CN113314090B - Controllable acoustic super surface for generating acoustic track angular momentum - Google Patents
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Abstract
The invention discloses a controllable acoustic super surface for generating sound track angular momentum, which comprises a super surface fixing structure and a super surface movable structure, wherein the fixing structure is provided with eight partitions surrounding a symmetry axis in a circle, each partition is internally provided with an outer layer super surface unit, a middle layer super surface unit and an inner layer super surface unit, each movable structure can rotate around the symmetry axis of the fixing structure within a certain range, a row of side branch resonant cavity structures are arranged in the fixing structure of each layer, a gap with a certain angle is formed between the side wall of each movable structure and the resonant cavity structure, and the size of the angle gap is determined by the relative position of the corresponding movable structure and the fixing structure; this simple structure, the shaping is printed to easily 3D, installs and removes the convenience, has higher penetrating efficiency of energy, and full phase control's ability, can adjust the contained angle that baffle structure and super fixed surface structure formed according to the demand to realize required local phase control, can convert the plane wave transmission into the vortex beam that carries sound track angular momentum of design.
Description
Technical Field
The invention relates to the technical field of acoustic devices controlled by acoustic wave fronts, in particular to a controllable acoustic super surface for generating acoustic track angular momentum.
Background
The metamaterial has been developed rapidly in recent decades because the performance of the metamaterial is obviously superior to that of natural materials, realizes functions such as singular refraction and asymmetric transmission which are difficult to realize by natural materials, and has great influence in the fields of electromagnetic waves and acoustic waves. An acoustic super surface provided based on the generalized Snell's law is taken as a sub-wavelength thickness structure of an acoustic super material, so that the acoustic super surface is widely concerned in recent years, and a new solution is provided for the difficult problem of controlling the acoustic wave front. Although the acoustic super-surface has excellent performance, the function of the acoustic super-surface aims at the manipulation of plane waves or spherical waves, the acoustic orbital angular momentum has important theoretical research significance and application value because the acoustic orbital angular momentum can generate an acoustic vortex field with spiral phase dislocation, the acoustic orbital angular momentum has potential in the fields of particle manipulation, cell manipulation and the like, and the realization of the acoustic orbital angular momentum by utilizing the acoustic super-surface is widely concerned by researchers. The existing acoustic super-surfaces capable of generating orbital angular momentum mainly use a passive structure with a fixed structure, but the newly proposed adjustable acoustic super-surfaces can only realize the manipulation of reflected sound waves, and the adjustable acoustic super-surfaces capable of realizing the orbital angular momentum of transmission sound are urgently needed to be developed.
Disclosure of Invention
The invention aims to provide a controllable acoustic super surface for generating sound track angular momentum, which has higher energy permeability, higher discrete precision and full phase control capability.
The embodiment of the invention is realized by the following steps:
a tunable acoustic metasurface for generating orbital angular momentum, comprising: fixed knot constructs and active structure, the active structure is rotatable around the symmetry axis that fixed knot constructs the central setting, fixed knot constructs a plurality of subregion around symmetry axis a week, outside has in every subregion, well, interior three-layer surpasses surface unit, fixed knot structure in every surpasses surface unit is provided with the passageway, the active structure cooperatees with fixed knot structure through the passageway, the active structure forms the angle crack with fixed knot structure in the passageway, fixed knot structure in every subregion includes the fixed knot structure skin that sets up from outside to inside, fixed knot constructs the middle level and fixed knot constructs the inlayer, the active structure in every subregion includes the outer active structure that sets up from outside to inside, middle level active structure and inlayer active structure, each layer of active structure imbeds respectively and matches in the passageway that each layer of fixed knot constructs the setting, each layer of active structure can independently rotate around the symmetry axis, in order to realize the different regulation to the sound wave.
In a preferred embodiment of the present invention, the fixing structure outer layer, the fixing structure middle layer and the fixing structure inner layer are respectively provided with a plurality of helmholtz resonant cavities arranged along the symmetry axis direction.
