Local resonance metasurface structure used for bending wave guiding and gathering and design method of local resonance metasurface structure

Abstract

The invention provides a local resonance metasurface structure for curved wave guiding and gathering and a design method thereof, and the local resonance metasurface structure comprises a substrate, and a plurality of first local resonance unit cells and second local resonance unit cells which are uniformly and collinearly arranged on the substrate. The first local resonance unit cell and the second local resonance unit cell are located in a first area and a second area of the substrate respectively, each of the first local resonance unit cell and the second local resonance unit cell comprises a first mass spring resonator and a second mass spring resonator, and the arrangement sequences are only opposite. The first mass spring resonator and the second mass spring resonator are different in mass but the same in rigidity. When a specific frequency is triggered at the edge of the substrate and at the position close to the unit cell according to a set frequency to generate a bending wave, a very obvious energy gathering effect can be generated at the interface of the two metasurface. The structure is simple, the unit cell size is far smaller than the incident wave wavelength, the incident wave form is not limited, external energy supply is not needed, and economical efficiency and environmental adaptability are high.

Description

Technical Field

[0001] The present invention relates to elastic fluctuations in engineering structures, and in particular to a localized resonant metasurface structure for guiding and focusing bending waves and a design method thereof. Background Art

[0002] Elastic wave metamaterials have functions and properties that natural materials do not have, providing a new way to manipulate elastic waves. They usually generate band structures through periodic or quasi-periodic arrangement of unit cells, and use local resonance or Bragg band gap to manipulate the wave characteristics of elastic waves in metamaterials.

[0003] With the introduction of the generalized Snell's law, metasurfaces, as a metamaterial with a more compact configuration, have attracted widespread attention. The compact configuration here refers to the periodic dimension of the metamaterial structure being smaller than the dimension of the target wave vector, such as a layered structure in three-dimensional space or a strip structure in two-dimensional space. Most metasurfaces present phase gradients by introducing a gradient of unit cells, thereby achieving arbitrary modulation of the wave surface, such as anomalous reflection or refraction, phantom source, and focusing. These metasurfaces are also called phase gradient metasurfaces. In addition, there are other compact periodic structures without phase gradients, which are also called metasurfaces. One is a periodic or gradient structure of a half-space surface, usually composed of a periodic array of holes and slots, which can achieve surface wave regulation such as rainbow capture, mode conversion, Umklapp conversion, and topological edge states; the other is a one-dimensional periodic or gradient structure formed in an infinite or semi-infinite plate, usually constructed of a slot array, which can guide and manipulate bending waves. The wave manipulation theory and methods based on elastic metamaterials or metasurfaces have promoted the development of low-frequency vibration isolation, energy capture, and structural health monitoring.

[0004] The ultimate goal of elastic wave manipulation technology based on metamaterials or metasurfaces is to change the energy distribution or energy transmission path in solids. The former includes local energy enhancement or absorption, and the latter includes anomalous refraction, wave mode conversion, etc. If you want to enhance the energy of bending waves at a certain position on a free thin plate, the known means are nothing more than constructing two-dimensional metamaterials with point and line defects, two-dimensional high-order topological insulators, and metasurfaces, superlenses, and phononic crystals for focusing flexible waves. However, two-dimensional metamaterials and topological insulators require resonators to be spread over the entire plate surface, which is equivalent to adding a lot of mass to the original system (free thin plate), while the structure that can be used to focus bending waves requires that the waves must be incident in the form of plane waves or cylindrical waves, both of which greatly hinder the path from methods to applications of metamaterials and metasurfaces. Summary of the invention

[0005] The applicant has found that the resonator can produce a sharp phase jump at a position close to its natural frequency, and in the metasurface structure, only a few unit cells use resonance to generate phase delay of elastic waves, while most of them generate phase delay through the movement of the resonator; in addition, the local resonance mechanism can greatly reduce the design size of the structure, and realize the control of elastic waves with larger wavelengths through a small structure. Based on the above research, the present invention proposes a local resonance metasurface structure for guiding and focusing bending waves and a design method thereof.

