Long-beam acoustic focusing lens design method

Abstract

The present application relates to a method for designing a long-beam acoustic focusing lens, comprising the following steps: designing a two-dimensional lattice array, wherein the two-dimensional lattice array is composed of rigid star-shaped columns in the air. According to the two-dimensional lattice array, the sound pressure equation of the incident wave and the sound pressure equation of the first scattering of different star-shaped columns are constructed. According to the visco-thermal effect of the solid wall interface, the boundary conditions of the radial particle velocity on the surface of the star-shaped column are constructed. The sound pressure equation at any point on the plane is constructed. The method constructs the sound pressure equation of the incident wave and the sound pressure equation of the first scattering of different star-shaped columns by designing a two-dimensional lattice array, and constructs the boundary conditions of the radial particle velocity on the surface of the star-shaped column and the sound pressure equation at any point on the two-dimensional plane according to the visco-thermal effect of the solid wall interface. The two-dimensional lattice array composed of rigid star-shaped columns forms a topological structure. The characteristics of the topological structure enable the method to achieve more efficient long-beam projection for low-frequency broadband.

Description

Technical Field

[0001] The present application relates to the field of acoustic focusing technology, and in particular to a design method for a long-beam acoustic focusing lens. Background Art

[0002] Acoustic focusing using acoustic metasurfaces has broad application prospects in the efficient operation of electronic, medical, industrial, and testing equipment. In traditional homogeneous media dominated by the diffraction limit, the optimal resolution of wave focusing and imaging can only reach half the wavelength corresponding to the lowest operating frequency. The development of phononic crystals and acoustic metamaterials has achieved subwavelength focusing and super-resolution imaging. The characteristics of acoustic metamaterials derive from the interaction between sound waves and specially designed materials. Based on the physical principles of sound wave propagation, precise structures are designed to control sound wave propagation. Acoustic metasurfaces are artificially designed two-dimensional structures with subwavelength thickness. Through the ingenious design of subwavelength structures, the wavefront of sound waves can be controlled, thereby realizing functions such as sound focusing, anomalous refraction and reflection, sound absorption, and source illusion. These rationally designed subwavelength-thick two-dimensional materials provide new avenues for sound wave manipulation.

[0003] The concept of metamaterials began with the development of left-handed materials. In 1968, Soviet physicist Veselago, drawing on Maxwell's equations, analyzed the propagation characteristics of electromagnetic waves in materials with both negative magnetic permeability and negative dielectric constant, and proposed a theoretical model for left-handed materials. This theoretical analysis showed that in materials with negative dielectric constant and negative magnetic permeability, the direction of electromagnetic wave energy propagation (group velocity) and the direction of phase propagation (phase velocity) are opposite. In this case, the wave vector (K), electric field (E), and magnetic field (H) satisfy the left-handed helical rule. With the continued advancement of research in artificial electromagnetic structures such as binary optics and photonic crystals, Pendry et al. proposed in 1999 that a periodic structure based on split ring resonators could achieve negative equivalent magnetic permeability, paving the way for the realization of left-handed materials. Further research has revealed that by adjusting the geometric parameters and structural form of left-handed materials, the magnetic permeability and dielectric constant of the material can be arbitrarily controlled within the subwavelength frequency range. This wide range of material parameter tunability provides a broad design foundation for a variety of new functional devices. This kind of artificial material that has extraordinary physical properties that natural materials do not have is called metamaterial.

