Harmonic resonant seismic metamaterial for attenuating low-frequency elastic surface waves

Abstract

The application relates to the technical field of controlling earthquake propagation, in particular to a set harmonic resonant earthquake metamaterial for attenuating low-frequency elastic surface waves. The set harmonic resonant earthquake metamaterial comprises a plurality of periodically arranged set harmonic resonators, and each set harmonic resonator comprises a concrete platform which is hexahedral, the top surface and the bottom surface of which are square, and the bottom surface is fixedly connected with the ground; a plurality of steel thin-wall hollow square tubes which are vertically fixedly arranged at the inner sides of the middle parts of the respective side edges of the top surface of the concrete platform, and the bottoms of the steel thin-wall hollow square tubes are arranged in the insertion holes of the top surface of the concrete platform; and a rubber wrapping layer which is filled in the insertion holes and realizes the fixed connection between the steel thin-wall hollow square tubes and the concrete platform. The set harmonic resonant earthquake metamaterial is small in size and low in cost, and can effectively realize the attenuation of low-frequency earthquake surface waves by the subwavelength earthquake metamaterial.

Description

Technical Field

[0001] This invention relates to the field of earthquake propagation control technology, and in particular to a clustered resonant seismic metamaterial for attenuating low-frequency elastic surface waves. Background Technology

[0002] Earthquakes pose a serious safety threat to densely populated urban areas, with the immense destructive force of seismic waves causing widespread collapse and damage to buildings. To defend against potential earthquake disasters, seismic isolation pads, buckling-resistance braces, and shear walls have been widely adopted. However, past earthquake disasters have shown that while existing traditional seismic measures can prevent the progressive collapse of buildings to some extent, they often result in post-earthquake structural damage that is difficult to repair, leading to property losses. Severe post-earthquake property damage is a drawback of existing seismic measures. Furthermore, existing traditional seismic measures are often also important load-bearing components of the structure. This means that existing traditional seismic measures are insufficient for modifying or improving the seismic resistance of existing or historical buildings. Therefore, seismic metamaterials, installed on the periphery of the structure and directly controlling the propagation of seismic waves, represent an ideal disaster prevention and mitigation method to overcome the aforementioned limitations of traditional technologies.

[0003] Seismic waves are generally classified into seismic body waves and seismic surface waves. Seismic surface waves, characterized by long propagation distances, high energy carrying capacity, and poor attenuation, are often the primary cause of widespread structural damage during earthquakes. The formation of low-frequency surface wave bandgaps is key to the attenuation of seismic waves using existing seismic metamaterial technology; surface waves within the bandgap frequency range cannot propagate within metamaterials. Seismic metamaterials create low-frequency surface wave bandgaps by periodically embedding concrete piles within the soil or periodically arranging resonators on the surface. This novel disaster prevention and mitigation method separates seismic-resistant structures from the building itself, overcoming the shortcomings of traditional seismic resistance measures.

[0004] Existing embedded seismic metamaterials generally have band gaps above 10 Hz; spring-concentrated mass seismic metamaterials can attenuate surface waves around 5 Hz. Since seismic surface waves are ultra-low frequency waves, the lower the frequency of surface waves that a seismic metamaterial can attenuate, the better its earthquake protection capability.

[0005] However, existing embedded or resonator-type seismic metamaterials rely on Bragg scattering or local resonance mechanisms to open band gaps. The formation of low-frequency surface wave band gaps often depends on enormous structural dimensions or concentrated masses with extremely high weight, making the construction of seismic metamaterials extremely difficult and costly. The high construction cost and impractical size of existing seismic metamaterials are the main reasons why they are difficult to apply in practice. Developing novel surface wave control mechanisms within surface wave systems to construct small-sized, low-cost seismic metamaterials is a key technology for realizing the engineering application of such novel disaster prevention and mitigation methods. Summary of the Invention

[0006] The purpose of this invention is to overcome the above-mentioned defects in the prior art and to propose a clustered resonant seismic metamaterial for attenuating low-frequency elastic surface waves. It is small in size and low in cost, and effectively realizes the attenuation of low-frequency seismic surface waves by subwavelength seismic metamaterials.

[0007] The technical solution of this invention is: a clustered resonant seismic metamaterial for attenuating low-frequency elastic surface waves, comprising several periodically arranged clustered resonators, wherein the clustered resonators include:

[0008] The concrete platform is hexahedral in shape, with both its top and bottom surfaces being squares, and its bottom surface being fixedly connected to the ground.

