Double-sided elastic metasurface and design method thereof

Abstract

The invention belongs to the technical field of elastic metasurfaces, and particularly relates to a double-sided elastic metasurface which is formed by arranging a series of unit cells in the interface direction, each unit cell comprises a strip-shaped unit and a stand column, the sizes of the strip-shaped units in the unit cells are the same, every two adjacent unit cells are separated through a groove body, and the stand columns are arranged on the strip-shaped units. The stand columns in each unit cell are the same in size, and each unit cell comprises at least two stand columns. The structure is simple, the design is easy, the processing is convenient, the propagation of the bending wave can be flexibly regulated and controlled, and the application prospect in the aspects of multifunctional elastic wave device design, structural health detection and the like is realized. In addition, the invention also discloses a design method of the double-sided elastic metasurface.

Description

Technical Field

[0001] The present invention belongs to the technical field of elastic supersurfaces, and in particular relates to a double-sided elastic supersurface and a design method thereof. Background Art

[0002] Flexible control of flexural waves is of great significance in promoting the development of elastic wave devices and achieving efficient energy transmission, vibration control and non-destructive testing. Elastic metasurfaces provide an innovative way to manipulate elastic waves in a novel way. It consists of artificially designed unit cell structures arranged along the interface direction. By designing the unit cell structure and arrangement to achieve the desired phase shift or transmission / reflection coefficient, the elastic metasurface can arbitrarily reshape the wavefront according to the generalized Snell's law and / or the Huygens-Fresnel principle.

[0003] In the process of implementing the present invention, the inventors found that there are at least the following problems in the prior art:

[0004] Existing structures mainly focus on bending waves incident from a single direction, and achieving arbitrary asymmetric transmission of bending waves incident from both directions remains a challenge. In addition, most elastic metasurface manipulation functions (such as focus point and deflection angle) will change significantly with the change of the incident frequency, resulting in a narrow operating frequency band or even only a single frequency, which limits the application of elastic metasurfaces. Summary of the invention

[0005] The purpose of the present invention is to address the deficiencies of the prior art and, on the one hand, to provide a double-sided elastic metasurface that has a simple structure, is easy to design, and is convenient to process. It can flexibly regulate the propagation of bending waves within a wide frequency range and has application prospects in the design of multifunctional elastic wave devices and structural health detection.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A double-sided elastic metasurface comprises a plurality of unit cells arranged along an interface direction, wherein the unit cells comprise strip units and columns, the strip units in each unit cell have the same size, two adjacent unit cells are separated by a groove, and the columns in each unit cell have the same size.

[0008] In some possible implementations, each of the unit cells includes at least two of the columns.

[0009] In some possible implementations, a uniform substrate is further included, the elastic metasurface is embedded in the uniform substrate, the uniform substrate has a negative region and a positive region, the end of the negative region and the end of the positive region are correspondingly marked with a negative excitation position and a positive excitation position, which are the incident positions of the bending wave.

[0010] On the other hand, a design method of a double-sided elastic metasurface is provided, comprising the following steps:

[0011] Step 1: Calculate the wavelength of the bending wave according to the uniform substrate thickness t and the target frequency to determine the total length l and width w of the strip unit in the unit cell, where l is greater than 1.5 times the wavelength and w is less than a quarter of the wavelength;

[0012] Step 2: Determine the column thickness t based on the uniform substrate thickness t p , satisfying t p >t;

[0013] Step 3, deriving the propagation path expressions of the positive incident and negative incident bending waves after being reflected by the double-sided elastic metasurface;

[0014] Step 4: Set the number of cells so that the total width is greater than 6 wavelengths, based on the propagation path of the positive and negative reflected bending waves. Wherein, the subscripts p and n represent the positive and negative directions, respectively, and determine the effective working lengths in the positive and negative directions in each unit cell;

[0015] Step 5: Determine the position and number of columns according to the total length of the unit cell, the effective working length of the positive and negative areas, and the thickness of the columns;

[0016] Step 6: Arrange the designed unit cells in order to construct a double-sided elastic metasurface.