In a preferred embodiment of the present invention, the space between the fixing structure outer layer and the fixing structure middle layer, and the space between the fixing structure middle layer and the fixing structure inner layer are separated by a cylindrical outer wall, which is respectively the middle layer outer wall and the inner layer outer wall, and a cylindrical outer layer outer wall is arranged outside the fixing structure outer layer, so as to form three layers of outer walls.
In a preferred embodiment of the present invention, the outer layer movable structure, the middle layer movable structure and the inner layer movable structure are baffle structures arranged in a hollow manner, the baffle structures of the ultrasonic surface units of each partition independently rotate around the symmetry axis, the baffle structures are frame-shaped, and the outer sides and the inner sides of the baffle structures are opened and respectively face the outer walls of the adjacent layers.
In a preferred embodiment of the present invention, a slit is formed between a side surface of the baffle structure and the plurality of arranged helmholtz resonator cavities, and an angle formed by the slit is changed by rotating the baffle structure around the symmetry axis.
In a preferred embodiment of the present invention, the fixing structure outer layer, the fixing structure middle layer and the fixing structure inner layer are respectively provided with the same structure, which includes a resonance cavity neck, a resonance cavity body and an outer wall, the outer wall is the inner layer outer wall, the middle layer outer wall or the outer layer outer wall, the plurality of resonance cavity necks are equally spaced and arranged between the outer walls of adjacent layers, and divide each super-surface unit into a plurality of resonance cavity bodies arranged in parallel, and the resonance cavity bodies are helmholtz resonance cavities.
In a preferred embodiment of the present invention, the wall surface formed by the neck of the resonant cavity forms α with the side surfaces of the outer active structure, the middle active structure and the inner active structure 1 、α 2 And alpha 3 The angle between the wall formed by the neck of the resonant cavity and the wall at the back of the resonant cavity is alpha 0 After determining the parameters of the fixed structure, the angle alpha is adjusted 1 、α 2 And alpha 3 The adjustment of the sound wave is realized.
In a preferred embodiment of the present invention, the phase difference Φ of the planar acoustic wave after passing through a single super-surface unit is:
wherein, omega is the frequency of the plane sound wave, omega 0 Is the resonant cavity resonant frequency, W is the thickness of the acoustic super-surface along the symmetry axis, c 0 Is the speed of sound, S, of a sound wave in a transmission medium 0 Is the cross-sectional area, S, of the cavity of the resonant cavity n The cross-sectional area of a crack formed by the baffle structure and the fixing structure of the n-th layer of super-surface unit from outside to inside.
The invention has the beneficial effects that:
1. the acoustic super-surface provided by the invention has a simple structure, is easy for 3D printing and forming, and is convenient to assemble and disassemble.
2. The acoustic super surface provided by the invention has adjustability, and the included angle formed by the baffle structure and the super surface fixing structure can be adjusted according to requirements to obtain local phase distribution required by forming the acoustic track angular momentum, so that the required transmission acoustic track angular momentum is generated for plane waves with different frequencies.
3. The acoustic super-surface unit provided by the invention has higher energy permeation efficiency, can effectively utilize incident sound energy, improves the energy of the required sound wave after transmission as much as possible, and achieves the effect of energy saving.
4. The acoustic super-surface unit provided by the invention has full-phase control capability and can meet more complex acoustic wave control requirements.
Drawings
To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are required to be used in the embodiments will be briefly described below, and it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope.
FIG. 1 is a schematic representation of the conversion of a plane wave of the present invention into a vortex after passing through an acoustic super-surface of the present invention;
FIG. 2 is a schematic view of an adjustable acoustic super-surface assembly of the present invention;
FIG. 3 is a schematic cross-sectional half-section view of a super surface mount structure according to the present invention;
FIG. 4 is a schematic partial cross-sectional view of FIG. 1 of the present invention;
FIG. 5 is a schematic view of the structure size of one eighth quadrant of the super-surface of the present invention;
FIG. 6 isbase:Sub>A schematic structural dimension view of the plane A-A of FIG. 5;
FIG. 7 is a graph of simulation results of cell phase change capability and transmittance according to one embodiment of the present invention.