[0009] Several thin-walled hollow square steel tubes are vertically fixed to the inner side of the middle of each side of the top surface of the concrete platform, with their bottoms set in the insertion holes on the top surface of the concrete platform.

[0010] A rubber-coated layer is filled inside the socket to achieve a fixed connection between the steel thin-walled hollow square tube and the concrete platform.

[0011] In this invention, the clustered resonant seismic metamaterial comprises n×n clustered resonators, which are arranged in a square array.

[0012] The clustered resonant seismic metamaterial consists of n rows of clustered resonators, each row containing n clustered resonators, with adjacent clustered resonators spaced at equal intervals.

[0013] The spacing between two adjacent integrated resonators is 5m.

[0014] The integrated resonator is a first-order resonator, comprising:

[0015] First-stage concrete platform;

[0016] Several thin-walled hollow square steel tubes are provided on the inner side of the middle of each side of the top surface of the first-stage concrete platform. The thin-walled hollow square steel tubes are all the same size.

[0017] The top of the rubber wrapping layer is flush with the top surface of the first-stage concrete platform, and the rubber wrapping layer passes through the insertion hole in the first-stage concrete platform.

[0018] The first-stage concrete platform has a length and width of 2-4m and a height of 0.3m.

[0019] The cross-section of the steel thin-walled hollow square tube is square, with an outer side length of 0.25m, an inner side length of 0.21m, and a wall thickness of 20mm.

[0020] The height of the steel thin-walled hollow square tube is 2.8-3.5m, and the depth of its bottom embedded in a first-stage concrete platform is 0.25m.

[0021] The rubber wrapping layer is embedded to a depth of 0.3m into the first-stage concrete platform, and the thickness of the rubber wrapping layer is 100-125mm.

[0022] The frequency range of the integrated mode induced by the integrated resonant seismic metamaterial composed of first-order integrated resonators is 3.24-3.48 Hz.

[0023] The collector resonator is a second-order collector resonator, comprising:

[0024] An outer concrete platform, whose bottom surface is fixedly connected to the ground, and whose top surface has an inner concrete platform fixed at its center.

[0025] Several outer-step steel thin-walled hollow square tubes are vertically fixed on the inner side of the middle of each side of the top surface of the outer-step concrete platform, and located on the outer side of each side of the inner-step concrete platform. The outer-step steel thin-walled hollow square tubes are all the same size.

[0026] The bottom surface of the inner concrete platform is fixedly connected to the top surface of the outer concrete platform.

[0027] Several inner-step steel thin-walled hollow square tubes are vertically fixed on the inner side of the middle of each side of the top surface of the inner-step concrete platform. The inner-step steel thin-walled hollow square tubes are all the same size.

[0028] The outer steel thin-walled hollow square tube and the outer concrete platform, as well as the inner steel thin-walled hollow square tube and the inner concrete platform, are fixedly connected by a rubber wrapping layer. The top of the rubber wrapping layer is flush with the top surface of the outer and inner concrete platforms, respectively, and the rubber wrapping layer passes through the insertion holes in the outer and inner concrete platforms.

[0029] The top surface of the outer concrete platform has four inner sides with insertion holes in the middle of each side. Each insertion hole contains two outer steel thin-walled hollow square tubes, and there is a gap between the two outer steel thin-walled hollow square tubes in each insertion hole.

[0030] The length and width of the outer-stage concrete platform are 2.8-4.5m, and the height is 0.3m.

[0031] The outer side length of the outer-step steel thin-walled hollow square tube is 0.15m, the inner side length is 0.11m, the height of the outer-step steel thin-walled hollow square tube is 3.5m, and the depth of its bottom embedded in the outer-step concrete platform is 0.25m.

[0032] The gap between the two outer-step steel thin-walled hollow square tubes in the same socket is 0.3m, and the distance between the outer-step steel thin-walled hollow square tube and the side of the adjacent inner-step concrete platform is 0.3m.

[0033] The inner stepped concrete platform has a length and width of 1.8-2.1m and a height of 0.3m.

[0034] The outer side length of the inner-step steel thin-walled hollow square tube is 0.25m, the inner side length is 0.21m, the height of the inner-step steel thin-walled hollow square tube is 2.8m, and the depth of its bottom embedded in the outer-step concrete platform is 0.25m.

[0035] The height of the rubber wrapping layer is 0.3m.

