CN113314090A - Controllable acoustic super surface for generating acoustic track angular momentum - Google Patents
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Abstract
The invention discloses an adjustable and controllable acoustic super surface for generating acoustic track angular momentum, which comprises a super surface fixed structure and a super surface movable structure, wherein the fixed structure is provided with eight partitions surrounding a circle of a symmetry axis, 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 fixed structure within a certain range, a row of side support resonant cavity structures are arranged in the fixed 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 fixed 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. The acoustic super surface provided based on the generalized Snell's law is taken as a sub-wavelength thickness structure of the acoustic metamaterial, so that the acoustic metamaterial has wide attention in recent years, and a new solution is provided for the 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 in urgent need of development.
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: the movable structure is rotatable around a symmetrical shaft arranged at the center of the fixed structure, the fixed structure is provided with a plurality of partitions surrounding the symmetrical shaft for a circle, each partition is internally provided with an outer layer, a middle layer and an inner layer of super-surface units, the fixed structure in each super-surface unit is provided with a channel, the movable structure is matched with the fixed structure through the channel, the movable structure forms an angle crack with the fixed structure in the channel, the fixed structure in each partition comprises a fixed structure outer layer arranged from outside to inside, the movable structure in each partition comprises an outer movable structure, a middle movable structure and an inner movable structure which are arranged from outside to inside, each layer of the movable structure is embedded into a channel arranged in each layer of the fixed structure and matched with the channel, and each layer of the movable structure can independently rotate around a symmetry axis so as to realize different adjustment of sound waves.
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 outer layer of the fixing structure and the middle layer of the fixing structure, and the space between the middle layer of the fixing structure and the inner layer of the fixing structure are separated by a cylindrical outer wall, which is respectively the outer wall of the middle layer and the outer wall of the inner layer, and the outer side of the outer layer of the fixing structure is provided with a cylindrical outer wall of the outer layer, so that three outer walls are formed.
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 outer layer of the fixing structure, the middle layer of the fixing structure, and the inner layer of the fixing structure are respectively provided with the same structure, which includes a resonance cavity neck, a resonance cavity body, and an outer wall, where the outer wall is the inner outer wall, the middle outer wall, or the outer wall, and the plurality of resonance cavity necks are equally spaced and arranged between the outer walls of adjacent layers, so as to divide each super-surface unit into a plurality of resonance cavities arranged in parallel, respectively, where the resonance cavities 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 structure1、α2And alpha3The angle between the wall formed by the neck of the resonant cavity and the wall at the back of the resonant cavity is alpha0After determining the parameters of the fixed structure, the angle alpha is adjusted1、α2And alpha3The 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, omega0Is the resonant cavity resonant frequency, W is the thickness of the acoustic super-surface along the symmetry axis, c0Is the speed of sound, S, of a sound wave in a transmission medium0Is the cross-sectional area, S, of the cavity of the resonant cavitynThe 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 conservation.
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 of a super-surface anchoring structure in accordance with 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 structural dimensions of an eighth quadrant of a super-surface in accordance with the present invention;
FIG. 6 is 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 tunable 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 the 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 the embodiment 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 eight partitions surrounding the symmetry axis 14 for 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 layer is provided with eight super surface units uniformly distributed around the symmetry axis 14 in a circle, each partition is provided with three super surface units in total, thus the movable structure is provided with eight outer layer movable structures 2, eight middle layer movable structures 3 and eight inner layer movable structures 4 in total, each movable structure can rotate around the symmetry axis 14 of the fixed structure 1 in a certain range, the fixed structure 1 comprises a fixed structure outer layer 11, a fixed structure middle layer 12 and a fixed structure inner layer 13, a resonant cavity structure is arranged in each layer of the fixed structure 1, and an angle gap is arranged between the side wall of the movable structure and the resonant cavity structure, the size of the angle gap is determined by the relative position of the corresponding movable structure and the fixed structure 1.