Description of reference numerals: 1-a fixed structure; 2-outer layer movable structure; 3-middle layer active structure; 4-inner layer active structure; 11-a fixed structure outer layer; 12-fixed structure middle layer; 13-a fixed structure inner layer; 14-fixed structure symmetry axis; 21-baffle structure side; 111-resonance cavity neck-mouth; 112-resonant cavity; 113-outer wall.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. The components of 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 present invention, 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 derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
First embodiment
Referring to fig. 1 and 2, the present embodiment provides a controllable acoustic super-surface for generating orbital angular momentum, a plane wave is transmitted from the left side of the acoustic super-surface along the direction of arrow in the figure, and after passing through the acoustic super-surface of the present invention, a vortex carrying orbital angular momentum is formed on the right side of the super-surface; the acoustic super-surface of this embodiment includes fixed knot structure 1 and active structure, the active structure is rotatable around the symmetry axis 14 that fixed knot constructs 1 center setting, fixed knot constructs 1 and is provided with eight divisions around the symmetry axis 14 a week, have outer in every division, well, interior three-layer super surface unit, eight super surface unit that each layer is the circumference evenly distributed around symmetry axis 14 altogether, every division totally three super surface unit, like this, the active structure totally eight outer active structure 2, eight middle level active structure 3 and eight inner movable structure 4, each active structure can rotate around fixed knot constructs 1's symmetry axis 14 in certain extent, fixed knot constructs 1 and includes fixed knot and constructs outer 11, fixed knot constructs middle level 12 and fixed knot and constructs the inner 13, all be provided with the resonant cavity structure in every fixed knot constructs 1 on layer, the angle crack has between the lateral wall of active structure and the resonant cavity structure, the size of angle crack is decided with the relative position of corresponding active knot structure and fixed knot construct 1.
Referring to fig. 3 and 4, the fixed structure 1 in each partition of the present embodiment includes a fixed structure outer layer 11, a fixed structure middle layer 12, and a fixed structure inner layer 13, which are arranged from outside to inside, eight fixed structure outer layers 11 and eight fixed structure middle layers 12 are separated from each other by arrangement, the fixed structure middle layer 12 and the fixed structure inner layer 13 are separated from each other by arrangement, the outer side of the fixed structure outer layer 11 is provided with three outer walls 113, which are all cylindrical, so as to form three outer walls 113, a three-layer super surface unit structure is formed by separation of the outer walls 113, the fixed structure 1 of each super surface unit, i.e., the fixed structure outer layer 11, the fixed structure middle layer 12, and the fixed structure inner layer 13 are respectively provided with a channel, which is an internal space formed in the fixed structure 1, each layer of the movable structure in each super surface unit is embedded in each layer of the fixed structure 1 and is matched with the fixed structure 1 through the channel, the movable structure forms an angle gap with the fixed structure 1 in the channel, each layer of the movable structure can independently rotate around a symmetry axis 14, so as to realize different adjustments of sound waves; the movable structure in each partition comprises an outer movable structure 2, a middle movable structure 3 and an inner movable structure 4 which are arranged from outside to inside, the outer fixed structure layer 11, the middle fixed structure layer 12 and the inner fixed structure layer 13 are respectively provided with a plurality of branch Helmholtz resonance cavities which are distributed along the direction of the symmetry axis 14, and the Helmholtz resonance cavities are formed by the resonance cavity structures in the fixed structures.
The outer layer movable structure 2, the middle layer movable structure 3 and the inner layer movable structure 4 are respectively baffle structures which are arranged in a hollow mode, the baffle structures are in a frame shape, the cross section of the baffle structure of the embodiment is a square frame, the outer sides and the inner sides of the baffle structures are respectively opened and respectively face the outer walls 113 of the adjacent layers, if the outer sides of the baffle structures positioned in the middle layer are close to each other, the inner sides of the baffle structures positioned in the middle layer are close to each other, and the baffle structures of the ultrasonic surface units of all the subareas independently rotate around the symmetrical shaft 14; the baffle structure sides 21 have a gap with the plurality of arranged helmholtz resonator cavities, the angle formed by the gap being varied by rotation of the baffle structure about the axis of symmetry 14.
