Method for constructing hyperbolic acoustic superlensing device based on laplace-helmholtz correspondence
By using the core-shell structure and the Laplace-Helmholtz correspondence, the parameter acquisition of the hyperbolic acoustic super-focusing device is simplified, the problems of focusing efficiency and bandwidth in the design of acoustic wave concentrators are solved, and a high-efficiency, wide-bandwidth acoustic super-focusing effect is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIHANG UNIV
- Filing Date
- 2026-05-07
- Publication Date
- 2026-07-31
AI Technical Summary
Existing acoustic wave concentrator designs suffer from limited focusing efficiency and poor controllability of the focusing area, making it difficult to achieve efficient and compact acoustic energy convergence. Furthermore, hyperbolic metamaterial designs face challenges such as complex parameters and narrow operating frequency bands, lacking a universal and efficient design method for broadband acoustic super-concentrating devices.
The hyperbolic acoustic super-focusing device with a core-shell structure simplifies parameter acquisition through the Laplace-Helmholtz correspondence and directly determines the density tensor and bulk modulus distribution by utilizing the correlation between the Laplace equation and the Helmholtz equation, thereby achieving acoustic focusing function.
It simplifies the construction process of hyperbolic acoustic super-focusing devices, breaks through the traditional focus rate limit, realizes efficient sound wave focus in a wide frequency range, and allows for flexible adjustment of the focus rate with precise control over a large dynamic range.
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Figure CN122490800A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of acoustic metamaterials, and more specifically to a method for constructing hyperbolic acoustic super-aggregation devices based on the Laplace-Helmholtz correspondence. Background Technology
[0002] Sound wave concentrators are important acoustic functional devices designed to significantly enhance sound pressure or intensity in a specific area, with broad application prospects in energy harvesting, medical ultrasound, acoustic sensing, and communication. Traditional sound wave concentrator designs primarily rely on geometric acoustic principles. For example, they guide sound wave focusing through refractive index gradients or material structure design. However, these methods typically suffer from limited focusing efficiency, poor controllability of the focusing area, or dependence on complex three-dimensional curved surface structures, making it difficult to achieve efficient and compact sound energy focusing.
[0003] To improve focusing efficiency, researchers have introduced the concepts of metamaterials and metasurfaces, designing subwavelength structural units to control the propagation phase and amplitude of sound waves. However, such methods often face the dilemma of balancing broadband operation with high-efficiency focusing. Focusing structures designed under quasi-static or low-frequency approximations often exhibit a sharp decline in performance with increasing frequency. Furthermore, most designs aim for isotropic or elliptical dispersive materials, whose focusing capabilities are limited by the traditional diffraction limit, making it difficult to achieve breakthrough sound intensity enhancement ratios.
[0004] Hyperbolic metamaterials, due to their unique open isofrequency characteristics, can theoretically support high wave vector propagation and extremely compressed wavelengths, providing a new approach to breaking through traditional focusing limits. However, effectively designing acoustic focusers with hyperbolic dispersion characteristics still faces significant challenges. Traditional transform acoustic methods are difficult to directly apply to hyperbolic parameter prediction; while focuser designs based on scattering cancellation suffer from narrow operating bandwidths. Moreover, existing designs often require simultaneous and independent optimization of two parameters, mass tensor density and bulk modulus, which not only complicates the design process but also typically limits the achieved hyperbolic focusing effect to a narrow operating bandwidth, lacking a universal, efficient system design method that can operate over a wide frequency range. Therefore, there is an urgent need to develop a novel design method that can directly and concisely derive the hyperbolic material parameters for efficient, broadband acoustic super-focusing from physical principles, and overcome the fundamental limitations of existing methods in parameter realization, operating bandwidth, and focusing capability, for the fabrication of hyperbolic acoustic super-focusing devices. This invention aims to solve this key technical problem. Summary of the Invention
[0005] To address the shortcomings of the prior art, the present invention aims to provide a method for constructing a hyperbolic acoustic super-focusing device based on the Laplace-Helmholtz correspondence. By utilizing the Laplace-Helmholtz correspondence, the technical problems of complex parameter acquisition and limited focusing effect of the hyperbolic acoustic super-focusing device are solved.