[0017] In some possible implementations, the wavelength λ in step 1 may be calculated according to the following formula:

[0018]

[0019] Where ρ is the material density, ω = 2πf is the circular frequency, and D = Et 3 / 12(1-υ 2 ) is the bending stiffness, E is the Young's modulus of the material, and υ is the Poisson's ratio.

[0020] In some possible implementations, step 2 further includes:

[0021] According to the first-order Fano resonance frequency ω of the column F Equal to the target frequency band, determine the critical height of the column Column height meets The critical height can be calculated according to the following formula:

[0022]

[0023] Among them, β 4 =ρt p / D p , is the bending stiffness of the column.

[0024] In some possible implementations, step 3 is performed with (x 0 ,y 0 The focusing and reflection angle at point ) is θ r The deflection and path satisfy x = αy 2 The self-bending of , where α is the coefficient, the propagation path of the reflected bending wave changes with the distance y respectively:

[0025]

[0026] L r (y) = y sin θ r

[0027]

[0028] In some possible implementations, step 4 also includes

[0029] Step 4-1: Determine the effective working length in the positive and negative directions of each unit cell and The formula is as follows:

[0030]

[0031] Among them, j is the unit cell number, and is the effective working length of the positive and negative incident bending waves in the first unit cell, which is greater than one quarter wavelength, y j =w / 2+(j-1)w s is the coordinate of the jth unit cell, which is the sum of the unit cell width w and the slot width, and the slot width is 1 mm;

[0032] Step 4-2: Determine the effective working length of the unit cell and If it is greater than the maximum allowable length l M , then the length of the updated j-th unit cell satisfies:

[0033]

[0034] Wherein, m is a positive integer.

[0035] In some possible implementations, the step 5 further includes:

[0036] Step 5-1: In the jth unit cell, the positions of the first column and the last column are determined by the effective length and Determine, if the distance between the two columns Away from the FP resonance condition, the unit cell contains only two pillars;

[0037] Step 5-2: If the distance between the two pillars just meets the FP resonance condition, a third or even a fourth pillar needs to be introduced between the two pillars to change the distance between adjacent unit cells so that it meets the conditions in step 5-1.

[0038] In some possible implementations, in step 5, the unit cell spacing at the time of FP resonance can be determined according to the following formula:

[0039] kΔl=nπ+π / 2,(n∈Z)

[0040] Where k = (ρtω 2 / D) 1 / 4 is the wave number of the bending wave.

[0041] One of the above technical solutions has the following beneficial effects:

[0042] The double-sided elastic metasurface of the present invention has a simple structure, is easy to design, and is convenient to process. It can flexibly regulate the propagation of bending waves within a wide frequency range, and has application prospects in the design of multifunctional elastic wave devices, structural health detection, and the like.

[0043] The design method of the present invention introduces columns with a resonance frequency less than the control frequency in the strip unit, and designs the distance between adjacent columns to not meet the FP resonance condition, so that the reflection coefficients of the positive and negative incident bending waves are both 1, thereby achieving decoupling of the positive and negative incident bending waves. By adjusting the positions of the first and last columns, the effective propagation lengths of the positive and negative incident bending waves are changed, thereby independently adjusting the phase shifts of the positive and negative reflected bending waves. According to the desired wave propagation path and the phase shift compensation principle, the effective length required for the positive and negative incident bending waves in each unit cell is calculated, and the position and number of the columns are determined. The double-sided elastic metasurface constructed in this way can achieve any multifunctional independent regulation of the positive and negative incident bending waves, including but not limited to abnormal reflection, focusing, self-bending, etc., and the designed regulation effect can be achieved within a wide frequency range near the design frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Features, advantages, and technical effects of exemplary embodiments of the present invention will be described below with reference to the accompanying drawings.

[0045] Figure 1 It is a schematic diagram of the three-dimensional structure of the double-sided elastic supersurface of the present invention.

[0046] Figure 2 It is a schematic diagram of the top view structure of the double-sided elastic metasurface of the present invention.

[0047] Figure 3 It is a schematic diagram of the three-dimensional structure of the double-sided elastic metasurface unit cell of the present invention.

[0048] Figure 4 It is a schematic diagram of the front-view structure of the double-sided elastic metasurface unit cell of the present invention.

