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

Abstract

The invention discloses a full-angle elastic wave efficient absorption metasurface and a design method thereof. The full-angle elastic wave efficient absorption metasurface comprises plate shell structures, supercell structure layers are constructed by cutting part of the plate shell structures, and the cut plate shell structures are connected through the multiple supercell structure layers; the material and the thickness of the supercell structure layer are the same as those of the plate shell; on the plate shell structure, the supercell structure layers are periodically arranged, and damping layers are attached to the upper and lower surfaces of the supercell structure layers. According to the invention, unidirectional asymmetric elastic wave high-efficiency absorption can be realized, and bidirectional symmetric elastic wave high-efficiency absorption can also be realized.

Description

Technical Field

[0001] The present invention relates to the technical field of elastic wave absorption in plate-shell structures, and in particular to a full-angle elastic wave efficient absorption super surface and a design method thereof. Background Art

[0002] As the main carrier for transmitting vibration, plate and shell structures are widely used in the construction of main structures and components in the fields of aerospace, civil engineering, vehicles, ships, etc. The vibration level is an important indicator for measuring the safety of structures and equipment. At present, the vibration reduction and isolation methods for plates and shells are mainly divided into passive and active types. Passive vibration reduction and isolation technology has the advantages of not requiring 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 requirements of lightweight design to achieve low-frequency vibration isolation. The active vibration reduction and isolation system has the advantage of being able to flexibly adjust the vibration reduction and isolation frequency, but the system design is complex, it is greatly affected by the environment, and the high cost limits its engineering application. Therefore, the use of lightweight structures to achieve efficient energy absorption and vibration reduction of plates and shells is still a key technical problem that needs to be solved urgently.

[0003] The introduction of elastic metasurfaces provides a new way to solve the problem of vibration reduction and isolation of plate and shell structures. Elastic metasurfaces are artificial composite materials composed of periodic arrangements of unit cells at the subwavelength scale, and have excellent control functions for elastic waves. The elastic wave energy in plates and shells can be effectively absorbed through unit cell structure design and a small amount of damping. Especially for reflected waves at the edge of plates and shells, elastic metasurfaces can completely absorb incident waves to achieve zero reflection. However, it is more difficult to absorb elastic waves at any position in the plate and shell. For the absorption of transmitted waves, the upper limit of energy absorption of traditional elastic metasurfaces is only 0.5. How to use elastic metasurfaces to achieve efficient absorption of transmitted elastic waves in plate and shell structures is still an important issue.

[0004] Existing elastic metasurfaces can use asymmetric resonant unit cells to achieve efficient absorption of transmitted elastic waves. For example, the literature XIAOPENG LI, ZIQI YU, HIDEO LIZUKA, TAEHWALEE. Experimental demonstration of extremely asymmetric flexural wave absorption at the exceptional point [J]. Extreme Mechanics Letters, 2022, 101649. In this paper, an asymmetric resonant scatterer is obtained by introducing losses to achieve complete absorption of the incident wave on one side and complete reflection of the incident wave on the other side. However, this method is difficult to achieve complete absorption that is symmetrical on both sides, which limits the application of this design method in practical engineering. In addition, the propagation direction of elastic waves in plates and shells is generally random, so the absorption of omnidirectional incident waves must also be considered. Summary of the invention

[0005] In order to overcome the defects of the above-mentioned prior art, the present invention proposes a full-angle elastic wave efficient absorption metasurface and a design method thereof, based on which not only unidirectional asymmetric elastic wave efficient absorption can be achieved, but also bidirectional symmetric elastic wave efficient absorption can be achieved.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

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

[0008] On the plate-shell structure 1 , the supercell structure layers 2 are arranged periodically at various locations, and the damping layers 3 are attached to the upper and lower surfaces of the supercell structure layers 2 .

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

[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 Take 1 to 2mm.