[0006] A method for constructing a hyperbolic acoustic super-converging device based on the Laplace-Helmholtz correspondence includes the following steps: S1, Establish the structure of the hyperbolic acoustic super-converging device: It adopts a core-shell structure, with a core radius of [missing information]. The shell radius is ; S2, establish the Laplace-Helmholtz correspondence; S3, determine the tensor density and bulk modulus of the shell hyperbolic density material; S31, Determine the coordinates of the hyperbolic acoustic super-converging device; S32, set the parameters of the hyperbolic acoustic super-converging device; S33, the pressure field distribution is determined by the Laplace equation; By applying the boundary conditions of the Laplace equation, the pressure field distribution at each location in the core, shell, and background, expressed in polar coordinates, is obtained. , and ; S34, determine the tensor density; Distribution of pressure field , and Substituting these into the boundary conditions, we obtain the tensor density of the core and the tensor density of the shell: (18) (19) in, and These are the tensor densities of the core and the shell, respectively. For a unit tensor, the first parameter Second parameter ,in , and These are the three components of the tensor density of the shell; S35, determine the bulk modulus; Based on the Laplace-Helmholtz correspondence, the bulk modulus of the core and the bulk modulus of the shell are obtained as follows: (20) ;(twenty one) in, and These are the bulk modulus of the core and the bulk modulus of the shell, respectively. ( ) represents the coordinate point in the polar coordinate system, and the third parameter is set. Set the fourth parameter ; S4, Simulation of hyperbolic acoustic super-convergence device; S5, Solidified Hyperbolic Acoustic Super-Concentration Device; Based on the simulation in S4, m and n are selected, and the tensor density and bulk modulus of the hyperbolic density material of the shell are obtained from S3. Artificial composite structures with corresponding acoustic responses are screened out, thereby finally determining the material composition of the core and shell, and materializing the hyperbolic acoustic super-aggregation device.
[0007] Preferably, the hyperbolic acoustic super-focusing device in S1 adopts a core-shell structure, specifically: The core is located at the center of the shell. The core is a solid sphere structure made of a single-density material, and the shell is a sphere structure made of hyperbolic density material with a certain thickness that tightly wraps around the core.
[0008] Preferably, the Laplace-Helmholtz correspondence in S2 is as follows: The density tensor and bulk modulus in a Helmholtz field can be directly solved using the density tensor and sound pressure gradient in a Laplace field. The specific calculation formula is as follows: (2) (3) In this context, the subscripts H and L represent the corresponding physical quantities in the Helmholtz field and the Laplace field, respectively. and Let these represent the density tensors in the Helmholtz field and the Laplace field, respectively. Denotes the bulk modulus in a Helmholtz field. Represents the sound pressure gradient in the Laplace field. It is a globally conserved quantity; Preferably, Set as .
[0009] Preferably, S31 determines the coordinates of the hyperbolic acoustic super-focusing device, specifically as follows: The hyperbolic acoustic superconcentrator is placed in a Cartesian coordinate system, with the origin at the center of the core. The center of the core coincides with the center of the shell and the center of the background. The upper and lower edges of the background satisfy the acoustic hard boundary condition, and the left and right edges satisfy the pressure boundary condition. A polar coordinate system is used ( Design of a hyperbolic acoustic super-focusing device; The transformation relationship between polar coordinates and rectangular coordinates is as follows: (4) (5) in,( () is the coordinate point in the polar coordinate system. , () is a coordinate point in a rectangular coordinate system.
[0010] Preferably, S32 sets the parameters of the hyperbolic acoustic super-focusing device as follows: Based on the structure of the hyperbolic acoustic super-focusing device in S1, determine the known quantities of the hyperbolic acoustic super-focusing device, including the core radius. and shell radius The background density is isotropic. ; Tensor density of the nucleus and shell tensor density It has the following characteristics: the nucleus has only one density, therefore The density is isotropic; the shell is a hyperbolic density material, and the three components of the shell's tensor density are set. , and It means, Then the shell tensor density The shell is a hyperbolic density material, therefore .
