CN117709137A - Binding state construction method in continuum and sound absorption structure - Google Patents
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Abstract
The invention relates to a constraint state construction method in a continuum and a sound absorption structure, wherein the method comprises the steps of arranging a bridging tube in a two-state system consisting of two asymmetric cavities; constructing a Hamiltonian matrix of a two-state system, and deducing calculation formulas of two characteristic values; observing the changes of the real part and the imaginary part of the two eigenvalues and the radiation quality factor by adjusting the near field coupling contribution in the Hamiltonian matrix until a Friedel-crafts-Wen Tegen (FW) BICs structure is constructed; the sound absorption coefficient of the two-state system is calculated by adopting a time coupling mode theory, the position of the bridge connection pipe is adjusted, and the conditions of the BICs are deviated to obtain quasi-BICs, so that the low radiation loss of the quasi-BICs just compensates the internal loss, and the critical coupling condition of perfect absorption is achieved. Compared with the prior art, the invention opens up a way for researching FW BICs with bridging near field coupling in an asymmetric system, and provides opportunities for developing acoustic devices with high quality factors and asymmetric wave control.
Description
Technical Field
The invention relates to the field of acoustic devices, in particular to a method for constructing a binding state in a continuum and a sound absorption structure.
Background
In recent years, the bound state in the continuum has been of increasing interest due to its physical properties of resistance to taste, such as infinitely high quality factor (Q factor) and enhanced wave-substance interactions.
The bound state in the continuum is a completely isolated mode without radiation, but is present in the continuum spectrum of the radiated wave, optical, elastic and acoustic systems. The bound state in the continuum provides many physical properties that are resistant to human taste, such as an infinitely high quality factor and enhanced wave-substance interactions. When deviating from the bound state in a pure continuum, a so-called bound state in a quasi-continuum can be achieved, which possesses a very large Q-factor and allows interactions between the bound state in the quasi-continuum and the external environment. There are various physical formation mechanisms of the bound states in the continuum, such as the bound states in the symmetric protected continuum induced by geometrical symmetry properties, the bound states in the occasional continuum modulated based on wave field distribution, and the bound states in the Friedrich-Wen Tegen (Friedrich-Wintgen) continuum, fabry-perot (Fabry-perot) continuum achieved by adjusting far field and/or near field coupling between resonances. The different formation mechanisms and various modulation techniques help to efficiently manipulate the characteristics of the bound states in the continuum and the bound states in the quasi-continuum, resulting in various high performance and tunable lasers, sensors, non-linear generators, and the like.
In recent years, the bound state in acoustic continuum has gained increasing attention. Since the first discovery of the bound state in a symmetrically protected continuum in the "waveguide plate" system in the 60 s of the 20 th century, much research has been focused on this area of research and significant advances have been made in the physical formation mechanisms and applications of the bound state in acoustic continuums. For example, the bound states in a continuum of acoustic symmetry protection, the bound states in a friedrich-Wen Tegen continuum, and the bound states in a so-called "mirror-induced" continuum are achieved in a helmholtz resonator placed on one side of an acoustic waveguide. The confinement state in an acoustic fabry-perot continuum is constructed by modulating the radiated interference between two identical resonators at a distance in a waveguide system. The bound state in the acoustic friedrich-Wen Tegen continuum is achieved by two identical resonators being close to each other and located at the ends of the waveguide, wherein far-field radiation interference between the two resonators substantially contributes to the formation of the bound state in the continuum. However, despite the great importance and great potential of near field coupling in determining the mass of the bound states in the continuum, previous studies have rarely explored the bridging near field coupling phenomenon in the bound state configuration in acoustic friedrich-Wen Tegen continuum in experiments.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for constructing a bound state in a continuum and a sound absorption structure, and opens up a way for researching the bound state in an acoustic friedrich-Wen Tegen continuum with bridging near-field coupling in an asymmetric system.
The aim of the invention can be achieved by the following technical scheme:
a method of constrained state construction in a continuum comprising the steps of:
a bridge connection pipe for connecting the two asymmetric cavities is arranged in a two-state system consisting of the two asymmetric cavities;
constructing a Hamiltonian matrix of the two-state system, and deducing a calculation formula of two characteristic values of the Hamiltonian matrix;
and (3) observing the real part, the imaginary part and the change of the radiation quality factors of the two eigenvalues by adjusting the near field coupling contribution in the Hamiltonian matrix until a bound state structure in the Friedel-crafts-Wen Tegen continuum is constructed.