[0004] Wave focusing is another important function of metasurfaces, which can concentrate the energy of a wave at a certain point (point focusing) or a certain area (beam focusing, such as non-diffracting Bessel beams). In 2009, Lin et al. designed and characterized a two-dimensional, gradient-index phononic crystal to control the propagation of acoustic waves. The study found that the gradient coefficient is very sensitive to frequency. Numerical methods were used to prove that the gradient phononic crystal with a hyperbolic deflected refractive index distribution enables the acoustic wave to converge over a wide range of low frequencies, which is 5 times wider than the range provided by existing negative refractive gradient phononic crystals. In 2010, Climente et al. demonstrated the focusing performance of a two-dimensional GRIN acoustic wave lens made of aluminum rods. Through numerical simulations of the multiple scattering algorithm and ray theory analysis models, they found that in this type of flat lens, the index gradient is achieved by gradually modifying the crystal filling fraction along the direction perpendicular to the lens axis, confirming the broadband performance of the gradient-index phononic crystal. In 2011, Zigoneanu et al. designed a cross-shaped phononic crystal and adjusted the effective refractive index in the lens by controlling the effective density. The performance of this physically structured lens matched that of an ideal material. Prototypes were produced using stereolithography, and measurements of the resulting acoustic field confirmed the lens's excellent performance and design. In 2018, Ma et al. demonstrated through three-dimensional acoustic experiments that an independent anti-causal Green's function could be achieved over a large area of space away from the focal point by introducing a near-perfect spherical wave absorber at the focal point. They constructed this subwavelength absorber based on a membrane-type acoustic metamaterial and experimentally demonstrated that the focusing of spherical waves exceeded the diffraction limit.

[0005] In 2019, Ma et al. used a subwavelength curled acoustic metamaterial absorber and a point sink to change this interference, thereby eliminating or reducing the divergent waves to achieve a focusing point beyond the diffraction limit. This sub-diffraction focusing effect has been intuitively demonstrated in some three-dimensional time-reversal acoustic experiments, in which a planar spiral structure and two hemispherical spiral structures were designed. In the same year, Ma et al. used a simple Helmholtz resonant cavity structure, its perfect sound absorption effect and time-delay effect on sound waves to propose the concept of a sound sink. On this basis, a series of experimental studies on time-reversal focusing were conducted. On the one hand, the near-field evanescent wave amplification principle of the local resonant structure is used to ensure the evanescence of the waves around the sound sink opening; on the other hand, the perfect sound absorption function of the sound sink is used to achieve manipulation of the output sound waves. In 2021, Chen et al. constructed a planar structure tunable acoustic metasurface based on spiral units. The length of the acoustic channel can be adjusted by the spiral depth of the spiral. By twisting the spiral, various functions such as anomalous refraction, point focusing, beam focusing and self-bending can be achieved. Experiments on anomalous refraction and point focusing proved that the designed metasurface is effective. In 2022, Liang et al. designed a circular sawtooth structure connected to a ring array of cross-sectional plane sensors to generate acoustic Bessel vortex beams underwater, and demonstrated the non-diffraction and collimation characteristics through experimental measurements and simulations. In addition, focusing can also achieve energy harvesting by limiting or localizing sounds / noises from various environmental environments and converting them into electrical energy. On the other hand, the conversion of cylindrical or spherical wavefronts into plane wavefronts can be designed by following the reverse process of point focusing.

[0006] Currently, Publication No. CN107492370B proposes a metasurface structure with adjustable acoustic wave focusing. This structure is formed by a spiral structure screwed into a circular disc base with a hole. By adjusting the depth of the spiral structure screwed into the hole, the phase of the transmitted acoustic wave can be varied within a range of 2π. By adjusting the phase of the transmitted acoustic wave, the transmitted acoustic wave reaches its peak at a certain point, which is used to achieve acoustic wave focusing. This application combines the spiral structure with a perforated circular disc to obtain an adjustable spiral acoustic channel. By adjusting the spiral acoustic channel, the phase of the transmitted wave can be adjusted. By arbitrarily manipulating the phase, broadband acoustic focusing can be achieved.

[0007] Therefore, existing methods of adjusting transmitted waves are dedicated to focusing the sound on a single focal point at different positions and frequencies. For low-frequency wide-band, efficient long sound beam projection is difficult for manual sound manipulation. Summary of the Invention

[0008] Based on this, it is necessary to provide a long-beam acoustic focusing lens design method for achieving more efficient long-beam acoustic projection in a low-frequency wide band to address the above technical problems.

