Full-angle broadband elastic wave efficient absorption metasurface and design method thereof

Abstract

The application discloses a full-angle elastic wave efficient absorption metasurface and a design method thereof, and relates to the technical field of elastic wave absorption. The full-angle elastic wave efficient absorption metasurface comprises a plate shell structure, a supercell structure layer is constructed by cutting part of the plate shell structure, and the cut plate shell structure is connected by multiple supercell structure layers; the material and thickness of the supercell structure layer are the same as those of the plate shell; the supercell structure layers are periodically arranged on the plate shell structure, and damping layers are attached to the upper and lower surfaces of the supercell structure layers. The application can realize one-way asymmetric elastic wave efficient absorption and bidirectional symmetric elastic wave efficient absorption.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of elastic wave absorption in plate-shell structure, and particularly relates to a full-angle elastic wave efficient absorption metasurface and a design method thereof. BACKGROUND

[0002] Plate-shell structure is widely used as the main carrier of vibration transmission in the fields of aerospace, civil engineering, vehicles, ships and other fields. The vibration level is an important indicator to measure the safe operation of the structure and equipment. At present, the vibration reduction and isolation methods of plate-shell are mainly divided into passive and active. Passive vibration reduction and isolation technology has the advantages of no external energy input, simple device structure and easy implementation. However, the traditional passive vibration reduction and isolation system contains a large amount of additional damping, which cannot meet the lightweight design requirements to achieve low-frequency vibration isolation. Active vibration reduction and isolation system has the advantage of flexible regulation and control of vibration reduction and isolation frequency, but the system design is complex, is greatly affected by the environment, and has the disadvantages of high cost, which limits its engineering application. Therefore, it is still a key technical problem to be solved to realize efficient energy absorption and vibration reduction of plate-shell with lightweight structure.

[0003] The proposal of elastic metasurface provides a new way to solve the problem of plate-shell structure vibration reduction and isolation. Elastic metasurface is an artificial composite material composed of sub-wavelength unit cells arranged periodically, which has excellent regulation and control function on elastic wave. Through the design of unit cell structure and a small amount of damping, the elastic wave energy in the plate-shell can be effectively absorbed. Especially for the reflected wave at the edge of the plate-shell, the elastic metasurface can completely absorb the incident wave to achieve no reflection. However, it is difficult to absorb the elastic wave at any position in the plate-shell. For the absorption of transmitted wave, the upper limit of energy absorption of traditional elastic metasurface is only 0.5. How to use elastic metasurface to realize the efficient absorption of transmitted elastic wave in plate-shell structure is still an important problem.

[0004] Existing elastic metasurfaces can achieve high-efficiency absorption of transmitted elastic waves by using asymmetric resonant unit cells. As described in document XIAOPENG LI, ZIQI YU, HIDEO LIZUKA, TAEHWA LEE. Experimental demonstration of extremely asymmetric flexural wave absorption at the exceptional point[J]. Extreme Mechanics Letters, 2022, 101649, by introducing loss, asymmetric resonant scatterers are obtained, which can achieve complete absorption of one-side incident wave and complete reflection of the other-side incident wave. However, this method is difficult to achieve complete absorption on both sides, which limits the application of this design method in practical engineering. In addition, the propagation direction of elastic waves in the plate shell is generally random, so the absorption of omnidirectional incident waves must also be considered. SUMMARY

[0005] In order to overcome the defects of the prior art, the present application provides a full-angle elastic wave high-efficiency absorption metasurface and a design method thereof. Based on the design method, one-way asymmetric elastic wave high-efficiency absorption can be achieved, and two-way symmetric elastic wave high-efficiency absorption can also be achieved.

[0006] In order to achieve the above purpose, the technical scheme adopted by the present application is:

[0007] A full-angle elastic wave high-efficiency absorption metasurface, comprising a plate shell structure 1, a plurality of supercell structure layers 2 are constructed by cutting part of the plate shell structure 1, and the plurality of supercell structure layers 2 connect the cut plate shell structure 1.

[0008] The supercell structure layers 2 are periodically arranged on the plate shell structure 1, and the upper and lower surfaces of the supercell structure layers 2 are attached with damping layers 3.

[0009] The plate shell structure 1 is a classical thin plate, which satisfies the Kirchholf assumption. The density, Young's modulus and Poisson's ratio of the plate shell structure are determined by the material, and the length L1, the width W1 and the thickness h are determined by the working condition.

[0010] The width of the supercell structure layer 2 is consistent with the arrangement period P, the length l is 1 / 5 to 1 times the wavelength, the thickness of the supercell structure layer 2 and the thickness of the plate shell structure 1 are both h, the supercell structure layer 2 and the damping layer 3 have the same length l and width P, and the thickness of the damping layer 3 is h l 1 to 2 mm.