[0036] The frequency range of the clustered mode induced by the clustered resonant seismic metamaterial composed of second-order clustered resonators is 2.04-2.10Hz and 3.24-3.48Hz.

[0037] The beneficial effects of this invention are:

[0038] (1) The height of the integrated resonant seismic metamaterial constructed in this application is relatively low, and the internal structure of the steel thin-walled hollow square tube is hollow. Compared with other existing technologies, the construction cost of this application is lower.

[0039] (2) The clustered resonant seismic metamaterial of this application can form a clustered mode of about 2-4 Hz, which is in the range of ultra-low frequency surface waves and can more effectively attenuate seismic surface waves.

[0040] (3) The integrated resonant earthquake metamaterial structure constructed by the present invention is simple, consisting of only a steel thin-walled square column, an ordinary concrete platform and a rubber wrapping layer, and is also easy to install and easy to manufacture on a large scale. Attached Figure Description

[0041] Figure 1 This is a three-dimensional structural diagram of the first-order integrated resonator in Example 1;

[0042] Figure 2 This is a schematic diagram of the structure of the first-order integrated resonant seismic metamaterial array used in Example 1 to achieve surface wave protection against earthquakes in any specified area;

[0043] Figure 3 This is a schematic diagram illustrating the principle of regional seismic surface wave protection using a finitely repeated integrated resonant seismic metamaterial array;

[0044] Figure 4 It is the dispersion curve of a first-order clustered resonant seismic metamaterial in homogeneous soil and the induced clustered modes;

[0045] Figure 5It is the frequency domain response of a first-order integrated resonant seismic metamaterial finite repeating array in a uniform semi-infinite matrix;

[0046] Figure 6 It is the dispersion curve of a first-order integrated resonant seismic metamaterial in layered soil;

[0047] Figure 7 It is the frequency domain response of a first-order integrated resonant seismic metamaterial finite repeating array in layered soil;

[0048] Figure 8 This is a schematic diagram of the attenuation effect of a first-order integrated resonant seismic metamaterial finite repeating array on surface waves in uniform soil.

[0049] Figure 9 This is a three-dimensional structural diagram of the second-order integrated resonator in Example 2;

[0050] Figure 10 This is a top view of the second-order integrated resonator in Example 2;

[0051] Figure 11 The dispersion curves of a second-order clustered resonant seismic metamaterial in homogeneous soil and the induced clustered modes;

[0052] Figure 12 It is the frequency domain response of a second-order integrated resonant seismic metamaterial finite repeating array in a uniform semi-infinite matrix;

[0053] Figure 13 It is the dispersion curve of a second-order integrated resonant seismic metamaterial in layered soil;

[0054] Figure 14 It is the frequency domain response of a second-order integrated resonant seismic metamaterial finite repeating array in layered soil.

[0055] In the diagram: 1. Substrate; 2. Concrete platform; 3. Thin-walled hollow square steel tube; 4. Rubber coating layer; 5. Outer concrete platform; 6. Outer thin-walled hollow steel tube; 7. Outer rubber coating layer; 8. Inner concrete platform; 9. Inner thin-walled hollow steel tube; 10. Inner rubber coating layer. Detailed Implementation

[0056] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0057] Specific details are set forth in the following description to provide a full understanding of the invention. However, the invention can be practiced in many ways other than those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0058] The clustered resonant seismic metamaterial for attenuating low-frequency elastic surface waves described in this application comprises several periodically repeating clustered resonant seismic metamaterial unit cells. These unit cells are positioned outside the protected area, forming an overall array surrounding the protected area. In this application, the clustered resonant seismic metamaterial unit cells are designed as clustered resonators. Regardless of the direction from which the surface wave propagates to the protected area, the surface wave will pass through a certain number of clustered resonators and be attenuated. Buildings within the protected area will not be affected by earthquakes, achieving seismic resistance for the building structure. When the buildings in the protected area are existing or historical buildings, the clustered resonant seismic metamaterial can provide seismic protection for both existing and historical buildings.

[0059] Example 1

[0060] The clustered resonant seismic metamaterial in this embodiment is a first-order clustered resonant seismic metamaterial. The first-order clustered resonant seismic metamaterial is composed of several first-order clustered resonant seismic metamaterial unit cells arranged periodically. The first-order clustered resonant seismic metamaterial unit cell is also called a first-order clustered resonator.