Further, the method adjusts the near field coupling contribution in the hamilton matrix by modulating the diameter and position of the bridge tube.
Further, the Hamiltonian matrix has the following expression:
wherein H is the calculated value of Hamiltonian matrix, omega j And gamma j The resonant angular frequency and the radiation attenuation rate of the cavity are respectively, j is a cavity index, the value is 1 or 2, the different cavities are respectively represented, kappa is the near field coupling contribution of the cavity 1 and the cavity 2, and i is an imaginary unit.
Further, the calculation expression of the two eigenvalues of the hamiltonian matrix is:
in sigma 1 For one of the eigenvalues, sigma 2 As another characteristic value omega A Is the resonant angular frequency of a cavity omega R For the resonant angular frequency of the other cavity, gamma A Is the radiation attenuation rate of a cavity, gamma B Is the radiation decay rate of the other cavity.
Further, the value of the radiation quality factor is log 10 (Q rad1 ) Or log of 10 (Q rad2 ) Wherein Q is rad1 ＝Re{σ 1 }/(2Im{σ 1 })，Re{σ 1 [ sigma ] 1 Is the real part of (a), im { sigma }, of 1 [ sigma ] 1 Is a virtual part of (c).
Further, when there are eigenvalues with zero imaginary part and infinitely high radiation quality factors, the bound state structure in the friedrich-Wen Tegen continuum is constructed.
Further, the method further comprises the step of calculating the sound absorption coefficient of the two-state system by adopting a time coupling mode theory and evaluating the sound absorption effect of the two-state system.
Further, the sound absorption coefficient is calculated as:
α＝1-|r| 2
in the method, in the process of the invention,is the resonance mode of cavity j, +.>Representing the incident wave Γ m(n) Representing the natural decay rate of the cavity m or n,representing resonance +.>The re-radiation induced, m and n are the cavity indices, m=1, n=2, r is the overall systemReflection coefficient, α is the sound absorption coefficient.
Further, the computational expression of the inherent decay rate is:
wherein r is 0 Is the reflection coefficient of the system when resonating at normal incidence.
Further, the method also includes offsetting the condition of the bound state in the continuum by adjusting the position of the bridge pipe to obtain the bound state in the quasi-continuum, such that the low radiation loss of the quasi-bound state exactly compensates for the intrinsic loss, achieving the critical coupling condition of perfect absorption.
The invention also provides a sound absorption structure in a quasi-continuum obtained based on the constraint state construction method in the continuum, which comprises a first sound absorption cavity, a second sound absorption cavity and a bridging tube, wherein two ends of the bridging tube are respectively communicated with the first sound absorption cavity and the second sound absorption cavity;
the cross-sectional areas and the cavity depths of the first phonon absorbing cavity and the second phonon absorbing cavity are different;
different diameters and positions of the bridging tube correspond to different sound absorption effects of the bound sound absorption structure in the quasi-continuous body;
the wall thickness of the first phonon absorbing cavity, the second phonon absorbing cavity and the bridging tube is within the range of 4 mm-5.5 mm.
Further, the cross-sectional shape of the bridge tube is circular.
Further, the first phonon absorbing cavity and the second phonon absorbing cavity are both cuboid structures.
Further, the first phonon-absorbing cavity has a size of 48mm x 189mm; the size of the second phonon absorbing cavity is 15mm x 28mm x 160mm; the cross section of the bridging tube is circular, and the diameter of the bridging tube is 27mm; the distance from the center of the bridging tube to the front surfaces of the first and second phonon absorbing cavities is 50mm; the thickness of the bridging tube, the thickness of the side wall of the first phonon absorbing cavity and the thickness of the side wall of the second phonon absorbing cavity are all 5.5mm.
Further, the material of the bound sound absorption structure in the quasi-continuous body is photosensitive resin.
Further, the bound sound absorption structure in the quasi-continuous body is integrally formed.
Further, the bound sound absorbing structure in the quasi-continuum has a perfect sound absorbing effect of narrow bandwidth.