[0011] The relationship between the incident wave and the reflected wave of the supercell structure layer 2 can be expressed as: sinθ in +nλ / P=sinθ r ;

[0012] wherein θ in and θ r are the incident angle and the reflection angle respectively, n is the diffraction order, λ is the wavelength, and P is the supercell arrangement period, the wavelength is determined by the working frequency;

[0013] When the wavelength is determined, by adjusting P and n, the reflection angle satisfies -1 < sinθ r <1, then there is a corresponding order of reflected wave; when P < λ / 2, n = 0 satisfies the reflected wave existence condition, at this time, there is only 0 order diffraction, in order to realize full-angle high-efficiency wave absorption, the width (i.e. arrangement period) P of the supercell structure layer 2 is less than 1 / 2 wavelength.

[0014] The supercell structure layer 2 comprises at least two unit cells, a connected unit cell b and a cantilever unit cell a, the length l of the supercell structure layer 2 is consistent with the length of the connected unit cell b, and l is in the range of 1 / 5 to 1 times the wavelength.

[0015] The supercell structure layer 2 is divided into asymmetric supercells and symmetric supercells.

[0016] The asymmetric supercell is composed of two unit cells, a cantilever unit cell a and a connected unit cell b, one end of the cantilever unit cell a is connected to the side of the plate shell structure 1 that needs to absorb incident waves, and the other end is free, the length and width of the connected end of the cantilever unit cell a are c; the connected unit cell b is connected to the plate shell structure 1 and is used to reduce the transmittance, so that most of the incident waves are reflected, and the reflected waves are absorbed by the cantilever unit cell a, so that the supercell realizes complete absorption of the incident waves. Therefore, when the wave is incident from the side connected to the plate shell structure 1 by the cantilever unit cell a, efficient absorption of the incident wave is realized; when the wave is incident from the other side, total reflection of the incident wave is realized.

[0017] The symmetric supercell is composed of a cantilever unit cell a, a cantilever unit cell a' and a connected unit cell b, the connected ends of the cantilever unit cell a and the cantilever unit cell a' are connected to the two sides of the plate shell structure 1 respectively, and the other ends are free, the connected unit cell b is connected to the plate shell structure 1 and is used to reduce the transmittance, so that most of the incident waves are reflected, and the reflected waves are absorbed by the cantilever unit cell a, so that the supercell realizes complete absorption of the incident waves. Therefore, when the wave is incident from the side connected to the plate shell structure 1 by the cantilever unit cell a, efficient absorption of the incident wave is realized; when the wave is incident from the other side, total reflection of the incident wave is realized.

[0018] The cantilever unit cell a is a bent beam, the connected unit cell b is a straight beam, the gap and the thickness of the bent beam are both c, and the overall length is less than l, the height d1 of the cantilever unit cell is adjusted so that the reflectivity at the working frequency is 0; the height d2 of the connected unit cell b is adjusted so that the transmittance at the working frequency is less than 0.3.

[0019] According to the wavelength λ determined by the frequency of the incident wave, by adjusting the supercell arrangement period P, P<λ / 2 is met, high-order diffraction is suppressed, and full-angle high-efficiency elastic wave absorption is realized; the geometric parameters of the supercell are designed, the length l of the supercell is determined according to the wavelength of the incident wave, and l is in the range of 1 / 5 to 1 times the wavelength; the gap and thickness c of the cantilever type cell are determined, and the total length of the cantilever type cell after bending is less than l; the height d1 of the cantilever type cell with the damping layer 3 is designed to realize complete absorption of reflected waves, and the height d2 of the connecting type cell is adjusted to reduce the transmittance; the cell gap is less than or equal to P / 2, and the sum of the cell gap and the height of all cells is less than the arrangement period P of the supercell structure layer 2; according to actual requirements, the connecting side of the cantilever type cell and the plate shell structure 1 is arranged to realize unilateral asymmetric or bilateral symmetric high-efficiency elastic wave absorption.

[0020] The connecting type cell b and the cantilever type cell a are combined to obtain a supercell, and the cell gap is less than or equal to P / 2, and the sum of the cell gap and the height of all cells is less than P.

[0021] The supercell structure layer 2 is arranged in a straight line or arranged in a circular ring circumferential array.

[0022] The supercell structure layer 2 is arranged in a straight line according to the period P to obtain a metasurface, the length of the metasurface is the same as the width W1 of the plate shell structure 1, the metasurface divides the plate shell structure 1 into two regions, and the elastic wave is absorbed when incident from the connecting side of the bent type cell and the plate; the angle θ of the circular ring array of the supercell structure layer 2 satisfies (d in +d out )sinθ=2P, wherein d in and d out are the inner diameter and the outer diameter, respectively, the inner diameter d in is determined according to actual working conditions, the bent type cell is connected with the inner circle to realize elastic wave absorption in the circular ring region.