[0011] Preferably, in S33, the pressure field distribution is determined using the Laplace equation, specifically as follows: By applying the boundary conditions of the Laplace equation, the pressure field distribution at each location in the core, shell, and background is obtained. , and Represented using polar coordinates: (6) (7) (8) Establish the boundary conditions for the Laplace equation, and solve for the first to fifth coefficients based on the boundary conditions and formula (8). , , , and The value of .
[0012] Preferably, the first to fifth coefficients to be determined are obtained by solving the equation. Specifically, the boundary conditions of the Laplace equation are: (9) (10) (11) (12) Meanwhile, the pressure boundary conditions at the left and right edges of the background must ensure that the pressure distribution in the background does not become disordered, therefore, let Based on the boundary conditions and formula (8), the undetermined coefficients are obtained. , , , and The values are respectively: (13) (14) (15) (16) (17) To simplify the formula, the first parameter is set. .
[0013] Preferably, S4 performs simulation of the hyperbolic acoustic super-focusing device, specifically as follows: S41, the hyperbolic acoustic super-focusing device can achieve acoustic focusing function; The specific parameters of the hyperbolic acoustic super-focusing device were set, and physical field simulation was performed. The physical field simulation results show that the acoustic focusing function in Laplace and Helmholtz fields can be achieved using hyperbolic acoustic metamaterials. S42, Aggregation rate and first parameter Second parameter The relationships are as follows: Keep parameters Keep it unchanged, only adjust the parameters With parameters The increase in aggregation rate It exhibits a monotonically decreasing trend and gradually flattens out; Keeping parameter n constant and only adjusting parameter m, the aggregation rate increases as parameter m increases. Aggregation rate As m increases, it first rises and then falls, experiencing a trough before rising again to reach its highest peak, and then falls again.
[0014] Preferably, S5, the solidified hyperbolic acoustic super-focusing device, specifically comprises: First, based on the core radius given in S1 and shell radius The aggregation rate is obtained through S4. Following the evolution of hyperbolic parameters m and n, hyperbolic characteristic parameters are selected by scanning within a preset parameter space. and hyperbolic feature parameters and Substituting into S34 and S35, we obtain the tensor density components of the kernel and shell in spatial coordinates. and and equivalent bulk modulus and By using the effective medium theory to reverse-engineer and screen artificial composite structures with corresponding acoustic responses, the material composition of the core and shell was finally determined, and the hyperbolic acoustic super-aggregation device was materialized.
[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention establishes a Laplace-Helmholtz correspondence, so that after the density tensor in the Laplace field achieves a certain function, the density tensor and bulk modulus distribution required to achieve the same function in the Helmholtz field can be obtained directly through the conserved quantities and the sound pressure gradient in the Laplace field. This simplifies the determination of the density tensor and bulk modulus of the core and shell in the construction of hyperbolic acoustic super-aggregating devices.
[0016] 2. This invention, through numerical simulation analysis, clearly obtains the aggregation rate R as a function of the hyperbolic parameters. and The evolutionary pattern of this technology not only greatly simplifies the material selection process for hyperbolic acoustic super-converging devices, but also allows designers to comprehensively balance the subwavelength scale and convergence gain of the device by scanning within a preset parameter space. This enables the rapid reverse deduction and screening of artificial composite structures with corresponding acoustic responses using effective medium theory, ultimately efficiently determining the material composition of the core and shell.
