive resin (UV curable resin) as the base material, using laser stereolithography (SLA, 140μm) and 3D printing technology (manufacturing accuracy of 0.1mm).

[0126] Experimental Measurements: The experiment was conducted in an impedance tube. During the measurement, a loudspeaker was mounted at the bottom center of one of the cavities, and the sample was connected to a waveguide with the same cross-section. The material was placed at the end of the waveguide during the experiment. Two 1 / 4-inch microphones (Brüel) were used in the experiment. (Type-4187). These microphones are designated as microphone A and microphone B, respectively. They are placed in specific locations to measure the amplitude and phase of the pressure. A Brüel microphone with a radius of 50 mm was used in this experiment. Impedance tube.

[0127] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for constructing bound states in a continuum, characterized in that, Includes the following steps: A bridge pipe is installed to connect the two asymmetric cavities in a two-state system consisting of two asymmetric cavities; Construct the Hamiltonian matrix of the two-state system and derive the formulas for calculating the two eigenvalues ​​of the Hamiltonian matrix; By adjusting the near-field coupling contribution in the Hamiltonian matrix, the changes in the real and imaginary parts of the two eigenvalues ​​and the radiation quality factor are observed until the bound state structure in the Friedrich-Wintergen continuum is constructed. The method adjusts the near-field coupling contribution in the Hamiltonian matrix by modulating the diameter and position of the bridge connector.

2. The method for constructing bound states in a continuum according to claim 1, characterized in that, The expression for the Hamiltonian matrix is: In the formula, This is the calculated value of the Hamiltonian matrix. and These are the resonant angular frequency and radiation attenuation rate of the cavity, respectively. This is the cavity index, with a value of 1 or 2, representing different cavities. Contributes to near-field coupling between two asymmetric cavities. It is the imaginary unit.

3. The method for constructing bound states in a continuum according to claim 2, characterized in that, The expressions for calculating the two eigenvalues ​​of the Hamiltonian matrix are as follows: In the formula, For one of the eigenvalues, For another eigenvalue, The resonant angular frequency of a cavity. The resonant angular frequency of another cavity, The radiation attenuation rate of a cavity, The radiation attenuation rate of the other cavity.

4. The method for constructing bound states in a continuum according to claim 3, characterized in that, The value of the radiation quality factor is or ,in , for The real part, for The imaginary part.

5. The method for constructing bound states in a continuum according to claim 2, characterized in that, When there are eigenvalues ​​with zero imaginary part and an infinitely high radiation quality factor, a bound state structure in the Friedrich-Wintergen continuum is constructed.

6. The method for constructing bound states in a continuum according to claim 1, characterized in that, The method also includes using time-coupled mode theory to calculate the sound absorption coefficient of the two-state system and evaluate the sound absorption effect of the two-state system. The formula for calculating the sound absorption coefficient is as follows: In the formula, For cavity j, the resonance mode is... Indicates the incident wave, Indicates cavity m or n The inherent decay rate, Indicates resonance The resulting reradiation, where m and n are cavity indices, m=1, n=2, The reflection coefficient of the entire system. is the sound absorption coefficient.

7. The method for constructing bound states in a continuum according to claim 6, characterized in that, The formula for calculating the intrinsic decay rate is: In the formula, It is the reflection coefficient of the system when it resonates under normal incidence.

8. The method for constructing bound states in a continuum according to claim 6, characterized in that, The method further includes adjusting the position of the bridging pipe to deviate from the conditions of the bound states in the continuum to obtain the bound states in the quasi-continuum, so that the low radiation loss of the bound states in the quasi-continuum just compensates for the intrinsic loss, achieving the critical coupling condition for perfect absorption.

9. A sound-absorbing structure obtained based on a confined state construction method in a continuum as described in any one of claims 1-8, characterized in that, It includes a first sound-absorbing sub-cavity (1), a second sound-absorbing sub-cavity (2), and a bridging pipe (3), wherein the two ends of the bridging pipe (3) are respectively connected to the first sound-absorbing sub-cavity (1) and the second sound-absorbing sub-cavity (2); The cross-sectional area and cavity depth of the first sound-absorbing sub-cavity (1) and the second sound-absorbing sub-cavity (2) are different; The different diameters and positions of the bridge pipe (3) correspond to different sound absorption effects of the bound state sound-absorbing structure in the quasi-continuum; The wall thickness of the first sound-absorbing sub-cavity (1), the second sound-absorbing sub-cavity (2), and the bridge pipe (3) is all within the range of 4mm to 5.5mm.

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