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

[0013] When the wavelength is determined, the reflection angle is adjusted to -1 by adjusting P and n. <sinθ r <1, there exists 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 full-angle efficient 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 includes at least two unit cell structures, a connection 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 connection type 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 connection 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 the incident wave, and the other end is free. The length and width of the connection end of the cantilever unit cell a are c; the connection unit cell b is connected to the plate-shell structure 1 to reduce the transmittance, so that most of the incident wave is reflected, and the reflected wave is absorbed by the cantilever unit cell a, so that the supercell can completely absorb the incident wave. Therefore, when the wave is incident from the side where the cantilever unit cell a is connected to the plate-shell structure 1, the incident wave is efficiently absorbed; when the wave is incident from the other side, the incident wave is completely reflected;

[0017] The symmetric supercell is composed of three unit cells: a cantilever unit cell a, a cantilever unit cell a' and a connecting unit cell b. The connecting ends of the cantilever unit cell a and the cantilever unit cell a' are respectively connected to the two sides of the plate-shell structure 1, and the other end is free. The connecting unit cell is connected to the plate-shell structure 1. The connecting unit cell b reduces the transmittance and reflects the incident wave. The reflected wave at the connecting end of the cantilever unit cell a is absorbed by the cantilever unit cell a, and the reflected wave at the connecting end of the cantilever unit cell a' is absorbed by the cantilever unit cell a', thereby achieving symmetrical and efficient absorption of the incident wave.

[0018] The cantilever unit cell a is a bent beam, the connection unit cell b is a straight beam, the gap and thickness of the bent 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 operating frequency; the height d2 of the connection unit cell b is adjusted so that the transmittance is less than 0.3 at the operating frequency.

[0019] The wavelength λ is determined according to the frequency of the incident wave, and the supercell arrangement period P is adjusted to meet P<λ / 2 to suppress high-order diffraction, thereby achieving full-angle efficient elastic wave absorption; the geometric parameters of the supercell are designed, and the supercell length l is determined according to the wavelength of the incident wave, and l can be in the range of 1 / 5 to 1 times the wavelength; the gap and thickness c of the bent cantilever unit cell are determined, and the total length of the cantilever unit cell after bending can be less than l; the height d1 of the cantilever unit cell with the damping layer 3 is designed to achieve complete absorption of the reflected wave, and the height d2 of the connecting unit cell is adjusted to reduce the transmittance; the unit cell gap is less than or equal to P / 2, and at the same time, the sum of the unit cell gap and the height of all unit cells is less than the arrangement period P of the supercell structure layer 2. According to actual needs, the connection side of the cantilever unit cell and the plate shell 1 is arranged to achieve unilateral asymmetric or bilateral symmetric efficient elastic wave absorption.

[0020] The connected unit cell b and the cantilever unit cell a are combined to obtain a supercell, and the unit cell spacing can be less than or equal to P / 2, and the sum of the unit cell spacing and the height of all unit cells can be less than P.

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

[0022] The supercell structure layer 2 is arranged along a straight line according to a period P to obtain a supersurface. The length of the supersurface is the same as the width W1 of the plate-shell structure 1. The supersurface divides the plate-shell structure 1 into two regions. The elastic wave is absorbed when it is incident from the side where the bending unit cell is connected to the plate. 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 outer diameter respectively, the inner diameter d in According to the actual working conditions, the bent unit cell is connected to the inner circle to achieve elastic wave absorption in the annular area.

[0023] A design method for a metasurface with high efficiency in absorbing elastic waves at all angles, the specific steps are as follows:

[0024] Step 1: Establish finite element models of plate-shell structure 1 and 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 connected unit cell in the supercell structure according to the wavelength of the incident wave. l can be in the range of 1 / 5 to 1 times the wavelength. Adjust the height d2 of the entire connected unit cell-2 so that the transmittance is less than 0.3.

[0027] Step 4: Design the bending gap and thickness c of the cantilever unit cell-1 in the supercell structure layer 2 according to l. The total length of the cantilever unit cell-1 after bending is less than l. Adjust the height d1 of the cantilever unit cell to achieve complete absorption of reflected waves at the working frequency.

[0028] Step 5: Arrange the cantilever unit cell a according to actual needs to achieve asymmetric single-sided elastic wave absorption or symmetric double-sided elastic wave absorption;

[0029] Step 6: Combine the required connected unit cell b and cantilever 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, to achieve 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 all unit cell heights is less than the arrangement period P of the supercell structure layer 2.

[0030] Step 7: Arrange supercells according to working conditions to obtain an elastic metasurface to achieve wave isolation and vibration reduction functions in any area.