[0006] To achieve the above object, the technical solution adopted by the present invention is: a local resonance metasurface structure for guiding and focusing bending waves, comprising a substrate with four free sides and a first local resonance unit cell and a second local resonance unit cell fixed on the substrate;

[0007] The substrate comprises a first region and a second region, a plurality of the first local resonance unit cells and a plurality of the second local resonance unit cells are uniformly arranged in the first region and the second region respectively, and the first local resonance unit cells and the second local resonance unit cells are collinearly arranged; it is defined that the spacing between adjacent first local resonance unit cells and the spacing between adjacent second local resonance unit cells are both the first spacing;

[0008] The first local resonance unit cell includes a first mass spring resonator and a second mass spring resonator arranged in sequence; the second local resonance unit cell includes a second mass spring resonator and a first mass spring resonator arranged in sequence; the first mass spring resonator and the first mass spring resonator have the same stiffness but different masses; it is defined that the spacing between the first mass spring resonator and the second mass spring resonator in the first local resonance unit cell and the second local resonance unit cell is the second spacing;

[0009] The second spacing is equal to the first spacing;

[0010] When a bending wave is generated at a set frequency at the edge of the substrate and close to the first local resonant unit cell or the second local resonant unit cell, the bending wave can propagate along the substrate and generate energy concentration at the interface between the first region and the second region.

[0011] Furthermore, the substrate is made of metal material.

[0012] Furthermore, when the local resonance metasurface structure is mounted on an excitation source, the excitation source is located at an edge of the substrate and close to the first local resonance unit cell or the second local resonance unit cell.

[0013] The present invention also provides a design method for a local resonant metasurface structure for guiding and focusing bending waves, comprising the following steps:

[0014] Step 1, obtaining the material density ρ, Young's modulus E, Poisson's ratio υ and thickness h of the substrate, and calculating the bending wave dispersion curve;

[0015] Step 2, determining the spacing between the first mass-spring resonator and the second mass-spring resonator in the first local resonance unit cell according to the set effective operating frequency band of the bending wave and the bending wave dispersion curve obtained in step 1, so that the first band edge frequency of the bending wave dispersion curve in the first Brillouin zone of the first local resonance unit cell is within the set effective operating frequency band of the bending wave;

[0016] Step 3, setting a bending wave effective operating frequency, wherein the bending wave effective operating frequency is within a set bending wave effective operating frequency band;

[0017] Step 4, establishing a finite element model including a first local resonant unit cell and a substrate corresponding to the first local resonant unit cell, performing characteristic frequency analysis based on the finite element model to obtain a band structure of the first local resonant unit cell, and determining whether a band gap of the first local resonant unit cell band structure corresponds to the effective operating frequency of the bending wave set in step 3, and if so, obtaining the stiffness and mass of the first mass-spring resonator and the second mass-spring resonator, and if not, adjusting the stiffness and mass of the first mass-spring resonator and the second mass-spring resonator until the band gap of the first local resonant unit cell band structure corresponds to the set effective operating frequency of the bending wave;

[0018] Step 5, using the spacing between the first mass spring resonator and the second mass spring resonator in the first local resonance unit cell as the unit cell spacing between adjacent first local resonance unit cells and adjacent second local resonance unit cells;

[0019] Step 6, determining the number of the first local resonance unit cell and the second local resonance unit cell according to the actual bending wave energy concentration interface position requirement;

[0020] Step 7: Determine the length of the substrate according to the determined unit cell numbers and unit cell spacings of the first local resonance unit cell and the second local resonance unit cell, and the spacing between the first mass-spring resonator and the second mass-spring resonator.

[0021] Furthermore, in step 6, the number of the first local resonance unit cell and the number of the second local resonance unit cell are both no less than 5.

[0022] Furthermore, when calculating the bending wave dispersion curve in step 1, the intrinsic loss is neglected.

[0023] Furthermore, in step 4, the spring masses in the first mass-spring resonator and the second mass-spring resonator are ignored.

[0024] The present invention has the following beneficial effects:

[0025] 1. The local resonance metasurface structure for guiding and focusing bending waves of the present invention comprises a first metasurface and a second metasurface on a substrate free on all sides, and a plurality of spring oscillator units are symmetrically distributed, wherein the spring oscillator unit cell comprises two oscillator spring resonators, namely a first mass spring resonator and a second mass spring resonator, wherein the two oscillator spring resonators have the same spring stiffness but different oscillator masses, and at the interface between the first metasurface and the second metasurface, energy of the bending waves is concentrated, and by adopting a metasurface structure with a simple structure and a small volume, the guiding and focusing of the bending waves is achieved, and the robustness is strong.