[0017] 3. The hyperbolic acoustic super-focusing device obtained using this invention can break through the focusing rate limit of traditional acoustic focusing devices. In the prior art, the focusing rate limit of acoustic focusing devices designed based on traditional transform acoustics is usually the radius ratio of the shell to the core. The hyperbolic acoustic super-focusing device constructed using the method provided by this invention allows for independent and flexible adjustment of hyperbolic parameters. and It breaks through the physical limit of aggregation rate of traditional structures, and can achieve precise control of aggregation rate within a large dynamic range. Attached Figure Description
[0018] Figure 1 This is a block diagram of the method for constructing a hyperbolic acoustic super-focusing device based on the Laplace-Helmholtz correspondence according to the present invention; Figure 2 This is a schematic diagram of the Laplace-Helmholtz correspondence principle of the present invention; Figure 3 This is a schematic diagram of the hyperbolic acoustic super-focusing device of the present invention in a rectangular coordinate system; Figure 4 This is a schematic diagram of the hyperbolic acoustic super-aggregation device of the present invention, in which the shell layer is made of hyperbolic density material; Figure 5 This is a schematic diagram of the tensor density distribution of the hyperbolic acoustic hyperaggregation device of the present invention; Figure 6 This is a schematic diagram of the volume modulus distribution of the hyperbolic acoustic super-aggregating device of the present invention; Figure 7 This is a schematic diagram illustrating the realization of hyperbolic acoustic super-focusing in a Laplace field according to the present invention; Figure 8 This is a schematic diagram illustrating the realization of hyperbolic acoustic super-aggregation in a Helmholtz field according to the present invention; Figure 9 This is an example diagram illustrating the relationship between the aggregation rate and parameter n in the hyperbolic characteristic parameters of this invention; Figure 10 This is an example diagram illustrating the relationship between the aggregation rate and parameter m in the hyperbolic characteristic parameters of this invention; Figure 11 This is a simulation diagram of the hyperbolic acoustic super-aggregation device with different aggregation rates according to the present invention. Detailed Implementation
[0019] To fully explain the technical content, objectives, and effects of this invention, the embodiments of the invention will be described in detail below with reference to the accompanying drawings. This invention discloses a method for constructing a hyperbolic acoustic super-focusing device based on the Laplace-Helmholtz correspondence, such as... Figure 1 It includes the following steps: S1, establish the structure of the hyperbolic acoustic super-converging device.
[0020] The hyperbolic acoustic super-focusing device employs a core-shell structure. The core is located at the center of the shell and is a solid sphere made of a single-density material. The shell is a spherical structure made of hyperbolic density material with a certain thickness that tightly encloses the core. The radius of the core is... The shell radius is .
[0021] S2, establish the Laplace-Helmholtz correspondence.
[0022] Sound propagation can be described by the Helmholtz equation. When the frequency of sound wave propagation approaches 0, the Helmholtz equation degenerates into the Laplace equation. It is assumed that wavefronts in a Helmholtz field correspond to equipotential lines in a Laplace field. Therefore, the propagation time between two adjacent wavefronts is equal, i.e. Figure 2 middle The propagation time of the wave can be determined as: , (1) in, , The sound pressure in a Laplace field. This represents the pressure difference between two adjacent isobars in a Laplace field. Represents the sound pressure gradient in the Laplace field. Represents the modulo operator. Let be the effective sound velocity along the direction of the sound pressure gradient in the Laplace field. Further, it is assumed that the wave propagation time remains constant throughout the field, i.e. Figure 2 middle Based on the formula for wave propagation time, the global conserved quantities can ultimately be obtained. The above formula uses Einstein's summation convention. For operators that yield partial derivatives, and These are the subscripts for two orthogonal directions. Let the anisotropic tensor be determined by the density tensor and the bulk modulus. For the components in the corresponding directions, Globally conserved quantities The parameters in the Laplace field are related to those in the Helmholtz field, based on global conserved quantities. The relationship between the Laplace equation and the Helmholtz equation can be understood. Based on this relationship, the density tensor and bulk modulus in the Helmholtz field can be directly solved using the density tensor and sound pressure gradient in the Laplace field. The specific calculation formula is as follows: (2) (3) In this context, the subscripts H and L represent the corresponding physical quantities in the Helmholtz field and the Laplace field, respectively. and Let these represent the density tensors in the Helmholtz field and the Laplace field, respectively. Denotes the bulk modulus in a Helmholtz field. This represents the sound pressure gradient in the Laplace field.
[0023] Therefore, according to the Laplace-Helmholtz correspondence, when the density tensor in the Laplace field... Once a certain function is achieved, the density tensor and bulk modulus distribution required to achieve the same function in a Helmholtz field can be obtained directly from the conserved quantities and the sound pressure gradient in the Laplace field. Furthermore, the globally conserved quantities... Theoretically, it can take any value; different values only affect the wave speed and not the specific function. Therefore, if... This would further simplify the Laplace-Helmholtz correspondence.