[0031] Beneficial effects of the present invention:

[0032] 1. The design of the present invention is divided into a structural layer and a damping layer. The structural layer is composed of a cantilever unit cell and a connected unit cell to form a supercell structure. The damping layer is symmetrically attached to both sides of the upper and lower surfaces of the structural layer to provide loss. Under the action of the damping layer, the connected unit cell reduces the transmittance, and the cantilever unit cell achieves complete absorption of the reflected wave on one side, so the supercell can achieve no reflection and no transmission. The elastic metasurface obtained by periodically arranging the supercell can achieve efficient absorption of elastic waves in any area of ​​the plate-shell structure.

[0033] 2. The present invention 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 is designed to be less than 2 times the wavelength, thereby suppressing the high-order diffraction of the elastic wave and achieving efficient absorption of elastic waves at different incident angles.

[0034] 3. The present invention has a simple structure, is easy to process, and has high reliability. This design method combines the low transmittance of the connected unit cell and the full absorption of the reflected wave of the cantilever unit cell to achieve efficient suppression of the transmitted elastic wave, providing a new design idea for the vibration control of the plate-shell structure. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0037] Figure 3 It is a curve diagram of transmission coefficient of d2-connected unit cells of different heights according to the present invention as a function of frequency.

[0038] Figure 4 yes Figure 1 The absorption coefficient of the asymmetric supercell shown is a graph of frequency variation at forward and reverse incidence.

[0039] Figure 5 yes Figure 1 The reflection and transmission coefficients of the asymmetric supercell shown are plotted as a function of frequency at forward and reverse incidence.

[0040] Figure 6 yes Figure 1 Density plot of the absorption coefficient of the asymmetric supercell shown as a function of frequency and angle of incidence at forward incidence.

[0041] Figure 7 yes Figure 1 Density plot of the absorption coefficient of the asymmetric supercell shown as a function of frequency and incident angle at reverse incidence.

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

[0043] Fig. 9 yes Figure 8 The absorption coefficient of the symmetric supercell shown is a graph of the variation with frequency under forward and reverse incidence, as well as the energy field diagram at 5.1kHz.

[0044] Fig.10 It is the arrangement of the linear elastic super surface of the present invention in the plate-shell structure.

[0045] Fig.11 yes Fig.10 Detailed diagram of the arrangement of the linear elastic metasurface structural layers is shown.

[0046] Fig.12 The invention relates to the arrangement of the annular elastic super surface in a plate-shell structure.

[0047] Fig.13 yes Fig.12 Detailed diagram of the donut-shaped elastic metasurface structure layer arrangement shown.

[0048] Fig.14 In the case of normal incidence, Fig.11 The energy field diagram of the plate and shell structure shown is when the incident wave is 5.1kHz.

[0049] Fig.15 In the case of reverse incidence, Fig.11The energy field diagram of the plate and shell structure shown is when the incident wave is 5.1kHz.

[0050] Fig.16 The vibration source is located at Fig.12 Energy field diagram of the plate and shell structure in the enclosed area shown when the incident wave is 5.1kHz.

[0051] Fig.17 The vibration source is located at Fig.12 Energy field diagram of the plate and shell structure outside the closed area shown when the incident wave is 5.1kHz.

[0052] Fig.18 It is a schematic diagram of the arrangement of elastic metasurfaces in plate and shell structures.

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

[0054] Fig.19 This is a side view of an asymmetric supercell.

[0055] Fig. 20 This is a schematic diagram of an asymmetric supercell periodic arrangement. DETAILED DESCRIPTION

[0056] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0057] The present invention provides a full-angle elastic wave efficient absorption metasurface for a plate-shell structure, comprising 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] like Fig.18 The plate and shell structure 1 shown is a classic thin plate that satisfies the Kirchholf assumption. The density, Young's modulus and Poisson's ratio of the plate and shell structure are determined by the material, and the length L1, width W1 and thickness h are determined by the working conditions.

[0059] The wavelength is determined by the operating 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. Figure 1 , Fig.19 , Fig. 20 As shown, the thickness of the supercell structure layer 2 is consistent with the thickness of the plate shell structure 1, both are 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 Take 1 to 2mm.