[0049] Figure 5 It is a schematic diagram of the three-dimensional structure of the double-sided elastic metasurface embedded in the plate of the present invention.

[0050] Figure 6 It is a schematic diagram of the top view structure of the double-sided elastic metasurface embedded in the plate of the present invention.

[0051] Figure 7 The figure is a graph showing the change of the unit cell reflection coefficient with frequency and the distance between the pillars of the present invention.

[0052] Figure 8 It is a schematic diagram of the wave field of the double-sided elastic metasurface of the present invention achieving focusing of negative incident bending waves and deflection of positive incident bending waves at frequencies of 5kHz, 6kHz and 7kHz.

[0053] Fig. 9 It is a distribution curve diagram of energy in the negative substrate of the double-sided elastic metasurface of the present invention at frequencies of 5kHz, 6kHz and 7kHz.

[0054] Fig.10 It is a curve diagram of energy directivity of the energy in the positive substrate of the double-sided elastic metasurface of the present invention at frequencies of 5kHz, 6kHz and 7kHz.

[0055] The reference numerals are described as follows:

[0056] 1- Strip unit;

[0057] 2- Pillar;

[0058] 3- Negative area;

[0059] 4- Positive area;

[0060] 5-the end of the negative zone;

[0061] 6- End of the positive zone. DETAILED DESCRIPTION

[0062] For example, certain words are used in the specification and claims to refer to specific components. Those skilled in the art should understand that hardware manufacturers may use different terms to refer to the same component. This specification and claims do not use differences in names as a way to distinguish components, but use differences in the functions of components as the criteria for distinction. For example, "including" mentioned throughout the specification and claims is an open term, so it should be interpreted as "including but not limited to". "Approximately" means that within an acceptable error range, those skilled in the art can solve technical problems within a certain error range and basically achieve technical effects.

[0063] Furthermore, the terms “first”, “second”, etc. are used for descriptive purposes only and are not to be understood as indicating or implying relative importance.

[0064] The present invention will be further described in detail below in conjunction with the accompanying drawings, but this is not intended to limit the present invention.

[0065] See also Figure 1-4 As shown, the double-sided elastic metasurface of the present invention is composed of a series of unit cells arranged along the interface direction, the unit cells include strip units 1 and pillars 2, the strip units 1 in each unit cell have the same size, and two adjacent unit cells are separated by fine grooves or grooves, and each unit cell contains at least two pillars 2, and the pillars 2 in each unit cell have the same size.

[0066] Among them, the unit cell configuration is to add several identical columns to the strip unit 1. The size of the strip unit, the position and number of the columns are designed according to the control frequency and the expected bending wave propagation path. While satisfying the positive and negative bending wave reflection coefficients of 1, independent adjustment of the reflection phase shift of bidirectional incident bending waves is achieved, and a double-sided elastic metasurface is constructed to achieve independent asymmetric path control of positive and negative incident bending waves.

[0067] See also Figure 5-6 As shown, the double-sided elastic metasurface is embedded in a uniform substrate, and the uniform substrate has a negative region 3 and a positive region 4. The end of the negative region and the end of the positive region are marked with a negative excitation position 5 and a positive excitation position 6, which are the incident positions of the bending wave.

[0068] Specifically, the double-sided elastic metasurface is composed of unit cells arranged along the interface direction and embedded in a uniform substrate. The unit cell includes a strip unit 1 and an additional column 2, and the unit cells are separated by fine grooves with the same width. The number and position of the columns 2 on different unit cells are different, which are determined according to the reflection coefficient and the phase shift, respectively. The strip unit 1 and the uniform substrate have the same thickness and are located on the same plane. The double-sided elastic metasurface and the uniform substrate have the same material, which can be metal, 3D printing material, etc.

[0069] According to the incident bending wave frequency and the desired wave propagation path, the unit cell structure is designed to form a double-sided elastic metasurface with a specific phase shift distribution, so as to achieve the purpose of independently regulating the bidirectional incident bending waves within a wide frequency range near the design frequency.