Referring to fig. 3 and 4, the fixing structure 1 in each partition of the present embodiment includes a fixing structure outer layer 11, a fixing structure middle layer 12 and a fixing structure inner layer 13 arranged from outside to inside, the eight fixing structure outer layers 11 and the eight fixing structure middle layers 12 are separated by arrangement, the fixing structure middle layer 12 and the fixing structure inner layer 13 are separated by arrangement, the outer side of the fixing structure outer layer 11 is provided, the three outer walls 113 are all cylindrical, thus forming the three outer walls 113, a three-layer super surface unit structure is formed by separation of the outer walls 113, the fixing structure 1 of each super surface unit, that is, the fixing structure outer layer 11, the fixing structure middle layer 12 and the fixing structure inner layer 13 are respectively provided with a channel, the channel is an internal space formed in the fixing structure 1, each layer of the movable structure in each super surface unit is embedded in each layer of the fixing structure 1 and is matched with the fixing structure 1 through the channel, the movable structure and the fixed structure 1 form an angle crack in the channel, and each layer of the movable structure can independently rotate around the symmetrical shaft 14 so as to realize different adjustment 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 arrayed 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 surface formed by the neck 111 of the resonant cavity forms alpha with the side surfaces of the outer active structure 2, the middle active structure 3 and the inner active structure 41、α2And alpha3When the dimensional parameters of the fixed structure 1 are determined, alpha0Is a fixed constant, and alpha1、α2And alpha3The wall formed by the neck 111 of the resonant cavity and its back wall are adjustable parameters within a certain rangeAt an included angle of alpha0After determining the parameters of the fixed structure 1, the angle alpha is adjusted1、α2And alpha3The adjustment of the sound wave is realized.
The phase difference phi of the planar sound wave after passing through a single super-surface unit is shown as formula 1:
wherein, omega is the frequency of the plane sound wave, omega0For the resonant cavity resonant frequency, W is the thickness of the acoustic super-surface along the axis of symmetry 14, c0Is the speed of sound, S, of a sound wave in a transmission medium0Is the cross-sectional area, S, of the resonant cavity 112nThe 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 l1、l2And l3The 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 r1、r2And r3The radius formed by the inner wall of the inner layer 13 of the fixed structure and the symmetry axis 14 is r0The 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 figure 5 shows a structure of one eighth quadrant of the super surface, which is composed of an outer layer, a middle layer and an inner layer super full unit, and the dimensional structure is shown in figures 6 and 7. The equivalent bulk modulus of the unit can be expressed as formula 2:
in the formula,
is the bulk modulus, omega, of air0Is the resonance angular frequency of the Helmholtz resonator, ω is the incident acoustic operating angular frequency, and F is S0/SnIs the cross-sectional area ratio of the cavity and the gap portion of the resonant cavity, S is shown in FIG. 60/Sn＝α0/αn(n ═ 1,2,)3, Γ is the intrinsic loss of the resonant cavity, i is the imaginary unit and i is the imaginary unit2Is-1. Wherein,
while
Is the acoustic volume of the air in the cavity of the resonant cavity, MHR＝ρ0heff/lnAcoustic mass of the air in the neck of the resonance chamber, /)nIs the neck width of resonant cavity of the nth layer, heffH +8l/3 pi is the effective length of the neck of the resonance cavity, and h is the actual length of the neck of the resonance 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 at this time, the effective sound velocity passing through the uniform medium can be expressed as
And the intrinsic loss Γ of the resonant cavity can be neglected. Thus, the phase difference between an incident acoustic wave and its transmitted wave after passing through the super-surface can be expressed as 2 π Wf/ceffThus, phi can be obtainednAnd alphanAnd incident acoustic operating frequency f, equation 3:
wherein f is omega/2 pi，f0＝ω0And/2 pi is the resonant cavity resonant frequency. The following parameters were selected in this example: r is0＝0.02m， r1＝0.04m，r2＝0.05m，r3＝0.0574m，l1＝0.001m，l2＝0.003m，l3＝0.004m， W＝0.035m，α0Pi/16. After finite element simulation software analysis, the corresponding phase change capability and transmittance are obtained, as shown in fig. 7, and it can be known from the results that the acoustic super-surface unit with the parameters has the included angle alphanThe full-phase regulation and control and high transmissivity can be realized within the range of 0-10 degrees, and the conditions required by realizing orbital angular momentum can be met.