Referring to fig. 5 and 6, the fixed structure outer layer 11, the fixed structure middle layer 12 and the fixed structure inner layer 13 are respectively provided with the same resonant cavity structures, and there are 24 resonant cavity structures in total, each resonant cavity structure includes a resonant cavity neck 111, a resonant cavity 112 and an outer wall 113, the outer wall 113 is, or, six resonant cavity necks 111 are equally spaced and arranged between the outer walls 113 of adjacent layers, so that five resonant cavities are formed between the adjacent resonant cavity necks 111, each super-surface unit is divided into a plurality of resonant cavities arranged in parallel by the resonant cavity necks 111, and the resonant cavities in this embodiment are helmholtz resonant cavities; the wall formed by the neck 111 of the resonant cavity forms α with the side surfaces of the outer active structure 2, the middle active structure 3 and the inner active structure 4 1 、α 2 And alpha 3 When the dimensional parameters of the fixed structure 1 are determined, alpha 0 Is a fixed constant, and alpha 1 、α 2 And alpha 3 The angle between the wall formed by the neck 111 of the resonance chamber and its back wall is α, which is an adjustable parameter within a certain range 0 After determining the parameters of the fixed structure 1, the angle alpha is adjusted 1 、α 2 And alpha 3 The adjustment of the sound waves is realized.
The phase difference phi of the plane acoustic wave after passing through a single super-surface unit is shown as formula 1:
wherein, omega is the frequency of the plane sound wave, omega 0 For the resonant cavity resonant frequency, W is the thickness of the acoustic super-surface along the axis of symmetry 14, c 0 Is the speed of sound, S, of a sound wave in a transmission medium 0 Is the cross-sectional area, S, of the resonant Cavity 112 n The cross-sectional area of a gap formed by the baffle structure side surface 21 of the n-th layer super-surface unit and the fixed structure 1 is counted from outside to inside.
The outer layer, middle layer and inner layer fixing structures 1 respectively comprise resonant cavity structures with three sizes, and the widths of the necks 111 of the resonant cavities of the outer layer, middle layer and inner layer are respectively l 1 、l 2 And l 3 The radii formed by the outer walls 113 of the outer layer 11, the middle layer and the inner layer of the fixing structure and the symmetry axis 14 are r 1 、r 2 And r 3 The radius formed by the inner wall of the inner layer 13 of the fixed structure and the symmetry axis 14 is r 0 The total thickness of the acoustic super surface mount structure 1 along the axis of symmetry 14 is W.
The working process and principle of the invention are as follows:
firstly, determining the working frequency of incident sound waves according to requirements, and thus calculating and determining the relative position relationship between all the outer-layer movable structures 2, the middle-layer movable structures 3 and the inner-layer movable structures 4 and the fixed structure 1, wherein the specific process is as follows:
the invention adopts the Helmholtz resonant cavity to realize the control of the phase of the transmitted sound wave. The structure of one eighth quadrant of the super surface shown in fig. 5 is composed of outer, middle and inner super full cells, and the dimensional structure is shown in fig. 6. The equivalent bulk modulus of the unit can be expressed as formula 2:
in the formula (I), the compound is shown in the specification,
is the bulk modulus, omega, of air 0 Is HelmholtzThe resonance angular frequency of the resonant cavity, ω is the incident acoustic operating angular frequency, F = S 0 /S n Is the cross-sectional area ratio of the cavity and the gap portion of the resonant cavity, S is shown in FIG. 6 0 /S n ＝α 0 /α n (n =1,2,) 3, Γ is the intrinsic loss of the resonant cavity, i is the imaginary unit and i is the imaginary unit 2 And (4) = -1. Wherein the content of the first and second substances,
while
Is the acoustic volume of the air in the cavity of the resonant cavity, M HR ＝ρ 0 h eff /l n Acoustic mass of the air in the neck of the resonance chamber, /) n Is the neck width of the resonant cavity of the nth layer, h eff And h is the effective length of the neck of the resonant cavity, and h is the actual length of the neck of the resonant cavity.