[0070] Specifically, the design method of the double-sided elastic metasurface includes the following steps:

[0071] Step 1: Calculate the wavelength of the bending wave according to the uniform substrate thickness t and the target frequency to determine the total length l and width w of the strip unit 1 in the unit cell. l should generally be greater than 1.5 times the wavelength, and w should generally be less than a quarter of the wavelength. The wavelength λ can be calculated according to the following formula:

[0072]

[0073] Where ρ is the material density, ω = 2πf is the circular frequency, and D = Et 3 / 12(1-υ 2 ) is the bending stiffness, E is the Young's modulus of the material, and υ is the Poisson's ratio;

[0074] Step 2: Determine the thickness t of column 2 based on the uniform substrate thickness t p , satisfying t p >t; According to the first-order Fano resonance frequency ω of column 2 F Equal to the target frequency band, determine the critical height of column 2 Column 2 height meets The critical height can be calculated according to the following formula:

[0075]

[0076] Among them, β 4 =ρt p / D p , is the bending stiffness of column 2.

[0077] Step 3: Give the propagation path expressions of the positive and negative incident bending waves after reflection by the double-sided elastic metasurface, with (x 0 ,y 0 The focusing and reflection angle at point ) is θ r The deflection and path satisfy x = αy 2 (α is the coefficient) as an example, where the propagation path of the reflected bending wave changes with the distance y (the interface direction of the double-sided elastic metasurface) respectively:

[0078]

[0079] L r (y) = y sin θ r

[0080]

[0081] Step 4: Set the number of cells so that the total width is generally greater than 6 wavelengths, based on the propagation path of the positive and negative reflected bending waves. Wherein, the subscripts p and n represent the positive and negative directions, respectively, and determine the effective working length of each unit cell;

[0082] Step 4-1: Determine the effective working length in the positive and negative directions of each unit cell and The formula is as follows:

[0083]

[0084] Among them, j represents the unit cell number, and is the effective working length of the positive and negative incident bending waves in the first unit cell, which is greater than one quarter wavelength, y j =w / 2+(j-1)w s is the coordinate of the jth unit cell, which is the sum of the unit cell width w and the slot width. The slot width is generally 1 mm;

[0085] Step 4-2: If the effective working length of the unit cell determined in step 4-1 is and Greater than the maximum allowed length l M , then the length of the updated j-th unit cell satisfies:

[0086]

[0087] Wherein, m is a positive integer.

[0088] Step 5: Determine the position and number of pillars 2 according to the total length of the unit cell, the effective working length of the positive and negative regions, and the thickness of the pillars 2;

[0089] Step 5-1: In the jth unit cell, the positions of the first column 2 and the last column 2 are determined by the effective length and Determine, if the distance between the two columns 2 Away from the FP resonance condition, the unit cell contains only two pillars 2;

[0090] Step 5-2: If the distance between two pillars 2 just meets the FP resonance condition, a third or even a fourth pillar 2 needs to be introduced between the two pillars 2 to change the distance between adjacent unit cells so that it meets the condition in step 5-1.

[0091] The unit cell spacing at FP resonance can be determined according to the following formula:

[0092] kΔl=nπ+π / 2,(n∈Z)

[0093] Where k = (ρtω 2 / D) 1 / 4 is the wave number of the bending wave;

[0094] Step 6: Arrange the designed unit cells in order to construct a double-sided elastic metasurface.

[0095] The double-sided elastic supersurface of the present invention is specifically described below with reference to an embodiment:

[0096] Step 1: Determine the uniform substrate thickness to be 1mm and the target frequency to be 6kHz. The uniform substrate and the unit cell are both made of aluminum alloy, with a Young's modulus of 70Gpa, a density of 2700kg / m3, and a Poisson's ratio of 0.33. The wavelength is 40.4mm. The total length of the strip unit 1 is selected to be 80mm and the width is 8mm.

[0097] Step 2: Based on the thickness of the uniform substrate of 1 mm, the thickness of the pillar 2 is selected to be 2 mm. At 6 kHz, the height of the pillar 2 corresponding to the first-order Fano resonance frequency of the pillar 2 is 12.05 mm, and the height of the pillar 2 is selected to be 20 mm.