[0026] 2. The substrate in the local resonance metasurface structure of the present invention is integrated and made of the same material, which is convenient for production and processing. In addition, since the substrate is not cut, the rigidity of the substrate is guaranteed. The guidance and aggregation of the bending waves are achieved without destroying the original structure of the substrate. The substrate can be designed into any shape according to actual needs, and has strong environmental adaptability.

[0027] 3. There is no restriction on the excitation frequency in the local resonance metasurface structure of the present invention. It is only necessary to adjust the parameters of the first mass-spring resonator and the second mass-spring resonator according to the frequency band of the incident wave. It is universal, especially applicable to low-frequency meter-scale substrates or high-frequency micro-nanoscale substrates.

[0028] 4. The local resonant metasurface structure of the present invention has no restrictions on the incident form of bending waves, and only needs to apply excitation at the edge of the substrate and close to the first mass-spring resonator or the second mass-spring resonator. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0030] Figure 1 It is a schematic diagram of the structure of the localized resonant metasurface for guiding and focusing bending waves of the present invention;

[0031] Figure 2 is a schematic diagram of the first local resonance unit cell and the corresponding mounted substrate;

[0032] Figure 3 It is a comparison diagram of the wave energy distribution along the local resonance metasurface structure of the present invention and along a single metasurface at different excitation frequencies;

[0033] Figure 4 It is a field distribution diagram of the regional displacement amplitude of the local resonance metasurface structure of the present invention when the excitation frequency is 1.79kHz.

[0034] Explanation of the reference numerals: 1 - substrate, 2 - first metasurface, 3 - second metasurface, 4 - first local resonant unit cell, 5 - second local resonant unit cell, 6 - first mass-spring resonator, 7 - second mass-spring resonator. DETAILED DESCRIPTION

[0035] Embodiments of the present invention are described in detail below. The embodiments are exemplary and intended to be used to explain the present invention, but should not be construed as limiting the present invention.

[0036] Reference Figure 1 and Figure 2 This embodiment provides a local resonance metasurface structure for guiding and focusing bending waves, comprising a substrate 1 and a first local resonance unit cell 4 and a second local resonance unit cell 5 fixed on the substrate 1. The substrate comprises a first region 2 and a second region 3, a plurality of the first local resonance unit cells 4 and a plurality of the second local resonance unit cells 5 are uniformly arranged in the first region 2 and the second region 3, respectively, and the first local resonance unit cells 4 and the second local resonance unit cells 5 are collinearly arranged; it is defined that the spacing between adjacent first local resonance unit cells and the spacing between adjacent second local resonance unit cells are both the first spacing.

[0037] The first local resonance unit cell 4 and the second local resonance unit cell 5 each include two oscillator spring resonators, namely, a first mass spring resonator 6 and a second mass spring resonator 7. The two oscillator spring resonators in the first local resonance unit cell 4 and the second local resonance unit cell are arranged in opposite order, and the spacing between the first mass spring resonator 6 and the second mass spring resonator 7 in the unit cell is defined as a second spacing. The second spacing is equal to the first spacing. The mass of the first mass spring resonator 6 is different from the mass of the second mass spring resonator 7, but the stiffness is the same.

[0038] The first region on the substrate and a plurality of first local resonant unit cells arranged in the region constitute a first metasurface, and the second region on the substrate and a plurality of second local resonant unit cells arranged in the region constitute a second metasurface. The first metasurface and the second metasurface have the same dispersion curve, but the wave modes corresponding to the different-order curves of the first metasurface and the second metasurface are opposite, that is, the two metasurfaces have opposite topological properties. When a bending wave is generated on the substrate at a set frequency, when the bending wave is incident on the local resonant metasurface composed of the first metasurface and the second metasurface, a special frequency point will appear within the band gap range, and the bending waves at this frequency point will gather at the interface between the first metasurface and the second metasurface, resulting in energy concentration, thereby forming a one-dimensional topological interface state of the bending wave.