[0009] A method for designing a long-beam acoustic focusing lens, the method comprising:

[0010] designing a two-dimensional lattice array consisting of rigid star-shaped columns in air;

[0011] Constructing the sound pressure equation of the incident wave and the sound pressure equation of the primary scattering of different star-shaped columns according to the two-dimensional lattice array;

[0012] According to the visco-thermal effect of the solid wall interface, the boundary conditions of the radial particle velocity on the surface of the star-shaped column are constructed;

[0013] Construct the sound pressure equation at any point on the plane.

[0014] In one embodiment, the designing of the two-dimensional lattice array comprises:

[0015] The designed two-dimensional lattice array consists of N=n×m rigid star-shaped rods in the air.

[0016] The above-mentioned long-beam acoustic focusing lens design method constructs the sound pressure equation of the incident wave and the sound pressure equation of the first scattering of different star-shaped columns by designing a two-dimensional lattice array. Based on the visco-thermal effect of the solid wall interface, the boundary conditions of the radial particle velocity on the surface of the star-shaped column and the sound pressure equation at any point on the two-dimensional plane are constructed. The two-dimensional lattice array composed of rigid star-shaped columns forms a topological structure. The characteristics of the topological structure enable this method to achieve more efficient long-beam acoustic projection for low-frequency wide bands.

[0017] In one embodiment, the designing of the two-dimensional lattice array further comprises:

[0018] The star-shaped columns are respectively located on the R i (i=1, 2, 3...).

[0019] In one embodiment, the designing of the two-dimensional lattice array further comprises:

[0020] The R i (i=1, 2, 3...) is located in R s An incident plane wave at a given frequency f passes through the two-dimensional lattice array along the x-axis direction.

[0021] In one embodiment, the sound pressure equation of the incident wave is:

[0022]

[0023] Where x is the horizontal distance from the center of the star column to the sound source, r is the straight-line distance from the center of the star column to the sound source, θ is the angle between r and the x-axis, and s is the Bessel function J s The order of .

[0024] In one embodiment, the sound pressure equations of the first scattering of the different star-shaped columns are:

[0025]

[0026] Where r is the straight-line distance from the center of the star column to the sound source, θ is the angle between r and the x-axis, and s is the Hankel function H s The order of .

[0027] In one embodiment, the step of constructing the boundary conditions for radial particle velocity on the surface of the star-shaped column includes:

[0028] Due to the visco-thermal effect of the solid wall interface, the radial particle velocity on the surface of the star-shaped column is zero, and the velocity is proportional to the pressure gradient. The boundary conditions are:

[0029]

[0030] Among them, R in is the inner diameter of the star-shaped column.

[0031] In one embodiment, constructing the sound pressure equation at any point on the plane includes:

[0032] When considering scattering, the sound pressure equation at any point (x, y) in the plane is:

[0033]

[0034] In one embodiment, the method further comprises:

[0035] The two-dimensional lattice array is calculated by Matlab to obtain the predicted calculation effect.

[0036] In one embodiment, the calculating the two-dimensional lattice array by using Matlab includes:

[0037] The predicted calculation result is compared with the simulation calculation result. If the predicted calculation result is consistent with the simulation calculation result, the long-beam acoustic focusing lens design method is feasible. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is a flow chart of a method for designing a long-beam acoustic focusing lens according to one embodiment of the present application;

[0039] Figure 2 This is a schematic diagram of the xy plane coordinates of the star column of this embodiment;

[0040] Figure 3 This is a schematic diagram of the inner diameter structure of the star-shaped column in this embodiment;

[0041] Figure 4This is a design diagram of the two-dimensional lattice array of this embodiment;