[0060] The width of the supercell structure layer 2 is the arrangement period P, which is determined by the generalized Snell's law. According to the generalized Snell's law, the relationship between the incident wave and the reflected wave can be expressed as: sinθ in +nλ / P=sinθ r ;like Figure 1 As shown, where θin and θ r are the incident angle and the reflection angle, n is the diffraction wave 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, there is a corresponding order of reflected wave; when P<λ / 2, only n=0 satisfies the condition of reflected wave existence, at this time, there is only 0th order diffraction. In order to achieve full-angle efficient wave 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 cell structures, a connection type unit cell and a cantilever type unit cell. Figure 1 , the length l of the supercell structure layer 2 is consistent with the length of the connected unit cell-2, 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 damping layer 3 is considered at the same time during the design process. The damping layer 3 is symmetrically attached to the upper and lower surfaces of the structural layer. Figure 1 , the cantilever unit cell-1 is a bent beam, and the connection unit cell b is a straight beam. The gap and thickness of the bent 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 to make the reflectivity 0 at the working frequency; the height d2 of the connection unit cell-2 is adjusted to make the transmittance 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 unit cell spacing can be less than or equal to P / 2, and the sum of the unit cell spacing and the height of all unit cells can be less than P.

[0064] like Fig.11 As shown, the supercell structure layer 2 is arranged in a straight line according to the period P to obtain a supersurface. The length of the supersurface is the same as W1 of the plate-shell structure 1. The supersurface divides the plate-shell structure 1 into two regions. The elastic wave is absorbed when it is incident from the side where the bending unit cell is connected to the plate; Fig.13 As shown, the angle θ of the supercell structure layer 2 of the ring array satisfies (d in +d out )sinθ=2P, where d in and d out are the inner diameter and outer diameter respectively, the inner diameter d in According to the actual working conditions, the bent unit cell is connected to the inner circle to achieve elastic wave absorption in the annular area.

[0065] refer to Figure 1The asymmetric supercell is composed of two unit cells, a cantilever unit cell a and a connection unit cell b. One side of the cantilever unit cell a is connected to the plate-shell structure 1, and the other side is not connected. The connection unit cell b is connected to both sides of the plate-shell structure 1. The connection unit cell b reduces the transmittance, so that most of the incident wave is reflected, and the reflected wave is absorbed by the cantilever unit cell a, so that the supercell can completely absorb the incident wave. Therefore, when the wave is incident from the side where the cantilever unit cell a is connected to the plate-shell structure 1, the incident wave is efficiently absorbed; when the wave is incident from the other side, the incident wave is completely reflected.

[0066] refer to Figure 8 The supercell is composed of three units: cantilever unit cell a, cantilever unit cell a' and connection unit cell b. Cantilever unit cell a and cantilever unit cell a' are connected to the two sides of the plate-shell structure 1 respectively, and the other side is not connected. The connection unit cell b is connected to the two sides of the plate-shell structure 1. The connection unit cell b reduces the transmittance and reflects the incident wave. The reflected wave of the incident wave on the left is absorbed by the cantilever unit cell a, and the reflected wave of the incident wave on the right is absorbed by the cantilever unit cell a', so as to achieve symmetrical and efficient absorption of the incident wave.

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

[0068] The full-angle high-efficiency absorbing elastic super surface of the present invention is explained below with specific embodiments:

[0069] Fig.10 The figure shows a linear elastic metasurface, in which a supercell structure layer 2 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 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] refer to Fig.11 The supercell structure layer 2 is composed of two unit cells, and the cantilever unit cell a is connected to the left plate shell; the plate shell structure 1 is L1 = 468mm long, W1 = 405mm wide, and the plate thickness h = 0.91mm; the plate shell structure 1 is made of 304 steel plate, and its density, Young's modulus and Poisson's ratio are 7900kg / m 3, 200 GPa and 0.3; the damping layer 3 is made of VHB 4910, whose density, Young's modulus and Poisson's ratio are 1200 kg / m 3 , 0.22(1+0.2i)MPa and 0.49.