[0039] In this embodiment, the substrate is made of metal. Compared with other materials, the bending wave energy gathering effect on the metal substrate is more obvious.

[0040] Since the unit cell parameters and quantity of the first local resonance unit cell and the second local resonance unit cell are different, the interface positions of the first metasurface and the second metasurface are different, and the energy gathering effect is also different. Next, we need to design the unit cell parameters, quantity and spacing of the first local resonance unit cell and the second local resonance unit cell according to the effective working frequency band of the bending wave and the energy gathering position requirements. The specific steps are as follows:

[0041] Step 1, obtaining the material density ρ, Young's modulus E, Poisson's ratio υ and thickness h of the substrate, and calculating the bending wave dispersion curve. When calculating the bending wave dispersion curve, the intrinsic loss is ignored.

[0042] Step 2: determining the spacing between the first mass-spring resonator and the second mass-spring resonator in the first local resonance unit cell according to the set effective operating frequency band of the bending wave and the bending wave dispersion curve obtained in step 1, so that the first band edge frequency of the bending wave dispersion curve in the first Brillouin zone of the first local resonance unit cell is within the set effective operating frequency band of the bending wave.

[0043] Step 3: setting the effective working frequency of the bending waves, wherein the effective working frequency of the bending waves is within the set effective working frequency band of the bending waves.

[0044] Step 4, establishing a finite element model including a first local resonant unit cell and a substrate corresponding to the first local resonant unit cell, performing characteristic frequency analysis based on the finite element model to obtain a band structure of the first local resonant unit cell, and determining whether a band gap of the first local resonant unit cell band structure corresponds to the effective operating frequency of the bending wave set in step 3, and if so, obtaining the stiffness and mass of the first mass-spring resonator and the second mass-spring resonator; if not, adjusting the stiffness and mass of the first mass-spring resonator and the second mass-spring resonator until the band gap of the first local resonant unit cell band structure corresponds to the set effective operating frequency of the bending wave.

[0045] When adjusting the mass of the first mass-spring resonator and the second mass-spring resonator, only the mass of the oscillator is considered and the mass of the spring is ignored.

[0046] In order to further confirm the stiffness and mass of the first mass-spring resonator and the second mass-spring resonator, and whether the second local resonance unit cell band structure meets the requirements, before step 5, a verification step of the second local resonance unit cell band structure is also included, and the specific process is as follows:

[0047] Using the parameters of the first mass spring resonator and the second mass spring resonator obtained in step 2 and step 4, a finite element model including the second local resonance unit cell and the substrate corresponding to the second local resonance unit cell is established, and characteristic frequency analysis is performed to obtain the band structure of the second local resonance unit cell, and whether the band structure of the second local resonance unit cell is consistent with the band structure of the first local resonance unit cell obtained in step 4 is checked. If consistent, it is determined that the parameters of the first mass spring resonator and the second mass spring resonator obtained in step 4 meet the band structure design requirements of the first local resonance unit cell and the second local resonance unit cell. Since the first local resonance unit cell and the second local resonance unit cell both include the first mass spring resonator and the second mass spring resonator arranged at the same interval, only the arrangement order is different, in theory, the parameters of the first mass spring resonator and the second mass spring resonator in the designed first local resonance unit cell are applied to the second local resonance unit cell, and the band structures of the two units will be the same, but in actual engineering design, verification and confirmation are required to ensure that the band structures of the two units are the same.

[0048] Step 5: Using the spacing between the first mass-spring resonator and the second mass-spring resonator in the first local resonance unit cell as the unit cell spacing between adjacent first local resonance unit cells and adjacent second local resonance unit cells.

[0049] Step 6, according to the actual bending wave energy gathering interface position requirement, determine the number of the first local resonance unit cell and the second local resonance unit cell. In order to obtain a better energy gathering effect, the number of the first local resonance unit cell and the second local resonance unit cell is not less than 5. According to different interface position requirements, the number of the first local resonance unit cell and the second local resonance unit cell can be the same or different.