[0023] A design method of a full-angle elastic wave high-efficiency absorption metasurface, the specific steps are as follows:

[0024] Step 1: Establish a finite element model of the plate shell structure 1 and the supercell structure layer 2;

[0025] Step 2: Determine the material and size of the plate shell structure 1 according to the working conditions, and determine the wavelength λ of the elastic wave in the plate shell structure 1;

[0026] Step 3: Design the length l of the connecting type cell in the supercell structure according to the wavelength of the incident wave, l is in the range of 1 / 5 to 1 times the wavelength, and adjust the height d2 of the connecting type cell b to make the transmittance less than 0.3;

[0027] Step 4: According to the design of the cantilever cell a in the supercell structure layer 2, the bending gap and the thickness c are designed, the total length of the cantilever cell a after bending is less than l, the height d1 of the cantilever cell is adjusted, and the reflection wave is completely absorbed at the working frequency;

[0028] Step 5: According to the actual demand, the cantilever cell a is arranged to realize asymmetric unilateral elastic wave absorption or symmetric bilateral elastic wave absorption;

[0029] Step 6: The required connecting cell b and cantilever cell a are combined to form a supercell, and according to the generalized Snell's law sinθ in +nλ / P=sinθ r , the supercell array period P is designed to be less than λ / 2, so that the incident wave absorption at any angle is realized; the cell gap is less than or equal to P / 2, and the sum of the cell gap and the height of all cells is less than the arrangement period P of the supercell structure layer 2.

[0030] Step 7: The supercell is arranged according to the working condition to obtain an elastic super surface, and the wave isolation and vibration reduction function of any area is realized.

[0031] The beneficial effects of the present application are:

[0032] 1、The present application is designed as a structure layer and a damping layer, the structure layer is composed of a cantilever cell and a connecting cell to form a supercell structure, and the damping layer is symmetrically attached to the upper and lower surfaces of the structure layer to provide loss. Under the action of the damping layer, the connecting cell reduces the transmittance, and the cantilever cell realizes complete absorption of the reflected wave on one side, so that the supercell can realize no reflection and no transmission. The elastic super surface obtained by periodically arranging the supercell can realize efficient absorption of elastic waves in any area of the plate and shell structure.

[0033] 2、The present application is designed according to the generalized Snell's law, the wavelength λ of the wave at the working frequency of the plate and shell structure, the arrangement period P of the supercell is designed to be less than 2 times the wavelength, so as to suppress the high-order diffraction of the elastic wave, and the elastic wave with different incident angles can be efficiently absorbed.

[0034] 3、The present application has simple structure, easy processing and strong reliability. The design method combines the low transmittance of the connecting cell and the full absorption of the reflected wave of the cantilever cell to realize efficient suppression of the transmitted elastic wave, and provides a new design idea for the vibration control of the plate and shell structure. DETAILED DESCRIPTION

[0035] Figure 1 It is a schematic diagram of an asymmetric supercell structure of the present application.

[0036] Figure 2 It is a curve graph of the absorption coefficient of the cantilever cell with different heights d1 to the reflected elastic wave with frequency.

[0037] Figure 3 This is a graph showing the transmission coefficient of the d2-connected unit cell of the present invention as a function of frequency.

[0038] Figure 4 yes Figure 1 The graphs shown depict the absorption coefficient of the asymmetric supercell as a function of frequency under normal and reverse incident conditions.

[0039] Figure 5 yes Figure 1 The graphs shown depict the reflection and transmission coefficients of the asymmetric supercell as a function of frequency under normal and reverse incident conditions.

[0040] Figure 6 yes Figure 1 The density plot shown illustrates the absorption coefficient of an asymmetric supercell as a function of frequency and incident angle under normal incidence.

[0041] Figure 7 yes Figure 1 The density plot shown is a representation of the absorption coefficient of an asymmetric supercell as a function of frequency and incident angle under reverse incidence.

[0042] Figure 8 This is a schematic diagram of a symmetrical supercell structure design with symmetrical wave absorption capability obtained by the optimization of the present invention.

[0043] Figure 9 yes Figure 8 The graphs shown depict the absorption coefficient of the symmetric supercell under normal and reverse incident conditions, along with the energy field at 5.1 kHz.

[0044] Figure 10 This invention relates to the arrangement of linear elastic metasurfaces in a plate and shell structure.

[0045] Figure 11 yes Figure 10 The diagram shows a detailed arrangement of the linear elastic metasurface structure layers.

[0046] Figure 12 The present invention relates to the arrangement of the annular elastic metasurface in a plate and shell structure.

[0047] Figure 13 yes Figure 12 The diagram shows a detailed arrangement of the annular elastic metasurface structure layers.

[0048] Figure 14 Under normal incidence conditions, Figure 11 The energy field diagram of the plate and shell structure shown is given when the incident wave is 5.1 kHz.

[0049] Figure 15 In the case of reverse incidence, Figure 11The energy field diagram of the plate-shell structure at an incident wave of 5.1 kHz is shown.

[0050] Figure 16 The vibration source is located Figure 12 in the closed area shown, the energy field diagram of the plate-shell structure at an incident wave of 5.1 kHz is shown.