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

[0072] Fig.11 and Fig.13 The details of the supercell structure layer 2 and the damping layer 3 are as follows Figure 1 As shown, the supercell is composed of a cantilever unit cell a and a connected unit cell b; the geometric parameters marked in the figure are c = 1mm, d1 = 2.5mm, d2 = 1mm, l = 10mm, P = 20mm, and the thickness of the damping layer 3 is h l = 1mm. It is defined that the elastic wave is incident from the side where the cantilever unit cell a is connected to the plate-shell structure 1 as forward incidence, and vice versa, as reverse incidence.

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

[0074] Figure 2 The figure shows the variation of the absorption coefficient α of the cantilever unit cell a with different heights d1 with the frequency when the reflected elastic wave is incident normally (the incident angle is 0°). The absorption coefficient is expressed as α=1-R, where the reflection coefficient R=|r| 2 , the optimal absorption frequency moves toward low frequency as d1 increases; Figure 3 The transmission coefficient T = |t| for the connected unit cell b with different heights d2 when the transmitted elastic wave is incident normally (the incident angle is 0°). 2As the frequency changes, the transmittance decreases as d2 increases; at 5.1kHz, the absorption coefficient of the cantilever unit cell a is about 1, and the transmission coefficient of the connected unit cell b is 0.2.

[0075] Figure 4 When the incident light is at normal incidence (the incident angle is 0°), Figure 1 The finite element simulation results of the absorption coefficient α of the asymmetric supercell changing with frequency at forward and reverse incidence, where the absorption coefficient is expressed as α=1-RT. At forward incidence, the absorption coefficient of the asymmetric supercell exceeds 0.5 in the frequency range of 3 to 6.35kHz, and reaches a maximum value of 0.93 at 5.1kHz; at reverse incidence, the asymmetric supercell has almost no energy absorption function. Figure 5 The figure shows the change of the reflection coefficient R and transmission coefficient T of the asymmetric supercell with frequency. When the incident light is forward, at 5.1kHz, the reflection coefficient is 0 and the transmission coefficient is about 0.05; when the incident light is reverse, the transmission coefficient is the same as that of the forward incident light, while the reflection coefficient increases significantly. The results show that Figure 1 The asymmetric supercell realizes asymmetric broadband and efficient absorption of incident waves.

[0076] Figure 6 Shows Figure 1 The finite element simulation results of the absorption coefficient of the non-opposite supercell at normal incidence varies with the incident angle and frequency. According to the generalized Snell's law, high-order diffraction is suppressed by adjusting the arrangement period of the supercell, so when the supercell is at normal incidence, the supercell can achieve efficient absorption, and then the absorption efficiency can be similar at oblique incidence. Figure 1 The asymmetric supercell arrangement period P is 20 mm. When the frequency is 5.4 kHz, the wavelength of the elastic wave in the plate shell 1 is 40 mm, and P<λ / 2 is satisfied below 5.4 kHz. Figure 6 The absorption coefficient at normal incidence is shown in the figure. At 5.1kHz, the incident angle is in the range of -80° to 80°, and the average absorption coefficient reaches 0.92. The dotted line in the figure is the limit of the absorption coefficient of 0.5. With the increase of frequency and incident angle, the proportion of high-order diffraction of elastic waves gradually increases, resulting in a decrease in the absorption coefficient. Figure 7 The absorption coefficient at reverse incidence is shown. At 3kHz to 6.5kHz, the average absorption coefficient is only 0.11 when the incident angle is in the range of -80° to 80°. Figure 6 and Figure 7 show Figure 1 The asymmetric supercell shown can achieve full-angle, wide-band and highly efficient absorption of single-side incident waves.

[0077] Based on the design method of the present invention, Figure 8The design of a bilaterally symmetrical supercell is given. The optimized symmetrical supercell includes a cantilever unit cell a, a connection unit cell b and a cantilever unit cell a', where unit cells a and a' are connected to one side of the plate shell 1 respectively. The geometric parameters of the optimized supercell are c = 1mm, d1 = 2.5mm, d2 = 1mml = 10mm, P = 20mm. The finite element method is used to simulate the absorption effect of the symmetrical supercell on elastic waves. Fig. 9 The figure shows the change of the absorption coefficient α of the symmetric supercell with frequency under forward and reverse incidence, as well as the energy field diagram at 5.1kHz. The symmetric supercell has symmetric wave absorption ability and the maximum absorption coefficient reaches 0.98. The results show that the optimized symmetric supercell can achieve symmetric elastic wave absorption.