[0050] Step 7: Determine the length of the substrate according to the determined number of first local resonance unit cells and second local resonance unit cells, the unit cell spacing, and the spacing between the first mass spring resonator and the second mass spring resonator. The length of the substrate is not less than the sum of the overall lengths of all uniformly arranged first local resonance unit cells and second local resonance unit cells.

[0051] Finally, the parameters of the first local resonance unit cell and the second local resonance unit cell are obtained, and the first local resonance unit cell and the second local resonance unit cell are fixed on the substrate with the obtained unit cell spacing of adjacent first local resonance unit cells, and the mass and stiffness of the first mass spring resonator and the second mass spring resonator, to obtain the local resonance metasurface structure of the present invention. When in use, the local resonance metasurface structure is placed on an excitation source, and the excitation source is located at the edge of the substrate and close to the first local resonance unit cell or the second local resonance unit cell.

[0052] In order to verify that the local resonance metasurface structure of the present invention has the effect of focusing incident waves of a specific frequency, the following simulation analysis is performed on the specific local resonance metasurface structure designed by the above design method. In this example, the substrate is an aluminum rectangular substrate with four free sides. The overall dimensions of the rectangular substrate are: width l = 160mm, length W = 320mm, thickness h = 1.5mm, and the density, Young's modulus and Poisson's ratio of the rectangular substrate are 2700kg / m 3 , 70Gpa and 0.3; the effective working frequency band of the bending wave is 1.5kHz to 2.2kHz, the effective working frequency of the bending wave is 1.79kHz, the masses of the first mass spring resonator and the second mass spring resonator are 3g and 5g respectively, and the stiffness is 10 6 N / m. The spacing between the first mass spring resonator and the second mass spring resonator in the unit cell is 8 mm, and the unit cell spacing between adjacent first local resonance unit cells and adjacent second local resonance unit cells is 8 mm. The number of the first local resonance unit cells and the number of the second local resonance unit cells are both 10.

[0053] We use COMSOL Multiphysics finite element analysis software to establish a finite element model of the entire local resonance metasurface structure, including a rectangular substrate and 10 first local resonance cells and 10 second local resonance cells set on the rectangle. In the shell unit module of the finite element analysis software, the thickness of the rectangular substrate is set to 1.5 mm, and a force point load of 1 and a vertical downward direction is set at the edge of the first metasurface and close to the first local resonance cell; the rectangular substrate is divided by a free triangular grid, and the maximum grid size is selected as one twelfth of the current frequency wave field. At the same time, a finite element model containing only the first metasurface or only the second metasurface is established, and the material and structural parameters are the same as the parameters of each region in the above-mentioned local resonance metasurface structure.

[0054] Add a frequency domain analysis study, set the sweep range to 1.5kHz to 2.2kHz, and the frequency interval to 0.05kHz. Number all resonators in the local resonance metasurface structure in order, and extract the displacement amplitude of the substrate below the oscillator spring resonator numbered 5-15 at different frequencies, that is, the distribution of the bending wave energy along the metasurface, such as Figure 3 As shown. Figure 3It can be seen that for the first metasurface alone or the second metasurface alone, the frequency band from 1.6kHz to 2kHz is an obvious bending wave band gap, and the bending wave cannot propagate along the metasurface. The displacement amplitude below the oscillator spring resonators numbered 5-15 is basically 0; while for the local resonant metasurface structure, within the band gap range of 1.6kHz to 2kHz, an obvious highlight area appears. The frequency corresponding to this area is 1.79kHz, and the energy is strongest at the interface between the two metasurfaces in the local resonant metasurface structure (that is, between the oscillator spring resonators numbered 10-11), forming a topological interface state of the bending wave.

[0055] In order to more clearly demonstrate the rainbow reflection effect of the local resonance metasurface structure in this example, the displacement amplitude wave field of the entire bending wave when the incident frequency is 1.79kHz is extracted, as shown in Figure 4 From the wave field diagram, it can be found that for an excitation frequency of 1.79 kHz, the bending wave cannot propagate along the first metasurface alone or the second metasurface alone, but can propagate along the local resonance metasurface and produce an energy concentration effect at the interface.

[0056] It can be seen that the local resonant metasurface structure of the present invention can produce a very ideal energy gathering effect at the interface for bending waves excited by a specific frequency. The unit cell size is much smaller than the wavelength of the incident wave, there is no requirement for the incident form of the incident wave, and no external energy supply is required when in use, so it is highly economical.