[0098] Step 3: Set the reflection path of the negative incident bending wave to focus, and the focus position is (50mm, 30mm). According to the unit cell width of 8mm, the coordinate of each unit cell along the y direction is y j =[4+9*(j-1)]mm, so the reflection path at the jth unit cell is Assuming the reflection path of the forward incident bending wave is deflected along the -15° direction, the reflection path at the jth unit cell is

[0099] Step 4: Set the number of unit cells to 37. According to the propagation path of positive and negative reflected bending waves at different coordinates and the maximum allowable length of 35 mm, determine the effective working length l of 37 unit cells for incident waves in positive region 4 and negative region 3. p and l n , as shown in Table 1:

[0100] Table 1. Effective length of positive and negative regions of a unit cell (unit: mm)

[0101]

[0102] Step 5: Determine the distance between the first and last unit cells according to the effective working lengths of the positive and negative regions of the unit cell in Table 1. According to the formula kΔl=nπ+π / 2, (n∈Z), the relationship between the reflection coefficient of the incident bending wave and the spacing between the two columns and the frequency is analyzed, as shown in Figure 7 As shown in the figure, it is shown that in order to avoid FP resonance, the distance between the columns 2 should be Figure 7The intervals marked (A) and (B) are selected. Here, the 2nd, 6th, 7th, 8th, 12th to 18th, 26th, 28th, 29th, 31st to 33rd, and 35th to 37th cells contain 3 pillars 2. Pillar 2 close to the negative region 3 is taken as the first pillar. The distance between the first pillar and the second pillar is shown in Table 2, and the distance between the second pillar and the third pillar can be determined accordingly. The 27th cell contains 4 pillars, and the distance between the first pillar and the second pillar, and the distance between the second pillar and the third pillar are all 3 mm.

[0103] Table 2. Spacing between the first column and the second column in a unit cell (unit: mm)

[0104]

[0105] Step 6: The double-sided elastic metasurface constructed by the above unit cell is as follows Figure 1 and 2 As shown, embedded in a uniform substrate, such as Figure 5 and 6 shown.

[0106] For the double-sided elastic metasurface designed above, a corresponding finite element model is established in COMSOL finite element software. Figure 6 As shown in FIG. 1 , the negative excitation position 5 and the positive excitation position 6 are respectively applied to generate negative and positive incident bending waves, and the negative and positive reflected wave fields at 5 kHz, 6 kHz and 7 kHz are obtained, as shown in FIG. Figure 8 As shown. It can be seen that although the double-sided elastic metasurface is designed for a single frequency of 6kHz, under the three excitation frequencies, the negative incident bending wave has achieved a good focusing effect, while the positive incident bending wave is basically deflected along the -15° direction, showing the asymmetric transmission of the bidirectional incident bending wave consistent with the expectation. In order to further prove the wave control characteristics of the designed elastic metasurface in a wide frequency range, the x-direction and y-direction ( Figure 8 The energy distribution of the white dashed line in the middle is as follows: Fig. 9 As shown in Figure 1, it can be seen that at these three frequencies, the x and y coordinates corresponding to the maximum energy maintain a high consistency, indicating that the focus position hardly changes with frequency. Similarly, in the forward region 4, the directivity of the bending wave energy at frequencies of 5kHz, 6kHz and 7kHz is shown in Figure 1. Fig.10 As shown, it shows that the deflection angle maintains a high consistency with the design angle of -15° at these three frequencies, achieving deflection within a wide frequency range. The results prove the effectiveness of the double-sided elastic metasurface proposed in the present invention in independently regulating bidirectional incident bending waves within a wide frequency range.

[0107] According to the disclosure and teaching of the above description, those skilled in the art to which the present invention belongs can also change and modify the above embodiment. Therefore, the present invention is not limited to the above specific embodiments, and any obvious improvement, replacement or modification made by those skilled in the art on the basis of the present invention belongs to the protection scope of the present invention. In addition, although some specific terms are used in this specification, these terms are only for the convenience of description and do not constitute any limitation to the present invention.