[0078] by Fig.10 Take the asymmetric supercell shown in the figure as an example to obtain Fig.10 and Fig.12 The elastic metasurface shown verifies its wave-absorbing performance.

[0079] refer to Fig.10 and Fig.11 ,Will Figure 1 The straight line arrangement shown obtains a linear elastic metasurface; the vibration source 4 is located 109 mm away from the elastic metasurface, and the vibration frequency is 5.1 kHz.

[0080] The energy field of the plate-shell structure 1 under forward and reverse incidence is as follows: Fig.14 and Fig.15 As shown in the figure. For both forward and reverse incidence, the energy of the transmitted field is low, which is consistent with the simulation results of the asymmetric supercell isolating the incident wave; for forward incidence, the energy of the reflected field is small, indicating that the incident wave is absorbed by the elastic metasurface; for reverse incidence, the superposition of the reflected wave and the incident wave shows obvious ripples, indicating that the incident wave is reflected. Figure 8 This shows that the designed elastic metasurface can achieve all-angle asymmetric wave absorption.

[0081] refer to Fig.12 and Fig.13 ,Will Figure 1 The asymmetric supercells shown are arranged in a circular ring to obtain a circular elastic supersurface.

[0082] Fig.16 The figure shows the energy field diagram of the plate-shell structure 1 when the vibration source 4 is 42 mm away from the center of the circle and the incident wave frequency is 5.1 kHz. Since the elastic metasurface can achieve low transmittance in the entire range of elastic wave incident angles, the energy field outside the circular ring area is very small, achieving elastic wave isolation; due to the efficient absorption of reflected waves, the energy in the circular ring area is also low; Fig.16 This shows that the elastic metasurface can not only isolate elastic waves, but also prevent the elastic waves in the closed area from being enhanced due to multiple reflections.

[0083] Fig.17 This is the energy field diagram of the plate-shell structure 1 when the vibration source 4 is located outside the annular area and 142 mm from the center of the circle, where the incident wave frequency is 5.1 kHz. Outside the annular area, there are obvious interference fringes due to the superposition of the incident wave and the reflected wave; while the energy inside the annular area is lower, indicating that the elastic metasurface has the ability to protect any closed area from external elastic wave interference.

[0084] The design method of the present invention for full-angle efficient absorption of elastic waves in a plate-shell structure transmission scenario comprises the following specific steps:

[0085] Step 1: Establish finite element models of plate-shell structure 1 and supercell structure layer 2;

[0086] 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;

[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 can be in the range of 1 / 5 to 1 times the wavelength. Adjust the height d2 of the entire 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 cantilever unit cell after bending can be less than l. Adjust the height d1 of the cantilever unit cell 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 required connected unit cells and cantilever unit cells 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, to achieve 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 all unit cell heights is less than the arrangement period P of the supercell structure layer 2.

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

Claims

1. A metasurface with high efficiency of absorbing elastic waves at all angles, characterized in that: It comprises a plate-shell structure (1), a supercell structure layer (2) is constructed by cutting a part of the plate-shell structure (1), and a plurality of supercell structure layers (2) connect the cut plate-shell structure (1); On the plate-shell structure (1), the supercell structure layers (2) are arranged periodically at various locations, and damping layers (3) are attached to the upper and lower surfaces of the supercell structure layers (2).

2. The all-angle elastic wave efficient absorption metasurface according to claim 1, characterized in that: 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 Take 1 to 2mm.

3. The all-angle elastic wave efficient absorption metasurface according to claim 1, characterized in that: 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 ; Where θ in and θ r are the incident angle and reflection angle respectively, n is the diffraction wave order, λ is the wavelength, P is the supercell arrangement period, and the wavelength is determined by the operating frequency; When the wavelength is determined, the reflection angle is adjusted to -1 by adjusting P and n. <sinθ r <1, there exists 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 full-angle efficient wave absorption, the width (i.e., arrangement period) P of the supercell structure layer 2 is less than 1 / 2 wavelength.