Compared with the prior art, the invention has the following advantages:
(1) The invention provides a two-state system consisting of two asymmetric cavities and a bridging tube, the near-field coupling effect of the proposed system can be effectively regulated by adjusting the diameter and the position of the bridging tube, the bound state in the friedrich-Wen Tegen continuum is realized, a way for researching the bound state in the acoustic friedrich-Wen Tegen continuum with bridging near-field coupling in the asymmetric system is opened up, the field of the bound state in the acoustic continuum is enriched, and opportunities are provided for developing acoustic devices with high Q factors and asymmetric wave control.
(2) The present invention proposes to modulate the binary system to deviate from the bound state in the continuum, which provides a bound state in the quasi-continuum, which enables a high Q perfect absorption when the radiation loss and intrinsic loss of the bound state support system in the quasi-continuum reach critical coupling conditions. The experimental results verify the theoretical and simulation results, demonstrating the existence of bound states in the continuum and perfect absorption based on bound states in the quasi-continuum.
(3) The bound sound absorption structure in the quasi-continuous body has the advantages of simple structure, low manufacturing cost, high adjustability and the like.
Drawings
FIG. 1a is a schematic diagram of near field and far field interactions between two resonant modes;
FIG. 1b is a schematic diagram of the interaction of two corresponding two-state systems consisting of two acoustic resonators with bridge connection and sharing the same radiation field;
FIG. 1c shows the radiation quality factor log 10 (Q rad1 ) With kappa and omega in the proposed two-state system 2 /ω 1 Schematic diagram of conceptual demonstration of variation, in analysis, parameter is set to γ 1 ＝0.2ω 1 ，γ 2 ＝0.04ω 2 ；
FIG. 1d shows the radiation quality factor log 10 (Q rad1 ) With kappa and gamma in the proposed two-state system 2 /γ 1 Schematic diagram of concept demonstration of variation; in the analysis, the parameter is set to ω 1 ＝1Hz，ω 2 ＝1.2Hz；
FIG. 2a is a schematic diagram of the real part of eigenvalues of a two-state system;
FIG. 2b is a schematic diagram of the imaginary part of the eigenvalues of a two-state system;
FIG. 2c is a graph showing the radiation quality factor of a two-state system with parameters set to ω as κ varies 2 /ω 1 =1.2 and γ 2 /γ 1 ＝0.24；
FIG. 3a is a schematic illustration of an experimental sample, the wall thickness being set to 5.5 mm;
FIG. 3b shows a dual chamber system with d a And ω/2π change reflection amplitude (|r|) schematic, tube distance l h Fixed at 146 mm;
FIG. 3c shows a dual chamber system with l h And ω/2π change reflection amplitude (|r|) schematic, tube diameter d a Fixing to be 27mm;
FIG. 3d is d a =27 mm and l h Simulation results of the characteristic frequency, pressure field (represented by color) and acoustic intensity field (represented by green arrow) of the dual-cavity system=146 mm;
FIG. 3e is diameter d a Schematic of experimental and simulated reflection amplitudes (|r|) for two-chamber systems of 2.2mm, 8.4mm and 27mm, distance l of tube h Fixed at 146 mm;
FIG. 3f is a pipe distance l h Experimental and simulated reflection amplitude (|r|) schematic diagrams for 50mm, 90mm and 146mm dual-chamber systems, tube diameter d a Fixed at 27mm;
FIG. 4a is at d a =27 mm and l h Characteristic frequency and pressure field of a dual-cavity system of =50mmSchematic of simulation results (represented by color) and acoustic intensity field (represented by green arrow);
FIG. 4b is at d a =27 mm and l h Theoretical, experimental and simulated absorption coefficient diagrams at=50mm, theoretical results are calculated using time-coupled die theory;
FIG. 5 is a schematic flow chart of a method for constructing a bound state in a continuum according to an embodiment of the invention;
FIG. 6 is a schematic front view of a bound sound absorbing structure in a quasi-continuum according to an embodiment of the invention;
FIG. 7 is a schematic left-hand view of a bound sound absorbing structure in a quasi-continuum according to an embodiment of the invention;
FIG. 8 is a schematic top view of a bound sound absorbing structure in a quasi-continuum according to an embodiment of the invention;
in the figure, 1, a first phonon absorbing cavity, 2, a second phonon absorbing cavity, 3, a bridging tube, 4 and a side wall.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that: like reference numerals and letters denote like items in the following figures, and thus once an item is defined in one figure, no further definition or explanation thereof is necessary in the following figures.