[0042] Figure 5 The following are the Matlab prediction calculation effect (a) and simulation calculation effect (b) of this embodiment. DETAILED DESCRIPTION

[0043] To make the purpose, technical solutions, and advantages of the embodiments of this application more clear, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the drawings in the embodiments of this application. Obviously, the described embodiments are part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0044] It should be noted that when a component is referred to as being "fixed to" or "disposed on" another component, it may be directly on the other component or there may be a central component. When a component is considered to be "connected to" another component, it may be directly connected to the other component or there may be a central component at the same time. The terms "vertical", "horizontal", "upper", "lower", "left", "right" and similar expressions used in the specification of this application are for illustrative purposes only and do not represent the only implementation method.

[0045] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of such features. Throughout the description of this application, "plurality" means at least two, for example, two, three, etc., unless otherwise specifically defined.

[0046] In this application, unless otherwise expressly specified or limited, when a first feature is "above" or "below" a second feature, it can mean that the first feature is directly in contact with the second feature, or the first feature and the second feature are indirectly in contact through an intermediary. Furthermore, when a first feature is "above," "above," or "above" a second feature, it can mean that the first feature is directly above or diagonally above the second feature, or simply means that the first feature is higher in level than the second feature. When a first feature is "below," "below," or "below" a second feature, it can mean that the first feature is directly below or diagonally below the second feature, or simply means that the first feature is lower in level than the second feature.

[0047] Unless otherwise defined, all technical and scientific terms used in the specification of this application have the same meaning as commonly understood by those skilled in the art to which this application belongs. The terms used in the specification of this application are only for the purpose of describing specific embodiments and are not intended to limit this application. The term "and / or" used in the specification of this application includes any and all combinations of one or more of the relevant listed items.

[0048] like Figures 1 to 4 As shown, in one embodiment, a method for designing a long-beam acoustic focusing lens includes the following steps:

[0049] Step S110 , designing a two-dimensional lattice array, where the two-dimensional lattice array is composed of rigid star-shaped columns in the air.

[0050] Specifically, the designed two-dimensional lattice array consists of N = n × m rigid star-shaped columns in the air, and the star-shaped columns are located at R i (i=1,2,3...), R i (i=1, 2, 3...) is located in R s An incident plane wave at a given frequency f passes through the two-dimensional lattice array along the x-axis.

[0051] Step S120 : constructing a sound pressure equation of the incident wave and a sound pressure equation of primary scattering of different star-shaped columns according to the two-dimensional lattice array.

[0052] Specifically, the acoustic pressure equation of the incident wave is:

[0053]

[0054] Where x is the horizontal distance from the center of the star column to the sound source, r is the straight-line distance from the center of the star column to the sound source, θ is the angle between r and the x-axis, and s is the Bessel function J s The order of .

[0055] The sound pressure equations for primary scattering of different star-shaped columns are:

[0056]

[0057] Where r is the straight-line distance from the center of the star column to the sound source, θ is the angle between r and the x-axis, and s is the Hankel function H s The order of .

[0058] Step S130 : constructing the boundary conditions of radial particle velocity on the surface of the star-shaped column according to the visco-thermal effect of the solid wall interface.

[0059] Due to the visco-thermal effect of the solid wall interface, the radial particle velocity on the surface of the star-shaped column is zero, and the velocity is proportional to the pressure gradient. The boundary conditions are:

[0060]

[0061] Among them, R in is the inner diameter of the star column.

[0062] Step S140: constructing a sound pressure equation at any point on the plane.

[0063] Specifically, when considering scattering, the sound pressure equation at any point (x, y) in the plane is:

[0064]

[0065] Step S150: Calculate the two-dimensional lattice array using Matlab to obtain a predicted calculation result.

[0066] Specifically, the two-dimensional lattice array is calculated by Matlab to obtain the predicted calculation effect, and the predicted calculation effect is compared with the simulation calculation effect, such as Figure 5 As shown in the figure, the predicted calculation effect (a) is consistent with the simulation calculation effect (b), so the long-beam acoustic focusing lens design method is feasible.