[0051] Figure 17 The vibration source is located Figure 12 outside the closed area shown, the energy field diagram of the plate-shell structure at an incident wave of 5.1 kHz is shown.

[0052] Figure 18 The schematic diagram of the elastic metasurface arrangement in the plate-shell structure is shown.

[0053] In the figure, 1 is a plate-shell structure, 2 is a structure layer, 3 is a damping layer, and 4 is a vibration source.

[0054] Figure 19 The side view of the asymmetric supercell is shown.

[0055] Figure 20 The schematic diagram of the periodic arrangement of the asymmetric supercell is shown. DETAILED DESCRIPTION

[0056] The application will be further described in detail below with reference to the accompanying drawings.

[0057] The application provides a full-angle elastic wave efficient absorption metasurface for a plate-shell structure, which comprises a plate-shell structure 1, a plurality of periodically arranged supercell structure layers 2, and a damping layer 3 attached to the upper and lower surfaces of the structure layer 2.

[0058] As Figure 18 shown, the plate-shell structure 1 is a classic thin plate, which satisfies the Kirchholf assumption, and the density, Young's modulus and Poisson's ratio of the plate-shell structure are determined by the material, and the length L1, the width W1 and the thickness h are determined by the working condition.

[0059] The wavelength is determined by the working frequency, the width of the supercell structure layer 2 is consistent with the arrangement period P, and the length l is 1 / 5 to 1 times the wavelength. As Figure 1 、 Figure 19 、 Figure 20 shown, the thickness of the supercell structure layer 2 is consistent with the thickness of the plate-shell structure 1, both of which are h, the supercell structure layer 2 and the damping layer 3 have the same length l and width P, and the thickness h of the damping layer 3 is 1 to 2 mm. l .

[0060] The width of the supercell structure layer 2 is the arrangement period P, which is determined by the generalized Snell law; according to the generalized Snell law, the relationship between the incident wave and the reflected wave can be expressed as: sinθ in +nλ / P=sinθ r ; as Figure 1 shown, in the formula, θin and θ r are the incident angle and the reflection angle respectively, n is the diffraction order, λ is the wavelength, and P is the supercell arrangement period. When the wavelength is determined, by adjusting P and n, the reflection angle satisfies -1 < sinθ r <1, then there is a corresponding order of reflected waves; when P < λ / 2, n = 0 satisfies the reflected wave existence condition, at this time, there is only 0 order diffraction. In order to realize full-angle high-efficiency absorption, the width (i.e. arrangement period) P of the supercell structure layer 2 is less than 1 / 2 wavelength.

[0061] The supercell structure layer 2 includes at least two unit cells, a connected unit cell and a cantilever unit cell. As shown in Figure 1 , the length l of the supercell structure layer 2 is consistent with the length of the connected unit cell b, and l is in the range of 1 / 5 to 1 times the wavelength.

[0062] The structures of the connected unit cell and the cantilever unit cell are designed respectively, and the design process considers the damping layer 3, which is symmetrically pasted on the upper and lower surfaces of the structure layer. As shown in Figure 1 , the cantilever unit cell a is a bent beam, and the connected unit cell b is a straight beam. The gap and thickness of the bent beam of the cantilever unit cell a are both c, and the overall length is less than l. The height d1 of the cantilever unit cell is adjusted so that the reflectivity is 0 at the working frequency; the height d2 of the connected unit cell b is adjusted so that the transmittance is less than 0.3 at the working frequency.

[0063] The connected unit cell b and the cantilever unit cell a are combined to obtain a supercell, and the cell spacing can be less than or equal to P / 2, and the sum of the cell spacing and the height of all cells can be less than P.

[0064] As shown in Figure 11 , the supercell structure layer 2 is arranged linearly according to the period P to obtain a metasurface, and the length of the metasurface is the same as W1 of the plate-shell structure 1. The metasurface divides the plate-shell structure 1 into two regions, and the elastic wave is absorbed when it is incident from the side of the connection between the bent unit cell and the plate; as shown in Figure 13 , the angle θ of the supercell structure layer 2 of the circular ring array satisfies (d in +d out )sinθ = 2P, where d in and d out are the inner diameter and the outer diameter respectively, and the inner diameter d in is determined according to the actual working condition. The bent unit cell is connected with the inner circle to realize the absorption of the elastic wave in the circular ring region.

[0065] Reference Figure 1, the asymmetric supercell is composed of two unit cells, cantilever type unit cell a and connecting type unit cell b, one side of the cantilever type unit cell a is connected with the plate shell structure 1, and the other side is not connected, and the connecting type unit cell b is connected with both sides of the plate shell structure 1. The connecting type unit cell b reduces the transmittance, so that most of the incident waves are reflected, and the reflected waves are absorbed by the cantilever type unit cell a, so that the supercell realizes complete absorption of the incident waves. Therefore, when the wave is incident from the side connected with the plate shell structure 1 of the cantilever type unit cell a, efficient absorption of the incident wave is realized; when the wave is incident from the other side, total reflection of the incident wave is realized.