When the super-surface thickness W is smaller than the incident acoustic wave wavelength λ, the super-surface unit can be regarded as a uniform medium, and the effective sound velocity through the uniform medium can be expressed
And the intrinsic loss Γ of the resonant cavity can be neglected. Thus, the phase difference of an incident acoustic wave and its transmitted wave after passing through the super-surface can be expressed as φ =2 π Wf/c eff Thus, phi can be obtained n And alpha n And incident acoustic operating frequency f, equation 3:
wherein, f = omega/2 pi, f 0 ＝ω 0 And/2 pi is the resonant cavity resonant frequency. The following parameters were selected in this example: r is 0 ＝0.02m， r 1 ＝0.04m，r 2 ＝0.05m，r 3 ＝0.0574m，l 1 ＝0.001m，l 2 ＝0.003m，l 3 ＝0.004m， W＝0.035m，α 0 And (3) = pi/16. The finite element simulation software is analyzed to obtain the final productCorresponding phase change capability and transmittance, as shown in FIG. 7, it can be seen from the results that the acoustic super-surface unit with such parameters has included angle α n Can realize full phase regulation and control and higher transmissivity within the range of 0-10 degrees, and can meet the conditions required by realizing orbital angular momentum.
Next, we analyze how to theoretically achieve the conversion of planar acoustic waves into orbital angular momentum. The propagation phase of the vortex beam required to generate the angular momentum of the sound track is helical with respect to its central axis and propagates forward along the direction of the central axis, which can be expressed as exp (im θ), where θ is the azimuth angle, m is the topological charge number, i.e., the order of the vortex field (m =0,1, 2.. And.. The.), and m can also be understood as the number of revolutions along the central axis when the vortex propagates forward a distance of one wavelength. It is clear that when m =0, the wavefront does not contain vortices, i.e. is a plane wave. The acoustic super-surface presented by the invention comprises a 3-layer structure and 8 partitions, so that the phase change corresponding to each partition is represented by formula 4:
φ＝2πm(j-1)/8
where j is the super-surface cell of the j-th partition (j =1, 2.., 8). Simultaneous relations 3 and 4 may be solved as needed to obtain each super surface element.
In addition to the phase requirements, the cut-off frequency corresponding to each cell needs to be analyzed. For the sound pressure at the exit of the 8 azimuthal units of the hypersurface (i.e. z = 0) there is equation 5:
wherein, because W < lambda we regard the super surface unit as a uniform medium, so
The effective wavenumber of the acoustic wave passing through the jth super-surface element, here (j-1) π/4 < θ < j π/4. Therefore, we can obtain a cylindrical bessel mode acoustic pressure field distribution as formula 6:
wherein A is m,n Is the amplitude, J m (k m,n r) is a Bessel equation of order m, k m,n r is the equation
The n-th positive root of (2),
the central axial wavenumber. When m is determined, the cut-off frequencies corresponding to different wave numbers can be calculated, and whether the super-surface unit can achieve the expected effect at the working frequency or not is analyzed.
In summary, in the embodiment of the present invention, the fixed structure is divided into multiple regions to form multiple structures, each region is divided into multiple layers by the outer wall to form multiple multilayer super-surface units, each unit has the same structure and is provided with a channel, an adjustable structure is formed by arranging a movable structure in the channel, the movable structure is rotatable around the symmetry axis, multiple helmholtz resonant cavities are formed by arranging the resonant cavities, a crack is formed between the side surface 21 of the baffle structure and the side surface of the resonant cavity structure by arranging the baffle structure, and three angles α are realized by adjusting the cracks of the outer layer, the middle layer and the inner layer 1 、α 2 And alpha 3 Thereby enabling adjustment of the acoustic super-surface; this simple structure, the shaping is printed to easy 3D, installs and removes the convenience, can adjust the baffle structure and surpass the contained angle that fixed surface structure formed according to the demand, has higher penetrating efficiency of energy, and full phase control's ability, can be with the plane wave transmission conversion for carrying the vortex wave beam of sound track angular momentum.