Example 1
As shown in fig. 5, the embodiment provides a method for constructing a binding state in a continuum, which includes the following steps:
s1: a bridge connection pipe for connecting the two asymmetric cavities is arranged in a two-state system consisting of the two asymmetric cavities;
s2: constructing a Hamiltonian matrix of a two-state system, and deducing calculation formulas of two characteristic values of the Hamiltonian matrix;
s3: and (3) observing the real part, the imaginary part and the change of the radiation quality factors of the two eigenvalues by adjusting the near field coupling contribution in the Hamiltonian matrix until a bound state structure in the Friedel-crafts-Wen Tegen continuum is constructed.
As a preferred embodiment, the above method further comprises S4: calculating the sound absorption coefficient of the two-state system by adopting a time coupling mode theory, and evaluating the sound absorption effect of the two-state system;
by adjusting the position of the bridge connection pipe, the condition of the bound state in the continuum is deviated to obtain the bound state in the quasi-continuum, so that the low radiation loss of the bound state in the quasi-continuum just compensates the internal loss, and the critical coupling condition of perfect absorption is achieved.
This embodiment introduces bridged near field coupling in a two-state acoustic system and achieves a bound state in an acoustic friedrich-Wen Tegen continuum with a highly asymmetric structure. The bridging near field coupling is provided by a bridging tube between two air cavities having different cross-sectional areas and different cavity depths. The tuning can be controlled by changing the bridging near field coupling, which can effectively construct the bound state in the continuum and the bound state in the quasi-continuum with tunable properties.
To demonstrate the above concept, the present embodiment first devised the proposed system to achieve a bound state in the friedrich-Wen Tegen continuum, which is theoretically verified by the pure eigenvalues of the mode, experimentally witnessed by the disappearance of the linewidth of the reflection curve. Furthermore, we have established a bound state in a quasi-continuum by changing the condition that the position of the bridge tube deviates from the bound state in the continuum, which has radiation losses that exactly compensate for the intrinsic losses of the proposed system, resulting in perfect absorption. Compared with the previous research of realizing the constraint state in the acoustic continuum based on radiation coupling, the scheme embodies higher freedom of the constraint state modulation technology in the continuum and provides opportunities for a constraint state support system in more asymmetric continuum by introducing bridging near field coupling. Our work suggests a new theoretical design and a tethered application platform in acoustic continuum that will pave the way for developing high Q and asymmetric acoustic devices.
The above-described scheme is specifically described below.
1. Concept of tethered states in friedrichs-Wen Tegen continuum with bridged near field coupling
The binding state in the friedrich-Wen Tegen continuum is a unique phenomenon that results from destructive interference of multiple radiation modes in a structure. In the theory of time coupling mode, when two resonances are located in the same cavity and coupled to the same radiation channel, a hamiltonian matrix of a system can be obtained:
here, theRepresents the resonant mode of the cavity, where j is the cavity index (j=1, 2), ω j And gamma j The resonant angular frequency and the radiation attenuation rate of the cavity are respectively. Kappa and->Representing near field and far field coupling of the cavity 1 and the cavity 2, respectively. By mathematical calculation based on formula (1), the condition that the constraint state in the friedrich-Wen Tegen continuum is satisfied can be obtained, wherein the imaginary part of one eigenvalue of the hamilton matrix is equal to 0, which is:
when gamma is as shown in formula (2) 1 ≈γ 2 Or kappa.apprxeq.0, the bound state in the Friedel-crafts Wen Tegen continuum exists in omega 1 ≈ω 2 . In previous studies, the tethered state in this friedrich-Wen Tegen continuum has been observed in two symmetrical cavities. However, for omega 1 ≠ω 2 And gamma 1 ≠γ 2 We need to adjust the value of k to construct the bound state in one continuum. In this study we introduced a bridge tube in a two-state system consisting of two asymmetric cavities to modulate near field coupling, as shown in fig. 1a-1 b. By modulating the diameter and position of the bridging tube, the bridging near field coupling of the two cavities is effectively regulated, so that the two-state system meets the condition of the formula (2) and leads to the constraint state in the continuum.