[0024] S3, determine the tensor density and bulk modulus of the shell hyperbolic density material.
[0025] S31, determine the coordinates of the hyperbolic acoustic super-converging device.
[0026] The hyperbolic acoustic super-focusing device is placed in a Cartesian coordinate system, such as... Figure 3 As shown, the origin of the rectangular coordinate system is located at the center of the nucleus, and the center of the nucleus coincides with the center of the shell and the center of the background. Figure 3 In this diagram, I represents the core, II represents the shell, and III represents the background; these are collectively referred to as the solution domain. According to the settings in S1, the core radius is... and shell radius The top and bottom edges of the background satisfy the acoustic hard boundary condition, while the left and right edges of the background satisfy the pressure boundary condition.
[0027] Use polar coordinates ( The design of a hyperbolic acoustic super-focusing device involves the following transformation relationship between polar and rectangular coordinate systems: ; (4) ; (5) in,( () is the coordinate point in the polar coordinate system. , () is a coordinate point in a rectangular coordinate system.
[0028] S32 sets the parameters of the hyperbolic acoustic super-convergence device.
[0029] Based on the structure of the hyperbolic acoustic super-focusing device in S1, determine the known quantities of the hyperbolic acoustic super-focusing device, including the core radius. and shell radius The background density is isotropic. .
[0030] Tensor density of the nucleus and shell tensor density It has the following characteristics: Based on the structure of the hyperbolic acoustic super-aggregating device in S1, the core has only one density, therefore The density is isotropic; the shell is a hyperbolic density material, and the three components of the shell's tensor density are set. , and This indicates that, without loss of generality and for ease of calculation, let Then the shell tensor density Because the shell needs to be a hyperbolic density material, therefore ,like Figure 4 As shown.
[0031] S33, the pressure field distribution is determined by the Laplace equation.
[0032] Pressure field distribution at each location in the core, shell, and background. , and Using polar coordinates, they can be represented as follows: ; (6) ; (7) ; (8) , , , and The first to fifth coefficients are to be determined. The boundary conditions for the Laplace equation are: ; (9) ; (10) ; (11) ;(12) Wherein, equation (9) represents the radius of the shell. place and Similarly, equation (10) represents the radius of the nucleus. place and Similarly, equation (11) represents the value at the shell radius. The normal flow is continuous at the point where the core radius is given by equation (12). The normal flow at that point is continuous.
[0033] At the same time, setting the pressure boundary conditions at the left and right edges of the background needs to ensure that the pressure distribution in the background does not become disordered and does not lose generality, which can make... Based on the boundary conditions and formula (8), the undetermined coefficients are obtained. , , , and The value of .
[0034] In this embodiment, the first to fifth coefficients to be determined are obtained. , , , and They are respectively: ; (13) ;(14) ; (15) ; (16) ; (17) To simplify the formula, the first parameter is set. .
[0035] S34, determine the tensor density.
[0036] After obtaining the first to fifth coefficients, substitute them into formulas (6)-(8) to obtain the pressure field distribution. , and Then , and Substituting the boundary conditions, we can calculate the following: ; (18) ; (19) in, and These are the tensor densities of the core and the shell, respectively. Set the second parameter for the unit tensor. .
[0037] S35, determine the bulk modulus.
[0038] Based on the Laplace-Helmholtz correspondence, the hyperbolic hyper-aggregation effect is achieved by using a hyperbolic acoustic hyperaggregation device in a Helmholtz field. According to equation (3), the required bulk modulus of the core and shell can be obtained respectively.
[0039] For the core, the density tensor in the Laplace field is: The pressure field in Laplace's field is Therefore, according to equation (3), the bulk modulus of the nucleus can be obtained as: (20) For the shell, the density tensor in the Laplace field is: The pressure field in Laplace's field is Therefore, according to equation (3), the bulk modulus of the shell can be obtained as: ; (twenty one) in, and These are the bulk modulus of the core and the bulk modulus of the shell, respectively. ( ) represents the coordinate point in the polar coordinate system, and the third parameter is set. Set the fourth parameter According to equation (21), the bulk modulus of the shell is different at different locations.