[0066] Reference Figure 8 , the supercell is composed of three unit cells, cantilever type unit cell a, cantilever type unit cell a' and connecting type unit cell b, and the cantilever type unit cell a and the cantilever type unit cell a' are respectively connected with both sides of the plate shell structure 1, and the other side is not connected. The connecting type unit cell b is connected with both sides of the plate shell structure 1. The connecting type unit cell b reduces the transmittance and reflects the incident wave, and the reflected wave of the left incident wave is absorbed by the cantilever type unit cell a, and the reflected wave of the right incident wave is absorbed by the cantilever type unit cell a', realizing efficient absorption of the symmetric incident wave.

[0067] According to the wavelength λ of the incident wave frequency, the arrangement period P of the supercell is adjusted to meet P<λ / 2, and high-order diffraction is suppressed, so that full-angle efficient elastic wave absorption is realized. The geometric parameters of the supercell are designed, the length l of the supercell is determined according to the wavelength of the incident wave, and l is in the range of 1 / 5 to 1 times the wavelength; the gap and the thickness c of the cantilever type unit cell are determined, and the total length of the cantilever type unit cell after bending is less than l; the height d1 of the cantilever type unit cell with the damping layer 3 is designed to realize complete absorption of the reflected wave, and the height d2 of the connecting type unit cell is adjusted to reduce the transmittance; the cell gap is less than or equal to P / 2, and the sum of the cell gap and the height of all the unit cells is less than the arrangement period P of the supercell structure layer 2. According to the actual requirement, the connected side of the cantilever type unit cell and the plate shell structure 1 is arranged to realize one-side asymmetric or two-side symmetric efficient absorption of the elastic wave.

[0068] The full-angle efficient absorption elastic super surface of the present application is explained and described below with specific embodiments:

[0069] Figure 10 As shown in the figure, the linear elastic super surface is obtained by cutting part of the plate shell structure 1, the material and thickness of the supercell structure layer 2 are the same as those of the plate shell structure 1; the supercell structure layer 2 is arranged in a straight line, and the damping layer 3 is attached to the upper and lower surfaces of the structure layer 2;

[0070] Reference Figure 11 , the supercell structure layer 2 is composed of two unit cells, the cantilever type unit cell a is connected with the left plate shell; the plate shell structure 1 has a length L1=468mm, a width W1=405mm and a plate thickness h=0.91mm; the material of the plate shell structure 1 is 304 steel plate, and its density, Young's modulus and Poisson's ratio are 7900kg / m 3200GPa and 0.3; Damping layer 3 uses VHB 4910, with a density, Young's modulus and Poisson's ratio of 1200kg / m³. 3 0.22(1+0.2i)MPa and 0.49.

[0071] Figure 12 The diagram shows a toroidal elastic metasurface. A supercell structure layer 2 is obtained by cutting a portion of the shell structure 1. The material and thickness of the structure layer 2 are the same as those of the shell structure 1. The supercell structure layers 2 are arranged in an array along the circumference of the ring, and a damping layer 3 is attached to the upper and lower surfaces of the structure layer 2. The inner diameter d of the ring is... in =176mm, outer diameter d out =196mm; Reference Figure 13 The supercell structure layer 2 consists of two unit cells, each with a central angle of θ. r =12.41°, where the cantilevered unit cell a is connected to the inner circle; the shell structure 1 has a length L2 = 800mm, a width W2 = 800mm, and a plate thickness h = 0.91mm; the shell structure 1 is made of 304 steel plate, with a density, Young's modulus, and Poisson's ratio of 7900kg / m3, 200GPa, and 0.3, respectively. The damping layer 3 uses VHB 4910, with a density, Young's modulus, and Poisson's ratio of 1200kg / m3. 3 0.22(1+0.2i)MPa and 0.49.

[0072] Figure 11 and Figure 13 Details of the supercell structure layer 2 and damping layer 3 are as follows: Figure 1 As shown, the supercell consists of a cantilevered unit cell a and a connected unit cell b; the geometric parameters are labeled in the figure as c = 1 mm, d1 = 2.5 mm, d2 = 1 mm, l = 10 mm, P = 20 mm, and the thickness of the damping layer 3 is h. l =1mm. An elastic wave is defined as being incident in the forward direction when it enters from the side where the cantilever unit cell a connects to the shell structure 1, and otherwise incident in the reverse direction.

[0073] In finite element software Figure 1 The supercell and constituent unit cells shown were simulated respectively.