2. Construction of bound states in friedrichs-Wen Tegen continuum with bridged near field coupling
In the following, this embodiment will demonstrate in theory how the tethering states in the friedrich-Wen Tegen continuum are built by adjusting the bridged near field coupling in the proposed system. Then, two eigenvalues of the hamiltonian matrix H shown in equation (1) can be derived as:
here, the As a conceptual demonstration of near-field coupling κ contribution, we first consider an ω 2 /ω 1 Two-state system of numerical value change, gamma 1 ＝0.2ω 1 ，γ 2 ＝0.04ω 2 . As shown in fig. 1c, for ω 2 /ω 1 A modified asymmetric binary system can achieve the tethered state in the friedrich-Wen Tegen continuum by properly adjusting the value of κ. Here, Q rad1 ＝Re{σ 1 }/(2Im{σ 1 }), where Re { sigma }, is 1 Sum Im { sigma } 1 [ sigma ] 1 Real and imaginary parts of (a) are provided. Further, for gamma 2 /γ 1 Varying asymmetric binary system (omega 1 ＝1Hz，ω 2 =1.2 Hz), the bound state in the friedrichs-Wen Tegen continuum can also be achieved by appropriate adjustment of the value of κ, as shown in fig. 1 d.
The above results in fig. 1 correspond to a two-state system of coupled resonator geometry change and bridge connection change. In the following, a system with fixed resonators but varying bridging connections will be analyzed. The present embodiment sets the parameters of the two resonators to ω 2 /ω 1 ＝1.2，γ 2 /γ 1 ＝0.24，ω 1 ＝1Hz，γ 1 ＝0.2ω 2 And as shown in FIGS. 2 a-2 c, when kappa approaches-0.129, the bound state in the friedrich-Wen Tegen continuum is reached, witnessing sigma 1 Zero imaginary part and infinite high Q rad . The results in FIGS. 1-2 show that effective modulation of κ provides a viable pathway for the construction of tethered states in the Friedel-crafts-Wen Tegen continuum in an asymmetric binary system.
3. Observing the coupling condition of the bound state and the bridging near field in the friedrich-Wen Tegen continuum
This example presents a practical dual-chamber system with bridging tubes to experimentally verify the existence of tethered states in the friedrich-Wen Tegen continuum with bridging near field coupling. As shown in fig. 3a, the two cavities are arranged with different cross-sectional areas and different cavity depths (lengths). Width of cavity 1 (W 1 ) 48mm, height (H 1 ) 48mm, length (l 1 ) 189mm. Width of cavity 2 (W 2 ) 15mm, height (H 2 ) Is 28mm in length (l 2 ) 160mm. The characteristic values of cavity 1 and cavity 2 are 437.36+83.83iHz and 516.85+17.54i Hz, which means ω 2 /ω 1 =1.18 and γ 2 /γ 1 =0.21. For introducing kappa, a bridging tube is added between the two cavities, the diameter of the tube (d a ) Or distance of the tube (l) h ) To adjust the bridging near field coupling of the two cavities. l (L) h Is the distance from the center of the tube to the front surface of the dual chamber system.
Since the bound state in the continuum is in a completely isolated mode, no interaction with the incident wave from the outside exists, the disappearance of the formants of the bound state in the continuum and the disappearance of the linewidths of the reflection, absorption and transmission curves can be seen in theory and experiment, which indicates that the bound state-support system in the continuum cannot be excited and has an infinitely high Q coefficient. As shown in FIGS. 3b and 3c, by varying the diameter or position of the bridge tube in the simulation, when d a =27 mm and l h At=146 mm, the linewidth of the reflection amplitude can be observed to disappear. The present example also calculates the characteristic frequency of the proposed system at the vanishing line width, showing a true characteristic frequency of 1074.7Hz, verifying the presence of the bound state in the friedrich-Wen Tegen continuum, as shown in fig. 3 d. Furthermore, the pressure field and the acoustic intensity field shown in fig. 3d indicate that no acoustic waves radiate to the far field of the two cavity systems, which indicates the nature of the bound states in the friedrich-Wen Tegen continuum. In the experiment, the reflection amplitude (|r|) of the dual-cavity system at different pipe diameters or pipe pitches was measured to investigate the disappearance of formants and the disappearance of line widths. Firstly, the pipe distance is fixed to be 146mm, and the pipe diameter is changed. As shown in FIG. 3e, when d a =2.2 mm and d a At=8.4mm, the dual-cavity system supports the leakage mode, which results in the formants of the reflection curve. However, when d a At 27mm, the two-chamber system supports the bound state in a pure friedrichs-Wen Tegen continuum, so a flat curve profile is observed around 1074.7Hz, indicating the disappearance of the resonance peak and the disappearance of the line width. In a similar manner, it is also possible to fix the tubeSub-diameters and varying tube distances to track the evolution of the bound state in the friedrichs-Wen Tegen continuum of the leak pattern, as shown in fig. 3 f. Thus, by analyzing the reflectance and characteristic frequency of the proposed dual-cavity system, we fully demonstrate the observation of bound states in acoustic friedrichs-Wen Tegen continuum with bridged near-field coupling.