[0040] In this embodiment, to simplify calculations, the globally conserved quantities are... Set as , In theory, it can take any value; different values only affect the wave speed and not the specific function.
[0041] S4 is used to simulate the hyperbolic acoustic super-convergence device.
[0042] S41, the hyperbolic acoustic super-focusing device, is capable of acoustic focusing.
[0043] By setting specific parameters for the hyperbolic acoustic super-focusing device and conducting physical field simulations, the results show that the hyperbolic acoustic metamaterial can achieve acoustic focusing in both Laplace and Helmholtz fields.
[0044] In this embodiment, the parameters of the hyperbolic acoustic super-convergence device are selected as an example. , , , Simulation verification is performed because , Therefore, m and n are also known as hyperbolic characteristic parameters. The physics simulation results are as follows: Figure 5 Tensor density distribution of hyperbolic acoustic super-aggregation device; Figure 6 The bulk modulus distribution of the hyperbolic acoustic super-aggregating device; Figure 7 This is shown as the realization of hyperbolic acoustic super-focus in a Laplace field; Figure 8 For the realization of hyperbolic acoustic super-aggregation in Helmholtz fields.
[0045] S42, Aggregation rate and first parameter Second parameter The relationship.
[0046] The effectiveness of an acoustic focusing device can be measured by its focusing rate. To characterize, aggregation rate This is the ratio of the core energy density to the background energy density. In existing technologies, the achievable focusing rate limit of acoustic focusing devices designed based on transformation acoustics is... .
[0047] In this invention, the aggregation rate of the hyperbolic acoustic super-aggregation device Precise adjustment can be achieved by independently adjusting the hyperbolic characteristic parameters m and n. As a demonstration, keep the parameters... Keep it unchanged, only adjust the parameters At this time, the aggregation rate With parameters Relationship such as Figure 9 As shown. According to Figure 9 The results shown show that, with the parameters The increase in aggregation rate It exhibits a monotonically decreasing trend. It is worth noting that... Figure 9 The green dashed line represents the traditional aggregation rate limit (marked as...). ).Depend on Figure 9 It can be seen that when When it is small, the aggregation rate Significantly higher than that limit; with With the increase of [a certain factor], the aggregation rate can exceed the traditional aggregation rate limit and gradually tend to level off. Three examples are taken: exceeding the aggregation rate limit, equal to the aggregation rate limit, and less than the aggregation rate limit. Simulations are performed using the S31 method, and the simulation results are as follows: Figure 10 As shown, both achieve a focusing effect based on acoustic hyperbolic media. This demonstrates that by flexibly adjusting the parameters... It can achieve precise control of the aggregation rate within a large dynamic range.
[0048] Keeping parameter n constant and only adjusting parameter m, the aggregation rate will then... The relationship with parameter n is as follows Figure 10 As shown. According to Figure 10 The results shown indicate the aggregation rate. As m increases, it first rises and then falls, experiencing a trough before rising sharply again to reach its highest peak, followed by another sharp decline. Simultaneously, due to... Figure 10 It can be seen that within a specific range of parameter m, the aggregation rate... It can significantly break through the traditional aggregation rate limit represented by the green dashed line.
[0049] S5, a physical hyperbolic acoustic super-convergence device.
[0050] When determining the specific structural parameters of the acoustic super-converging device, the core radius given by S1 is used as the first step. and shell radius The aggregation rate as a function of the hyperbolic characteristic parameter was obtained through numerical simulation analysis in S42 of S4. and The evolution pattern was then analyzed, and a scan was performed within a preset parameter space to achieve an aggregation rate greater than the traditional single-layer aggregation limit. (For example, the preset target aggregation gain is 2) As a design requirement to meet the aggregation gain, and to avoid extreme parameter values that would cause the calculated material density and bulk modulus to exceed actual processing capabilities, and as a trade-off standard for ease of manufacturing, appropriate parameter combinations are selected based on this. and As hyperbolic feature parameters. Subsequently, the selected hyperbolic feature parameters... and Substituting these values into step S3 yields the tensor density components of the kernel and shell in spatial coordinates. and and equivalent bulk modulus and Tensor density components and and bulk modulus and The parameter distribution is non-uniform. Further simulation using S41 confirmed that the acoustic super-focusing device meets the requirements. Figure 11 This is a simulation diagram of the effects of hyperbolic acoustic super-converging devices with different aggregation rates; finally, the effective medium theory is used to reverse-engineer and screen artificial composite structures with corresponding acoustic responses, thereby finally determining the material composition of the core and shell, and materializing the hyperbolic acoustic super-converging device.