[0074] Figure 2 The figure shows the absorption coefficient α as a function of frequency in a cantilever unit cell a with different heights d1 when the reflected elastic wave is incident normally (incident angle is 0°). The absorption coefficient is expressed as α = 1 - R, where the reflection coefficient R = |r| 2 The optimal absorption frequency shifts to lower frequencies as d1 increases; Figure 3 For a connected unit cell b with different heights d2, the transmission coefficient T = |t| is given when the transmitted elastic wave is incident normally (at an incident angle of 0°). 2With the change of frequency, the transmittance decreases with the increase of d2; at 5.1 kHz, the absorption coefficient of the cantilever type unit cell a is about 1, and the transmittance of the connecting type unit cell b is 0.2.

[0075] Figure 4 For normal incidence (the incidence angle is 0°), Figure 1 The finite element simulation results of the absorption coefficient alpha of the asymmetric unit cell with the change of frequency at normal incidence and reverse incidence, wherein the absorption coefficient is represented as alpha = 1-R-T. At normal incidence, the absorption coefficient of the asymmetric unit cell is more than 0.5 in the frequency range of 3 to 6.35 kHz, and the absorption coefficient reaches the maximum value of 0.93 at 5.1 kHz; at reverse incidence, the asymmetric unit cell almost has no effect on the absorption of energy. Figure 5 The reflection coefficient R and the transmittance T of the asymmetric unit cell with the change of frequency are shown. At normal incidence, the reflection coefficient is 0 and the transmittance is about 0.05 at 5.1 kHz; at reverse incidence, the transmittance is consistent with that at normal incidence, and the reflection coefficient increases obviously. The results show that Figure 1 The asymmetric unit cell realizes the asymmetric, wide-frequency and high-efficiency absorption of incident waves.

[0076] Figure 6 The finite element simulation results of the absorption coefficient of the asymmetric unit cell with the change of frequency at normal incidence are shown. Figure 1 At normal incidence, the finite element simulation results of the absorption coefficient of the asymmetric unit cell with the change of frequency are shown. According to the generalized Snell's law, the arrangement period of the unit cell is adjusted to suppress high-order diffraction, so that the unit cell can realize high-efficiency absorption at normal incidence, and then the approximate absorption efficiency can be realized at oblique incidence. Figure 1 The arrangement period P of the asymmetric unit cell is 20 mm, and the wavelength of the elastic wave in the plate-shell structure 1 is 40 mm at a frequency of 5.4 kHz, so P < lambda / 2 is met below 5.4 kHz. Figure 6 The absorption coefficient at normal incidence is shown, and the average absorption coefficient reaches 0.92 at 5.1 kHz and in the incidence angle range of-80° to 80°; the dotted line in the figure is the boundary of the absorption coefficient of 0.5; with the increase of the frequency and the incidence angle, the proportion of high-order diffraction of the elastic wave gradually increases, resulting in the decrease of the absorption coefficient; Figure 7 The absorption coefficient at reverse incidence is shown, and the average absorption coefficient is only 0.11 in the incidence angle range of-80° to 80° at 3 kHz to 6.5 kHz. Figure 6 And Figure 7 It is shown that Figure 1 The asymmetric unit cell can realize the full-angle, wide-frequency and high-efficiency absorption of the single-side incident wave.

[0077] Based on the design method of the application, Figure 8A two-side symmetric absorbing supercell is designed. The optimized symmetric supercell includes cantilevered cell a, connecting cell b and cantilevered cell a', where cell a and cell a' are connected to one side of the plate structure 1 respectively. The geometric parameters of the optimized supercell are c = 1 mm, d1 = 2.5 mm, d2 = 1 mm, l = 10 mm and P = 20 mm. The absorption effect of the symmetric supercell on elastic waves is simulated by using finite element method, Figure 9 The absorption coefficient α of the symmetric supercell with frequency is shown for forward and backward incidence, and the energy field diagram at 5.1 kHz. The symmetric supercell has symmetric wave absorbing ability and the maximum absorption coefficient reaches 0.98. The results show that the optimized symmetric supercell can realize symmetric elastic wave absorption.

[0078] The non-symmetric supercell shown in Figure 10 is taken as an example to obtain Figure 10 and Figure 12 elastic metasurfaces, and verify their wave absorbing performance.

[0079] Referring to Figure 10 and Figure 11 , the linear arrangement shown in Figure 1 obtains a linear elastic metasurface; the vibration source 4 is located at a distance of 109 mm from the elastic metasurface, and the vibration frequency is 5.1 kHz.

[0080] The energy field of the plate structure 1 for forward and backward incidence is shown in Figure 14 and Figure 15 . For forward and backward incidence, the transmitted field energy is low, which is consistent with the simulation results of the non-symmetric supercell isolating incident waves; for forward incidence, the reflected field energy is small, indicating that the incident wave is absorbed by the elastic metasurface; for backward incidence, the reflected wave is superimposed with the incident wave, showing obvious corrugation, indicating that the incident wave is reflected. Figure 8 It is shown that the designed elastic metasurface can realize full-angle non-symmetric wave absorption.