4. Perfect acoustic absorption based on bound states in quasi-continuum
By deviating from the bound state in the continuum, the bound state in the fully isolated continuum may become a bound state in a quasi-continuum, may interact with external incident waves, and also has a high radiation quality factor. The bound state in the quasi-continuum provides an ideal way to achieve frequency selective ultra-narrow band acoustic absorption. As shown in fig. 1-3, the radiation loss of the proposed dual-cavity system can be effectively modulated by adjusting the bridge. Perfect acoustic absorption can be achieved when the radiation loss and the inherent loss reach critical coupling conditions. The tethered state system in a quasi-continuum can achieve perfect absorption with relatively low intrinsic loss, resulting in an extremely narrow operating band, as compared to conventional acoustic systems that utilize relatively high intrinsic loss to achieve perfect absorption.
To achieve perfect acoustic absorption for a dual-cavity system, we can use the theory of time coupling modes to evaluate the acoustic absorption coefficient of the coupled system:
wherein the method comprises the steps ofRepresenting the incident wave Γ m(n) Indicating the natural decay rate of the cavity, +.>Representing resonance +.>The re-radiation is induced. Can use +.>Is to calculate Γ m(n) Wherein r is a value of 0 Is the reflection coefficient of the system at resonance at normal incidence, m, n is the cavity index (m=1, n=2). Then the reflection coefficient of the whole system is:
the sound absorption coefficient can then be calculated according to the following relationship:
α＝1-|r| 2
as shown in FIG. 4a, a quasi-continuum of constrained-state support system is designed with the same geometry as the two cavities of FIG. 3, and the bridge tube is set to d a ＝27mm，l h =50mm. The characteristic frequency of the bound state in the quasi-continuum supported by the system is 732.94+4.68i Hz. The pressure field and the sound intensity field of the bound state in the quasi-continuum exhibit leakage characteristics without intrinsic (hot tack) losses (fig. 4 a), unlike the localization characteristics of the bound state in the continuum (fig. 3 d). In a practical quasi-continuum in-bound support system, the intrinsic loss completely compensates for the radiation loss, and then a perfect absorption of the narrow bandwidth can be observed both theoretically and experimentally (fig. 4 b), proving the correctness of the theoretical results.
The above results demonstrate the ability of the bound states in friedrichs-Wen Tegen continuum with tunable bridging near field coupling in targeted narrowband acoustic absorption. More importantly, these results demonstrate that bridging near field coupling can be used as an effective tool to adjust the radiation quality factor of the system, which would be beneficial for the application of confinement states in acoustic continuum to improve tunability.
5. Bound sound absorbing structure in quasi-continuum
The embodiment also obtains a bound sound absorption structure in a quasi-continuum according to the method for constructing the bound state in the continuum, and as shown in fig. 6-8, the structure comprises a first phonon absorbing cavity 1, a second phonon absorbing cavity 2 and a bridging tube 3, wherein two ends of the bridging tube 3 are respectively communicated with the first phonon absorbing cavity 1 and the second phonon absorbing cavity 2.
The cross-sectional area and the cavity depth of the first phonon absorbing cavity 1 and the second phonon absorbing cavity 2 are different, and the two cavities are two highly asymmetric cavities.
The different diameters and positions of the bridge tubes 3 correspond to the different sound absorption effects of the bound sound absorption structure in the quasi-continuum.
The first and second phonon-absorbing chambers 1 and 2 are also of a structure of a size that can be adjusted in advance.
The cross-sectional shape of the bridge tube 3 may be circular, polygonal, irregular, etc., preferably circular.