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 and m is the topological charge number, i.e. the order of the vortex field ( m 0,1, 2), and m can also be understood as the number of rotations along the central axis when the vortex propagates forward a distance of one wavelength. Obviously, when m is 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
wherein j is the super surface unit of the j-th partition (j ═ 1, 2.. times.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 azimuth elements of the super-surface (i.e. z ═ 0), there is equation 5:
wherein, because W < lambda we regard the super surface unit as a uniform medium, therefore
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 ism,nIs the amplitude, Jm(km,nr) is a Bessel equation of order m, km,nr is the equation
The n-th positive root of (a),
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 layer1、α2And alpha3Thereby 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 (8)
1. A tunable acoustic metasurface for generating orbital angular momentum, comprising: fixed knot constructs (1) and active structure, the symmetry axis (14) that the active structure set up around fixed knot constructs (1) center is rotatable, fixed knot constructs (1) and is provided with a plurality of subregion around symmetry axis (14) a week, has outer, well, interior three-layer super surface unit in every subregion, and fixed knot structure (1) in every super surface unit is provided with the passageway, the active structure cooperatees with fixed knot structure (1) through the passageway, the active structure forms the angle crack with fixed knot structure (1) in the passageway, and fixed knot structure (1) in every subregion includes fixed knot structure skin (11), fixed knot structure middle level (12) and fixed knot structure inlayer (13) that set up from outside to inside, and the active structure in every subregion includes outer active structure (2), middle level active structure (3) and inlayer active structure (4) that set up from outside to inside, each layer of the movable structure is respectively embedded into a channel arranged in each layer of the fixed structure (1) to be matched, and each layer of the movable structure can independently rotate around the symmetrical shaft (14) so as to realize different regulation of sound waves.
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 fixed structure outer layer (11), fixed structure middle layer (12) and fixed structure inner layer (13) are respectively provided with a plurality of helmholtz resonator cavities arranged along the direction of the symmetry axis (14).
3. An adjustable acoustic super surface for generating angular momentum of sound tracks, according to claim 2, characterized in that the space between said fixed structure outer layer (11) and fixed structure middle layer (12) and between said fixed structure middle layer (12) and fixed structure inner layer (13) is separated by cylindrical outer walls, which are respectively middle layer outer wall and inner layer outer wall, and the outer side of said fixed structure outer layer (11) is provided with cylindrical outer wall, 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 layer active structure (2), the middle layer active structure (3) and the inner layer 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 super surface for generating angular momentum of sound tracks according to claim 2, wherein 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 structure, which comprises a resonance cavity neck (111), a resonance cavity body (112) and an outer wall (113), the outer wall (113) is an inner layer outer wall, a middle layer outer wall or an outer layer outer wall, a plurality of resonance cavity necks (111) are equidistantly spaced and arranged between the outer walls of adjacent layers, each super surface unit is respectively divided into a plurality of resonance cavities (112) arranged in parallel, and the resonance cavities (112) are helmholtz resonance cavities.
7. An acoustic super surface of tunable and controllable type for generating angular momentum of sound tracks, according to claim 5, characterized in that the wall surface formed by the neck (111) of said 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) respectively1、α2And alpha3The angle between the wall formed by the neck (111) of the resonance chamber and the back wall is alpha0After determining the parameters of the fixed structure (1), the angle alpha is adjusted1、α2And alpha3The adjustment of the sound wave is realized.
8. A tunable acoustic metasurface for generating orbital angular momentum according to claim 7, wherein the phase difference φ of the planar acoustic waves passing through the individual metasurface elements is:
wherein, omega is the frequency of the plane sound wave, omega0Is the resonant cavity resonant frequency, W is the thickness of the acoustic super-surface along the symmetry axis, c0Is the speed of sound, S, of a sound wave in a transmission medium0Is the cross-sectional area, S, of the cavity of the resonant cavitynThe 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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| CN114842823A (en) * | 2022-05-19 | 2022-08-02 | 西安交通大学 | Programmable ultrasonic forceps system and implementation method thereof |
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