[0051] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.
Claims
1. A method for constructing a hyperbolic acoustic super-focusing device based on the Laplace-Helmholtz correspondence, characterized in that, It includes the following steps: S1, Establish the structure of the hyperbolic acoustic super-converging device: A core-shell structure is adopted, with a core radius of [missing information]. The shell radius is ; S2, establish the Laplace-Helmholtz correspondence; S3, determine the tensor density and bulk modulus of the shell hyperbolic density material; S31, Determine the coordinates of the hyperbolic acoustic super-converging device; S32, set the parameters of the hyperbolic acoustic super-converging device; S33, the pressure field distribution is determined by the Laplace equation; By applying the boundary conditions of the Laplace equation, the pressure field distribution at each location in the core, shell, and background, expressed in polar coordinates, is obtained. , and ; S34, determine the tensor density; Distribution of pressure field , and Substituting these into the boundary conditions, we obtain the tensor density of the core and the tensor density of the shell: ； （18） ； （19） in, and These are the tensor densities of the core and the shell, respectively. For a unit tensor, the first parameter Second parameter ,in , and These are the three components of the tensor density of the shell; S35, determine the bulk modulus; Based on the Laplace-Helmholtz correspondence, the bulk modulus of the core and the bulk modulus of the shell are obtained as follows: ； （20） ； （21） in, and These are the bulk modulus of the core and the bulk modulus of the shell, respectively. ( ) represents the coordinate point in the polar coordinate system, and the third parameter is set. Set the fourth parameter ; S4, Simulation of hyperbolic acoustic super-convergence device; S5, Solidified Hyperbolic Acoustic Super-Concentration Device; Based on the simulation in S4, m and n are selected, and the tensor density and bulk modulus of the hyperbolic density material of the shell are obtained from S3. Artificial composite structures with corresponding acoustic responses are screened out, thereby finally determining the material composition of the core and shell, and materializing the hyperbolic acoustic super-aggregation device.
2. The method for constructing a hyperbolic acoustic super-focusing device based on the Laplace-Helmholtz correspondence according to claim 1, characterized in that, The hyperbolic acoustic super-focusing device in S1 adopts a core-shell structure, specifically: The core is located at the center of the shell. The core is a solid sphere structure made of a single-density material, and the shell is a sphere structure made of hyperbolic density material with a certain thickness that tightly wraps around the core.
3. The method for constructing a hyperbolic acoustic super-focusing device based on the Laplace-Helmholtz correspondence according to claim 1, characterized in that, The specific correspondence between Laplace-Helmholtz in S2 is as follows: The density tensor and bulk modulus in a Helmholtz field can be directly solved using the density tensor and sound pressure gradient in a Laplace field. The specific calculation formula is as follows: ； （2） ； （3） In this context, the subscripts H and L represent the corresponding physical quantities in the Helmholtz field and the Laplace field, respectively. and Let these represent the density tensors in the Helmholtz field and the Laplace field, respectively. Denotes the bulk modulus in a Helmholtz field. Represents the sound pressure gradient in the Laplace field. It is a globally conserved quantity.
4. The method for constructing a hyperbolic acoustic super-focusing device based on the Laplace-Helmholtz correspondence according to claim 3, characterized in that, Will Set as .