The wall thickness of the first phonon-absorbing cavity 1, the second phonon-absorbing cavity 2 and the bridging tube 3 is preferably within the range of 4 mm-5.5 mm.
The first phonon absorbing cavity 1 and the second phonon absorbing cavity 2 can be in a cubic structure, a sphere structure, an irregular structure and the like, and are preferably in a cuboid structure.
The scheme provides a constraint sound absorption structure in a preferable quasi-continuous body, which has the following dimensions: the size of the first phonon-absorbing cavity 1 is 48mm x 189mm; the dimensions of the second phonon-absorbing chamber 2 are 15mm x 28mm x 160mm; the cross section of the bridging tube 3 is circular, and the diameter is 27mm; the distance from the center of the bridging tube 3 to the front surfaces of the first and second phonon absorbing cavities 1 and 2 is 50mm; the thickness of the bridging tube 3, the thickness of the side wall 4 of the first phonon-absorbing cavity 1 and the thickness of the side wall 4 of the second phonon-absorbing cavity 2 are all 5.5mm.
The material of the bound sound absorption structure in the quasi-continuous body is photosensitive resin, and the whole body is an integrated structure.
The dimensions of the bound sound absorption structure in the above preferred quasi-continuum were tested to obtain the corresponding sound absorption characteristic curve as shown in fig. 4b, achieving near perfect and perfect sound absorption in the 720-740Hz range.
6. Summary
This example demonstrates the effect of bridging near field coupling on the construction of bound states in an acoustic friedrich-Wen Tegen continuum in a two-state acoustic system. A two-chamber system was further proposed to verify the theoretical results. The dual-cavity system consists of two highly asymmetric cavities and a bridging tube, and bridging near-field coupling can be effectively regulated by adjusting the diameter and the position of the bridging tube. By studying the reflection characteristics and eigenvalues of the tuned dual-cavity system, it is observed theoretically and experimentally that the resonance peak of the bound state in the friedrich-Wen Tegen continuum disappears, the linewidth disappears, and the pure real eigenvalue.
In addition, the present embodiment allows perfect absorption by adjusting the position of the bridge tube to deviate from the condition of the bound state in the continuum to obtain a bound state in a quasi-continuum. In the bound-support system in the quasi-continuum of this design, the low radiation loss of the bound in the quasi-continuum exactly compensates for the intrinsic loss, although the intrinsic loss is small, thus achieving the critical coupling condition of perfect absorption. The results of the experiment, the simulation and the theory are all very consistent, and the reliability of theoretical analysis is proved.
The field of tethering states in acoustic continuum is still rapidly evolving so far, and richer modulation techniques are highly desirable to facilitate the framework and application of tethering states in acoustic continuum. This embodiment provides an in-depth investigation of the bound state in an acoustic friedrich-Wen Tegen continuum with bridged near-field coupling in an asymmetric system, which would contribute to the framework and application of the bound state in an acoustic continuum.
7. Experimental part
Numerical simulation: simulation (numerical calculation) was performed using a commercial finite element software COMSOL Multiphysics, preset "pressure acoustics, frequency domain" module. Domain material: air, set to static air density ρ=1.21 kg/m 3 The sound velocity is c=343 m/s. Dynamic viscosity of air is μ=1.81×10 -5 N·S/m 2 The preset ambient temperature is t=293.15K (20 ℃). In the simulation, an "acoustic hard boundary" condition is set, which means that the structural boundary has a perfect reflection and no wave transmission. The proposed dual-cavity can be calculated by the characteristic frequency simulationCharacteristic frequency and characteristic field of the system. The reflection and absorption coefficients can be calculated by frequency domain modeling. In frequency domain simulations, the "hot tack boundary layer impedance" was used to calculate the hot tack loss of the proposed dual-cavity system.
Manufacturing: the experimental samples were manufactured using a laser stereolithography technique (SLA, 140 μm) and a 3D printing technique using a photosensitive resin (UV curable resin) as a base material (manufacturing accuracy is 0.1 mm).