Claims

1. A double-sided elastic metasurface, characterized in that: It is composed of a plurality of unit cells arranged along the interface direction, wherein the unit cells include strip units and columns, the strip units in each unit cell have the same size, two adjacent unit cells are separated by a groove body, and the columns in each unit cell have the same size.

2. A double-sided elastic metasurface according to claim 1, characterized in that: Each of the unit cells comprises at least two of the columns.

3. A double-sided elastic metasurface according to claim 2, characterized in that: It also includes a uniform substrate, the double-sided elastic metasurface is embedded in the uniform substrate, the uniform substrate has a negative region and a positive region, the end of the negative region and the end of the positive region are correspondingly marked with a negative excitation position and a positive excitation position, which are the incident positions of the bending wave.

4. A design method for a double-sided elastic metasurface, characterized in that: The steps include: Step 1: Calculate the wavelength of the bending wave according to the uniform substrate thickness t and the target frequency to determine the total length l and width w of the strip unit in the unit cell, where l is greater than 1.5 times the wavelength and w is less than a quarter of the wavelength; Step 2: Determine the column thickness t based on the uniform substrate thickness t p , satisfying t p >t; Step 3, deriving the propagation path expressions of the positive incident and negative incident bending waves after being reflected by the double-sided elastic metasurface; Step 4: Set the number of cells so that the total width is greater than 6 wavelengths, based on the propagation path of the positive and negative reflected bending waves. Wherein, the subscripts p and n represent the positive and negative directions, respectively, and determine the effective working lengths in the positive and negative directions in each unit cell; Step 5: Determine the position and number of columns according to the total length of the unit cell, the effective working length of the positive and negative areas, and the thickness of the columns; Step 6: Arrange the designed unit cells in order to construct a double-sided elastic metasurface.

5. The design method of a double-sided elastic metasurface according to claim 4, characterized in that: The wavelength λ of step 1 can be calculated according to the following formula: Where ρ is the material density, ω = 2πf is the circular frequency, and D = Et 3 / 12(1-υ 2 ) is the bending stiffness, E is the Young's modulus of the material, and υ is the Poisson's ratio.

6. A method for designing a double-sided elastic metasurface as claimed in claim 5, characterized in that: The step 2 also includes: According to the first-order Fano resonance frequency ω of the column F Equal to the target frequency band, determine the critical height of the column Column height meets The critical height can be calculated according to the following formula: Among them, β 4 =ρt p / D p , is the bending stiffness of the column.

7. A method for designing a double-sided elastic metasurface according to claim 6, characterized in that: In step 3, the focusing and reflection angles at the point (x0, y0) are θ r The deflection and path satisfy x = αy 2 The self-bending of , where α is the coefficient, the propagation path of the reflected bending wave changes with the distance y respectively: L r (y)=ysinθ r 8. The method for designing a double-sided elastic metasurface according to claim 7, characterized in that: The step 4 further includes: Step 4-1: Determine the effective working length in the positive and negative directions of each unit cell and The formula is as follows: Among them, j is the unit cell number, and is the effective working length of the positive and negative incident bending waves in the first unit cell, which is greater than one quarter wavelength, y j =w / 2+(j-1)w s is the coordinate of the jth unit cell, which is the sum of the unit cell width w and the slot width, and the slot width is 1 mm; Step 4-2: If the or Greater than the maximum allowed length l M , then the length of the updated j-th unit cell satisfies: Wherein, m is a positive integer.

9. A method for designing a double-sided elastic metasurface according to claim 8, characterized in that: The step 5 further includes: Step 5-1: In the jth unit cell, the positions of the first column and the last column are determined by the effective length and Determine, if the distance between the two columns Away from the FP resonance condition, the unit cell contains only two pillars; Step 5-2: If the distance between the two pillars just meets the FP resonance condition, a third or even a fourth pillar needs to be introduced between the two pillars to change the distance between adjacent unit cells so that it meets the conditions in step 5-1.

10. The design method of a double-sided elastic metasurface according to claim 9, characterized in that: In step 5, the unit cell spacing at the time of FP resonance can be determined according to the following formula: kΔl=nπ+π / 2,(n∈Z) Where k = (ρtω 2 / D) 1 / 4 is the wave number of the bending wave.

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