5. The method for constructing a hyperbolic acoustic super-focusing device based on the Laplace-Helmholtz correspondence according to claim 1, characterized in that, S31 determines the coordinates of the hyperbolic acoustic super-focusing device, specifically: The hyperbolic acoustic superconcentrator is placed in a Cartesian coordinate system, with the origin at the center of the core. The center of the core coincides with the center of the shell and the center of the background. The upper and lower edges of the background satisfy the acoustic hard boundary condition, and the left and right edges satisfy the pressure boundary condition. A polar coordinate system is used ( Design of a hyperbolic acoustic super-focusing device; The transformation relationship between polar coordinates and rectangular coordinates is as follows: ； （4） ； （5） in,( () is the coordinate point in the polar coordinate system. , () is a coordinate point in a rectangular coordinate system.
6. The method for constructing a hyperbolic acoustic super-focusing device based on the Laplace-Helmholtz correspondence according to claim 1, characterized in that, The parameters for the hyperbolic acoustic super-focusing device S32 are as follows: Based on the structure of the hyperbolic acoustic super-focusing device in S1, determine the known quantities of the hyperbolic acoustic super-focusing device, including the core radius. and shell radius The background density is isotropic. ; tensor density of the nucleus and shell tensor density It has the following characteristics: the nucleus has only one density, therefore The density is isotropic; the shell is a hyperbolic density material, and the three components of the shell's tensor density are set. , and It means, Then the shell tensor density The shell is a hyperbolic density material, therefore .
7. The method for constructing a hyperbolic acoustic super-focusing device based on the Laplace-Helmholtz correspondence according to claim 1, characterized in that, S33, the pressure field distribution is determined using the Laplace equation, specifically: By applying the boundary conditions of the Laplace equation, the pressure field distribution at each location in the core, shell, and background is obtained. , and Represented using polar coordinates: ； （6） ； （7） ； （8） Establish the boundary conditions for the Laplace equation, and solve for the first to fifth coefficients based on the boundary conditions and formula (8). , , , and The value of .
8. The method for constructing a hyperbolic acoustic super-focusing device based on the Laplace-Helmholtz correspondence according to claim 6, characterized in that, Solving for the first to fifth coefficients, we obtain the following: The boundary conditions for the Laplace equation are: ； （9） ； （10） ； （11） ； （12） Meanwhile, the pressure boundary conditions at the left and right edges of the background must ensure that the pressure distribution in the background does not become disordered, therefore, let Based on the boundary conditions and formula (8), the undetermined coefficients are obtained. , , , and The values are respectively: ； （13） ； （14） ； （15） ； （16） ； （17） To simplify the formula, the first parameter is set. .
9. The method for constructing a hyperbolic acoustic super-focusing device based on the Laplace-Helmholtz correspondence according to claim 1, characterized in that, S4 performs simulations of the hyperbolic acoustic super-focusing device, specifically as follows: S41, the hyperbolic acoustic super-focusing device can achieve acoustic focusing function; The specific parameters of the hyperbolic acoustic super-focusing device were set, and physical field simulation was performed. The physical field simulation results show that the acoustic focusing function in Laplace and Helmholtz fields can be achieved using hyperbolic acoustic metamaterials. S42, Aggregation rate and first parameter Second parameter The relationships are as follows: Keep parameters Keep it unchanged, only adjust the parameters With parameters The increase in aggregation rate It exhibits a monotonically decreasing trend and gradually flattens out; Keeping parameter n constant and only adjusting parameter m, the aggregation rate increases as parameter m increases. Aggregation rate As m increases, it first rises and then falls, experiencing a trough before rising again to reach its highest peak, and then falls again.
10. The method for constructing a hyperbolic acoustic super-focusing device based on the Laplace-Helmholtz correspondence according to claim 1, characterized in that, S5, the solidified hyperbolic acoustic super-focusing device is specifically as follows: First, based on the core radius given in S1 and shell radius The aggregation rate is obtained through S4. Following the evolution of hyperbolic parameters m and n, hyperbolic characteristic parameters are selected by scanning within a preset parameter space. and hyperbolic feature parameters and Substituting into S34 and S35, we obtain the tensor density components of the kernel and shell in spatial coordinates. and and equivalent bulk modulus and By using the effective medium theory to reverse-engineer and screen artificial composite structures with corresponding acoustic responses, the material composition of the core and shell was finally determined, and the hyperbolic acoustic super-aggregation device was materialized.