Experimental measurement: the experiment was performed in an impedance tube. During the measurement we mounted a speaker in the bottom center of one of the cavities and connected the sample to a waveguide with the same cross section, the material being placed at the end of the waveguide during the experiment. In the experiment two 1/4 inch microphones (Bruel)type-4187). These microphones are designated as microphone a and microphone B, respectively. They are placed at specific locations to measure the amplitude and phase of the pressure. The experiment used was a radius of 50mm of Bruel +.>An impedance tube.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention by one of ordinary skill in the art without undue burden. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (10)
1. A method of constructing a bound state in a continuum, comprising the steps of:
a bridge connection pipe for connecting the two asymmetric cavities is arranged in a two-state system consisting of the two asymmetric cavities;
constructing a Hamiltonian matrix of the two-state system, and deducing a calculation formula of two characteristic values of the Hamiltonian matrix;
and (3) observing the real part, the imaginary part and the change of the radiation quality factors of the two eigenvalues by adjusting the near field coupling contribution in the Hamiltonian matrix until a bound state structure in the Friedel-crafts-Wen Tegen continuum is constructed.
2. A method of constructing a bound state in a continuum according to claim 1, characterized in that the method adjusts the near field coupling contribution in the hamiltonian matrix by modulating the diameter and position of the bridge tubes.
3. The method of claim 1, wherein the Ha Midu matrix is expressed as:
wherein H is the calculated value of Hamiltonian matrix, omega j And gamma j The resonant angular frequency and the radiation attenuation rate of the cavity are respectively, j is a cavity index, the value is 1 or 2, the different cavities are respectively represented, kappa is the near field coupling contribution of the cavity 1 and the cavity 2, and i is an imaginary unit.
4. A method of constructing a bound state in a continuum according to claim 3, wherein the calculation expression of the two eigenvalues of the hamiltonian matrix is:
in sigma 1 For one of the eigenvalues, sigma 2 As another characteristic value omega A Is the resonant angular frequency of a cavity omega B For the resonant angular frequency of the other cavity, gamma A Is the radiation attenuation rate of a cavity, gamma B Is the radiation decay rate of the other cavity.
5. A method of constructing a bound state in a continuum according to claim 3, wherein the radiation quality factor has a value of log 10 (Q rad1 ) Or log of 10 (Q rad2 ) Wherein Q is rad1 ＝Re{σ 1 }/(2Im{σ 1 })，Re{σ 1 [ sigma ] 1 Is the real part of (a), im { sigma }, of 1 [ sigma ] 1 Is a virtual part of (c).
6. A method of constructing a bound state in a continuum according to claim 3, characterized in that the bound state structure in the friedrich-Wen Tegen continuum is constructed in the presence of eigenvalues with zero imaginary part and infinitely high radiation quality factors.
7. The method of claim 1, further comprising calculating the sound absorption coefficient of the two-state system using time-coupled mode theory, and evaluating the sound absorption effect of the two-state system;
the absorption coefficient is calculated as follows:
α＝1-|r| 2
in the method, in the process of the invention,is the resonance mode of cavity j, +.>Representing the incident wave Γ m(n) Representing the natural decay rate of the cavity m or n,representing resonance +.>The re-radiation induced, m and n are the cavity indices, m=1, n=2, r is the reflection coefficient of the whole system, and α is the sound absorption coefficient.
8. The method of claim 7, wherein the expression for calculating the natural decay rate is:
wherein r is 0 Is the reflection coefficient of the system when resonating at normal incidence.
9. The method of claim 7, further comprising deviating the condition of the bound state in the continuum by adjusting the position of the bridge tube to obtain the bound state in the quasi-continuum such that the low radiation loss of the bound state in the quasi-continuum exactly compensates for the intrinsic loss to achieve the critical coupling condition of perfect absorption.
10. Sound absorbing structure obtained based on the method of construction of a bound state in a continuum according to any of claims 1 to 9, characterized in that it comprises a first phonon cavity (1), a second phonon cavity (2) and a bridging tube (3), two ends of said bridging tube (3) being respectively connected to the first phonon cavity (1) and to the second phonon cavity (2);
the cross-sectional areas and the cavity depths of the first phonon absorbing cavity (1) and the second phonon absorbing cavity (2) are different;
different diameters and positions of the bridging tube (3) correspond to different sound absorption effects of the bound sound absorption structure in the quasi-continuous body;
the wall thickness of the first phonon absorbing cavity (1), the wall thickness of the second phonon absorbing cavity (2) and the wall thickness of the bridging tube (3) are all within the range of 4 mm-5.5 mm.
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