This description describes examples of embodiments of the invention, and is not intended to illustrate and describe all possible forms of the invention. It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (6)
1. A tunable acoustic metasurface for generating orbital angular momentum, comprising: the acoustic wave adjusting device comprises a fixed structure (1) and a movable structure, wherein the movable structure is rotatable around a symmetry axis (14) arranged at the center of the fixed structure (1), the fixed structure (1) is provided with a plurality of partitions surrounding the symmetry axis (14) in a circle, each partition is internally provided with an outer layer, a middle layer and an inner layer of a super-surface unit, the fixed structure (1) in each super-surface unit is provided with a channel, the movable structure is matched with the fixed structure (1) through the channel, the movable structure forms an angle crack with the fixed structure (1) in the channel, the fixed structure (1) in each partition comprises a fixed structure outer layer (11), a fixed structure middle layer (12) and a fixed structure inner layer (13) which are arranged from outside to inside, the movable structure in each partition comprises an outer layer movable structure (2), a middle layer movable structure (3) and an inner layer movable structure (4) which are arranged from outside to inside, each layer of the movable structure is respectively embedded into the channel arranged in each layer of the fixed structure (1) for matching, each layer of the movable structure can independently rotate around the symmetry axis (14) to realize different adjustment of acoustic waves;
the outer layer (11) of the fixed structure, the middle layer (12) of the fixed structure and the inner layer (13) of the fixed structure are respectively provided with the same structure and comprise resonant cavity necks (111), resonant cavity bodies (112) and outer walls (113), the outer walls (113) are the inner layer outer walls, the middle layer outer walls or the outer layer outer walls, the resonant cavity necks (111) are equidistantly spaced and arranged among the outer walls of the adjacent layers, each super-surface unit is respectively divided into a plurality of resonant cavities (112) which are arranged in parallel, and the resonant cavities (112) are Helmholtz resonant cavities;
the wall surface formed by the neck part (111) of the resonant cavity forms alpha with the side surfaces of the outer layer movable structure (2), the middle layer movable structure (3) and the inner layer movable structure (4) 1 、α 2 And alpha 3 The wall formed by the neck (111) of the resonance chamber and the back wall thereofThe included angle between is alpha 0 After determining the parameters of the fixed structure (1), the angle alpha is adjusted 1 、α 2 And alpha 3 The adjustment of the sound wave is realized.
2. An acoustic super surface of tunable and controllable type for generating angular momentum of the sound track, according to claim 1, characterized in that said outer fixed structure layer (11), said middle fixed structure layer (12) and said inner fixed structure layer (13) are respectively provided with a plurality of helmholtz resonator cavities arranged along the symmetry axis (14).
3. The tunable acoustic metasurface for generating angular momentum of sound track according to claim 2, wherein said fixed structure outer layer (11) and fixed structure middle layer (12) and said fixed structure middle layer (12) and fixed structure inner layer (13) are separated by cylindrical outer walls, which are respectively middle layer outer wall and inner layer outer wall, and said fixed structure outer layer (11) is provided with cylindrical outer wall on its outer side, thus forming three outer walls.
4. The tunable acoustic super surface for generating angular momentum of sound tracks according to claim 3, wherein the outer active structure (2), the middle active structure (3) and the inner active structure (4) are hollow baffle structures, the baffle structures of the ultrasonic surface units of each partition rotate independently around the symmetry axis (14), the baffle structures are frame-shaped, and the outer sides and the inner sides of the baffle structures are open and face the outer walls of the adjacent layers respectively.
5. A tunable acoustic metasurface for generating acoustic orbital angular momentum according to claim 4, wherein the sides of the baffle structure and the plurality of aligned Helmholtz resonators have a gap therebetween, the angle formed by the gap being varied by rotation of the baffle structure about the axis of symmetry.
6. The tunable acoustic metasurface of claim 1, wherein the phase difference Φ of the plane acoustic wave passing through the single metasurface unit is:
wherein, omega is the frequency of the plane sound wave, omega 0 Is the resonant cavity resonant frequency, W is the thickness of the acoustic super-surface along the symmetry axis, c 0 Is the speed of sound, S, of a sound wave in a transmission medium 0 Is the cross-sectional area, S, of the cavity of the resonant cavity n The cross-sectional area of a crack formed by the baffle structure and the fixing structure of the n-th layer of super-surface unit from outside to inside.
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