[0067] The above-mentioned long-beam acoustic focusing lens design method constructs the sound pressure equation of the incident wave and the sound pressure equation of the first scattering of different star-shaped columns by designing a two-dimensional lattice array. Based on the visco-thermal effect of the solid wall interface, the boundary conditions of the radial particle velocity on the surface of the star-shaped column and the sound pressure equation at any point on the two-dimensional plane are constructed. The two-dimensional lattice array composed of rigid star-shaped columns forms a topological structure. The characteristics of the topological structure enable this method to achieve more efficient long-beam acoustic projection for low-frequency wide bands. In addition, this method is more effective in the frequency band above 3000Hz.

[0068] It should be noted that focusing and imaging are crucial in wave physics, daily life, and practical engineering, with applications in medical diagnosis, ultrasonic lithotripsy, tumor hyperthermia, defect detection, biosensing, droplet migration, and cell migration. Long-beam acoustic focusing has potential applications in acoustic imaging, communications, stealth, camouflage, vibration / noise control, energy harvesting, nondestructive testing, particle manipulation, signal simulation and computing, information storage, and acoustic security.

[0069] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0070] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A method for designing a long-beam acoustic focusing lens, characterized in that: The method comprises: designing a two-dimensional lattice array consisting of rigid star-shaped columns in air; Constructing the sound pressure equation of the incident wave and the sound pressure equation of the primary scattering of different star-shaped columns according to the two-dimensional lattice array; According to the visco-thermal effect of the solid wall interface, the boundary conditions of the radial particle velocity on the surface of the star-shaped column are constructed; Construct the sound pressure equation at any point on the plane; The two-dimensional lattice array is calculated by MATLAB to obtain a predicted calculation effect, and the predicted calculation effect is compared with the simulation calculation effect. If the predicted calculation effect is consistent with the simulation calculation effect, the long-beam acoustic focusing lens design method is feasible.

2. The long-beam acoustic focusing lens design method according to claim 1, characterized in that: The design of the two-dimensional lattice array comprises: The designed two-dimensional lattice array consists of N=n×m rigid star-shaped rods in the air.

3. The long-beam acoustic focusing lens design method according to claim 2, characterized in that: The design of the two-dimensional lattice array further includes: The star-shaped columns are respectively located on the R i (i=1, 2, 3...).

4. The method for designing a long-beam acoustic focusing lens according to claim 3, wherein: The design of the two-dimensional lattice array further includes: The R i (i=1, 2, 3...) is located in R s An incident plane wave at a given frequency f passes through the two-dimensional lattice array along the x-axis direction.

5. The long-beam acoustic focusing lens design method according to claim 1, characterized in that: The sound pressure equation of the incident wave is: Where x is the horizontal distance from the center of the star column to the sound source, r is the straight-line distance from the center of the star column to the sound source, θ is the angle between r and the x-axis, and s is the Bessel function J s The order of .

6. The method for designing a long-beam acoustic focusing lens according to claim 1, wherein: The sound pressure equations of the first scattering of different star-shaped columns are: Where r is the straight-line distance from the center of the star column to the sound source, θ is the angle between r and the x-axis, and s is the Hankel function H s The order of .

7. The method for designing a long-beam acoustic focusing lens according to claim 1, wherein: The boundary conditions for constructing radial particle velocity on the surface of the star-shaped column include: Due to the visco-thermal effect of the solid wall interface, the radial particle velocity on the surface of the star-shaped column is zero, and the velocity is proportional to the pressure gradient. The boundary conditions are: Among them, R in is the inner diameter of the star-shaped column.

8. The method for designing a long-beam acoustic focusing lens according to claim 1, wherein: The sound pressure equation at any point on the constructed plane includes: When considering scattering, the sound pressure equation at any point (x, y) in the plane is:

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