[0081] Referring to Figure 12 and Figure 13 , the non-symmetric supercell shown in Figure 1 is arranged in a circular ring to obtain a circular ring-shaped elastic metasurface.

[0082] Figure 16 The energy field diagram of the plate structure 1 when the vibration source 4 is at a distance of 42 mm from the center and the incident wave frequency is 5.1 kHz is shown. Since the elastic metasurface can realize low transmittance in the full-angle range of the incident angle of the elastic wave, the energy field outside the circular ring-shaped area is very small, realizing elastic wave isolation; due to the high-efficiency reflected wave absorption effect, the energy in the circular ring-shaped area is also low; Figure 16 It is shown that the elastic metasurface not only can isolate elastic waves, but also can prevent the energy in the enclosed area from being enhanced due to multiple reflections of the elastic waves.

[0083] Figure 17 The energy field diagram of the plate shell structure 1 when the vibration source 4 is located outside the circular ring area at a distance of 142 mm from the center, and the incident wave frequency is 5.1 kHz. Outside the circular ring area, due to the superposition of incident waves and reflected waves, obvious interference fringes are presented; and the energy inside the circular ring area is low, indicating that the elastic metasurface has the ability to protect any closed area from external elastic wave interference.

[0084] The design method for the full-angle efficient absorption of elastic waves in the transmission scenario of the plate shell structure, and the specific steps are as follows:

[0085] Step 1: Establish a finite element model of the plate shell structure 1 and the supercell structure layer 2;

[0086] Step 2: Determine the material and size of the plate shell structure 1 according to the working condition, and determine the wavelength of the elastic wave in the plate shell structure 1;

[0087] Step 3: Design the length l of the connected unit cell in the supercell structure according to the wavelength of the incident wave, l is in the range of 1 / 5 to 1 times the wavelength, adjust the height d2 of the connected unit cell, so that the transmittance is less than 0.3;

[0088] Step 4: Design the bending gap and thickness c of the cantilever unit cell in the supercell structure layer 2 according to l, the total length of the bent cantilever unit cell is less than l, and the height d1 of the cantilever unit cell is adjusted to achieve complete absorption of reflected waves at the working frequency;

[0089] Step 5: Arrange the cantilever unit cells according to actual needs to achieve asymmetric single-sided elastic wave absorption or symmetric double-sided elastic wave absorption;

[0090] Step 6: Combine the connected unit cells and the cantilever unit cells to form a supercell, and design the supercell array period P according to the generalized Snell's law sinθ in +nλ / P=sinθ r , so that P<λ / 2, to achieve the absorption of incident waves at any angle; the cell gap is less than or equal to P / 2, and the sum of the cell gap and the height of all cells is less than the arrangement period P of the supercell structure layer 2.

[0091] Step 7: Arrange the supercell according to the working condition to obtain an elastic metasurface, and realize the wave isolation and vibration reduction function in any area. It should be noted that the above description is only one of the embodiments of the present application, and equivalent changes made to the system described in the present application are included in the protection scope of the present application. Those skilled in the art of the present application can make similar substitutions to the described specific examples, as long as they do not deviate from the structure of the present application or exceed the scope of the present claims.

Claims

1. A full-angle elastic wave high-efficiency absorbing metasurface, characterized in that, The application relates to a plate shell structure (1), a supercell structure layer (2) is constructed by cutting part of the plate shell structure (1), and the cut plate shell structure (1) is connected by multiple supercell structure layers (2); The supercell structure layers (2) are periodically arranged on the plate shell structure (1), and damping layers (3) are attached to upper and lower surfaces of the supercell structure layers (2); The supercell structure layer (2) comprises at least two unit cells, a connecting type unit cell b and a cantilever type unit cell a, the length l of the supercell structure layer (2) is consistent with the length of the connecting type unit cell b, and l is in the range of 1 / 5 to 1 times the wavelength; The supercell structure layer (2) is divided into asymmetric supercells and symmetric supercells; The asymmetric supercell is composed of two unit cells, the cantilever type unit cell a and the connecting type unit cell b, one end of the cantilever type unit cell a is connected to one side of the plate shell structure (1) that needs to absorb incident waves, and the other end is free, the length and width of the connecting end of the cantilever type unit cell a are c; the connecting type unit cell b is connected to the plate shell structure (1) and is used for reducing the transmittance, so that most of the incident waves are reflected, the reflected waves are absorbed by the cantilever type unit cell a, and thus the supercell realizes complete absorption of the incident waves; when the waves are incident from the side connected to the plate shell structure (1), efficient absorption of the incident waves is realized; when the waves are incident from the other side, total reflection of the incident waves is realized; The symmetric supercell is composed of the cantilever type unit cell a, the cantilever type unit cell a' and the connecting type unit cell b, the connecting ends of the cantilever type unit cell a and the cantilever type unit cell a' are connected to two sides of the plate shell structure (1) respectively, and the other ends are free, the connecting type unit cell b is connected to the plate shell structure (1) and is used for reducing the transmittance to reflect the incident waves, the reflected waves at the connecting end of the cantilever type unit cell a are absorbed by the cantilever type unit cell a, the reflected waves at the connecting end of the cantilever type unit cell a' are absorbed by the cantilever type unit cell a', and efficient absorption of the symmetric incident waves is realized.