[0057] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should be included in the protection scope of the present invention.

Claims

1. A localized resonant metasurface structure for flexural wave guiding and focusing, characterized in that: It includes a substrate with four free sides and a first local resonance unit cell and a second local resonance unit cell fixed on the substrate; The substrate comprises a first region and a second region, a plurality of the first local resonance unit cells and a plurality of the second local resonance unit cells are uniformly arranged in the first region and the second region respectively, and the first local resonance unit cells and the second local resonance unit cells are collinearly arranged; it is defined that the spacing between adjacent first local resonance unit cells and the spacing between adjacent second local resonance unit cells are both the first spacing; The first local resonance unit cell includes a first mass spring resonator and a second mass spring resonator arranged in sequence; the second local resonance unit cell includes a second mass spring resonator and a first mass spring resonator arranged in sequence; the first mass spring resonator and the first mass spring resonator have the same stiffness but different masses; Define that the distance between the first mass-spring resonator and the second mass-spring resonator in the first local resonance unit cell and the second local resonance unit cell is a second distance; The second spacing is equal to the first spacing; When a bending wave is generated at a set frequency at the edge of the substrate and close to the first local resonant unit cell or the second local resonant unit cell, the bending wave can propagate along the substrate and generate energy concentration at the interface between the first region and the second region.

2. The local resonant metasurface structure for guiding and focusing bending waves according to claim 1, characterized in that: The substrate is made of metal material.

3. The local resonant metasurface structure for guiding and focusing bending waves according to claim 1, characterized in that: When the local resonance metasurface structure is installed on an excitation source, the excitation source is located at the edge of the substrate and close to the first local resonance unit cell or the second local resonance unit cell.

4. The method for designing a localized resonant metasurface structure for guiding and focusing bending waves according to any one of claims 1 to 3, characterized in that: The following steps are involved: Step 1, obtaining the material density ρ, Young's modulus E, Poisson's ratio υ and thickness h of the substrate, and calculating the bending wave dispersion curve; Step 2, determining the spacing between the first mass-spring resonator and the second mass-spring resonator in the first local resonance unit cell according to the set effective operating frequency band of the bending wave and the bending wave dispersion curve obtained in step 1, so that the first band edge frequency of the bending wave dispersion curve in the first Brillouin zone of the first local resonance unit cell is within the set effective operating frequency band of the bending wave; Step 3, setting a bending wave effective operating frequency, wherein the bending wave effective operating frequency is within a set bending wave effective operating frequency band; Step 4, establishing a finite element model including a first local resonant unit cell and a substrate corresponding to the first local resonant unit cell, performing characteristic frequency analysis based on the finite element model to obtain a band structure of the first local resonant unit cell, and determining whether a band gap of the first local resonant unit cell band structure corresponds to the effective operating frequency of the bending wave set in step 3, and if so, obtaining the stiffness and mass of the first mass-spring resonator and the second mass-spring resonator, and if not, adjusting the stiffness and mass of the first mass-spring resonator and the second mass-spring resonator until the band gap of the first local resonant unit cell band structure corresponds to the set effective operating frequency of the bending wave; Step 5, using the spacing between the first mass spring resonator and the second mass spring resonator in the first local resonance unit cell as the unit cell spacing between adjacent first local resonance unit cells and adjacent second local resonance unit cells; Step 6, determining the number of the first local resonance unit cell and the second local resonance unit cell according to the actual bending wave energy concentration interface position requirement; Step 7: Determine the length of the substrate according to the determined unit cell numbers and unit cell spacings of the first local resonance unit cell and the second local resonance unit cell, and the spacing between the first mass-spring resonator and the second mass-spring resonator.

5. The design method according to claim 4, characterized in that: In step 6, the number of the first local resonance unit cell and the number of the second local resonance unit cell are both no less than 5.

6. The design method according to claim 4, characterized in that: When calculating the bending wave dispersion curve in step 1, the intrinsic losses are neglected.

7. The design method according to claim 4, characterized in that: In step 4, the spring masses in the first mass-spring resonator and the second mass-spring resonator are ignored.

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