4. The all-angle elastic wave efficient absorption metasurface according to claim 1, characterized in that: The supercell structure layer (2) comprises at least two unit cell structures, a connection 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 connection 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.

5. The all-angle elastic wave efficient absorption metasurface according to claim 4, characterized in that: The asymmetric supercell is composed of two unit cells, a cantilever unit cell a and a connection 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 the incident wave, and the other end is free. The length and width of the connection end of the cantilever unit cell a are c. The connection unit cell b is connected to the plate-shell structure (1) to reduce the transmittance, so that most of the incident wave is reflected, and the reflected wave is absorbed by the cantilever unit cell a, so that the supercell can completely absorb the incident wave. When the wave is incident from the side where the cantilever unit cell a is connected to the plate-shell structure (1), the incident wave is efficiently absorbed. When the wave is incident from the other side, the incident wave is completely reflected. The symmetric supercell is composed of three unit cells, namely a cantilever unit cell a, a cantilever unit cell a' and a connection unit cell b. The connection ends of the cantilever unit cell a and the cantilever unit cell a' are respectively connected to the two sides of the plate-shell structure (1), and the other end is free. The connection unit cell is connected to the plate-shell structure (1). The connection unit cell b reduces the transmittance and reflects the incident wave. The reflected wave at the connection end of the cantilever unit cell a is absorbed by the cantilever unit cell a, and the reflected wave at the connection end of the cantilever unit cell a' is absorbed by the cantilever unit cell a', thereby achieving symmetrical and efficient absorption of the incident wave.

6. The all-angle elastic wave efficient absorption metasurface according to claim 4, characterized in that: The cantilever unit cell a is a bent beam, the connection unit cell b is a straight beam, the gap and thickness of the bent 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 operating frequency; the height d2 of the connection unit cell b is adjusted so that the transmittance is less than 0.3 at the operating frequency.

7. The all-angle elastic wave efficient absorption metasurface according to claim 4, characterized in that: The connected unit cell b and the cantilever unit cell a are combined to obtain a supercell, and the unit cell spacing can be less than or equal to P / 2, and the sum of the unit cell spacing and the height of all unit cells can be less than P.

8. The all-angle elastic wave efficient absorption metasurface according to claim 4, characterized in that: The supercell structure layer (2) is arranged in a straight line or in a circular array.

9. The all-angle elastic wave efficient absorption metasurface according to claim 4, characterized in that: The supercell structure layer (2) is arranged along a straight line according to a period P to obtain a supersurface, the length of the supersurface is the same as the width W1 of the plate-shell structure (1), and the supersurface divides the plate-shell structure (1) into two regions, and elastic waves are absorbed when incident from the side where the bent unit cell is connected to the plate; The supercell structure layer (2) of the ring array has an angle θ that satisfies (d in +d out )sinθ=2P, where d in and d out are the inner diameter and outer diameter respectively, the inner diameter d in According to the actual working conditions, the bent unit cell is connected to the inner circle to achieve elastic wave absorption in the annular area.

10. A design method for a full-angle elastic wave efficient absorption metasurface based on any one of claims 1 to 9, characterized in that: The specific steps are as follows: Step 1: Establish finite element models of the plate-shell structure (1) and the supercell structure layer (2); 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); Step 3: Design the length l of the connected unit cell b in the supercell structure according to the wavelength of the incident wave. l can be in the range of 1 / 5 to 1 times the wavelength. Adjust the height d2 of the entire connected unit cell-2 so that the transmittance is less than 0.

3. Step 4: Design the bending gap and thickness c of the cantilever unit cell a in the supercell structure layer (2) according to l. The total length of the cantilever unit cell a after bending can be less than l. Adjust the height d1 of the cantilever unit cell a to achieve complete absorption of reflected waves at the working frequency. Step 5: Arrange the cantilever unit cell a according to actual needs to achieve asymmetric single-sided elastic wave absorption or symmetric double-sided elastic wave absorption; Step 6: Combine the required connected unit cell b and cantilever 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, and 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 height of all unit cells is less than the arrangement period P of the supercell structure layer (2); Step 7: Arrange supercells according to working conditions to obtain an elastic metasurface to achieve wave isolation and vibration reduction functions in any area.

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