2. The full-angle elastic wave high-efficiency absorbing metasurface of claim 1, wherein, The width of the supercell structure layer (2) is consistent with the arrangement period P, the length l is 1 / 5 to 1 times the wavelength, the thickness of the supercell structure layer (2) and the thickness of the plate shell structure 1 are both h, the supercell structure layer (2) and the damping layer (3) have the same length l and width P, and the thickness of the damping layer (3) is h l 1 to 2 mm.

3. The full-angle elastic wave high-efficiency absorbing metasurface of claim 1, wherein, The relationship of the incident wave and the reflected wave of the supercell structure layer (2) can be expressed as: sin θ in + nλ / P = sin θ r ; where θ in and θ r are the incident and reflected angles, n is the diffraction order, λ is the wavelength, and P is the supercell periodicity, which is determined by the operating frequency. When the wavelength is determined, by adjusting P and n, the reflection angle is made to satisfy -1. <sinθ r When P < 1, there is a reflected wave of the corresponding order; when P < λ / 2, only n = 0 satisfies the condition for the existence of the reflected wave. At this time, there is only 0th order diffraction. In order to achieve efficient absorption of waves at all angles, the width P of the supercell structure layer (2) is less than 1 / 2 wavelength.

4. The full-angle elastic wave high-efficiency absorbing metasurface of claim 1, wherein, The cantilever type unit cell a is a bent beam, the connecting type unit cell b is a straight beam, the clearance and the thickness of the bent beam are both c, and the overall length of the bent beam is less than l, the height d1 of the cantilever type unit cell a is adjusted so that the reflectivity is 0 at the working frequency, and the height d2 of the connecting type unit cell b is adjusted so that the transmittance is less than 0.3 at the working frequency.

5. The omnidirectional elastic wave high-efficiency absorbing metasurface of claim 1, wherein, The connecting type unit cell b and the cantilever type unit cell a are combined to obtain a supercell, the interval between the unit cells is less than or equal to P / 2, and the sum of the interval between the unit cells and the sum of the heights of all the unit cells is less than P.

6. The omnidirectional elastic wave high-efficiency absorbing metasurface of claim 1, wherein, The supercell structure layer (2) is arranged in a straight line or is arranged in a circular ring circumferential array.

7. The full-angle elastic wave high-efficiency absorbing metasurface of claim 1, wherein, The supercell structure layer (2) is arranged in a straight line according to the period P to obtain a super surface, the length of the super surface is the same as the width W1 of the plate shell structure (1), the super surface divides the plate shell structure (1) into two regions, and the elastic waves are absorbed when being incident from the side connected to the plate of the bent type unit cell; The angle θ of the supercell structure layer (2) of the circular ring array satisfies (d in +d out )sinθ=2P, where d in and d out are respectively an inner diameter and an outer diameter, the inner diameter d in is determined according to actual working conditions, the bending type single cell is connected with the inner circle, and elastic wave absorption in the circular ring area is realized.

8. The design method of a full-angle elastic wave high-efficiency absorption metasurface according to any one of claims 1-7, characterized in that, The specific steps are as follows: Step 1: establishing a finite element model of the plate shell structure (1) and the supercell structure layer (2); Step 2: determining the material and size of the plate shell structure (1) according to the working condition, and determining the wavelength lambda of the elastic wave in the plate shell structure (1); Step 3: designing the length l of the connecting type unit cell b in the supercell structure according to the wavelength of the incident wave, l is in the range of 1 / 5 to 1 times the wavelength, and the height d2 of the connecting type unit cell b is adjusted so that the transmittance is less than 0.

3. Step 4: According to the design of the cantilever cell a in the supercell structure layer (2), the bending gap and thickness c of the cantilever cell a are adjusted, and the total length of the cantilever cell a after bending is less than l, the height d1 of the cantilever cell a is adjusted, and the reflection wave is completely absorbed at the working frequency; Step 5: According to the actual demand, arrange the cantilever cell a to realize the asymmetric unilateral elastic wave absorption or symmetric bilateral elastic wave absorption; Step 6: combine the desired connected-type unit cell b and the cantilever-type unit cell a to form a supercell, according to the generalized Snell's law sinθ in + nλ / P = sinθ r , design the supercell array period P so that P < λ / 2, realize the absorption of incident waves at any angle; the unit cell gap is less than or equal to P / 2, and the sum of the unit cell gap and the sum of the heights of all unit cells is less than the arrangement period P of the supercell structure layer (2); Step 7: According to the working condition, arrange the supercell to obtain the elastic super surface, and realize the wave isolation and vibration reduction function in any area.

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