[0061] like Figure 1 As shown, the first-order integrated resonator includes a concrete platform 2 and several thin-walled hollow steel square tubes 3 fixedly mounted on the concrete platform. The concrete platform 2 is 2m long, 2m wide, and 0.3m high. The bottom surface of the concrete platform 2 is in firm contact with the base 1, which is soil. Concrete platforms with a length and width in the range of 2-4m can meet the arrangement requirements of the thin-walled hollow steel square tubes.

[0062] Four thin-walled hollow steel tubes 3 are fixedly fixed at intervals on the concrete platform 2, each located on the inner side of one of the four top sides of the concrete platform. The bottom of each steel tube 3 is set inside the concrete platform. The concrete platform 2 has four insertion holes, and the bottoms of the four steel tubes are respectively placed in these holes. A rubber coating layer 4 is provided between the outer wall of the steel tube and the inner wall of the insertion hole. The rubber coating layer securely connects the steel tubes to the concrete platform. The rubber coating layer provides elastic restoring force to the steel tubes and also reduces their natural frequency.

[0063] The steel thin-walled hollow square tube has a height of 2.8m, and its embedment depth into the concrete platform is 0.25m. The rubber wrapping layer is embedded into the concrete platform to a depth of 0.3m. The top of the rubber wrapping layer is flush with the top surface of the concrete platform. In other words, the insertion hole within the concrete platform is a through hole, and the rubber wrapping layer penetrates through this hole. The rubber wrapping layer is 100mm thick and tightly wraps around the steel thin-walled hollow square tube, achieving a fixed connection between the concrete platform and the steel thin-walled hollow square tube. In this embodiment, steel thin-walled hollow square tubes with heights ranging from 2.8m to 3.5m can induce ideal clustering modes.

[0064] To confine the scanning wave vector within the irreducible Brillouin zone, the first-order integrated resonator fixed to the soil surface should have at least four axes of symmetry within the top surface of the concrete platform. Simultaneously, the thin-walled hollow steel tubes need to be spaced at a certain distance to prevent collisions and stiffness reduction. In this embodiment, with the center of the top surface of the concrete platform as the origin, the center coordinates of each thin-walled hollow steel tube are (-0.6, 0), (0, -0.6), (0.6, 0), and (0, 0.6).

[0065] The cross-section of the steel thin-walled hollow square tube is square. The outer side length of the steel thin-walled hollow square tube is 0.25m and the inner side length is 0.21m. Therefore, the wall thickness of the steel thin-walled hollow square tube is 20mm.

[0066] like Figure 2 As shown, several first-order concentrated resonators described in this embodiment are arranged at equal intervals to form a square concentrated resonant seismic metamaterial array. In this embodiment, each square lattice array includes 4×4 first-order concentrated resonators, that is, the square lattice array has four first-order concentrated resonators arranged at equal intervals in the x and y directions respectively. The spacing between two adjacent first-order concentrated resonators is 5m. Several concentrated resonators are combined to form an overall array, surrounding the protected area.

[0067] In this embodiment, the concentrated resonant seismic metamaterial induces a special concentrated mode through several first-order concentrated resonators. The elastic strain energy of this mode is entirely concentrated within the first-order concentrated resonators. Since the first-order concentrated resonators are not interconnected, surface waves within the concentrated mode frequency range cannot propagate in this metamaterial array, thereby attenuating seismic surface waves and achieving the purpose of controlling surface waves. Compared with traditional seismic resistance measures, the concentrated resonant seismic metamaterial array described in this application is arranged on the periphery of the protected structure, which can effectively avoid potential structural damage; at the same time, it does not restrict the design of the building itself and can promote the diversification of building appearance.

[0068] like Figure 3As shown, in this embodiment, first-order clustered resonators are fixed at equal intervals in front of the protected area, forming a clustered resonant seismic metamaterial array in the x-direction. When surface waves at the frequency corresponding to the clustered mode reach the seismic metamaterial protection array, the clustered resonant seismic metamaterial is excited to a special clustered mode. Under the action of this clustered mode, the surface wave energy is redistributed, converging from the soil surface to the top of the resonators. Simultaneously, since there is also a volume wave mode at the frequency corresponding to the clustered mode of the clustered resonant seismic metamaterial, some surface waves are converted into volume waves, propagating to the deeper soil layers, further driving the waves away from the surface. In summary, the clustered resonant seismic metamaterial in this embodiment utilizes the clustered mode to significantly attenuate surface waves of a specified frequency, providing a new approach for low-frequency elastic surface wave control.

[0069] like Figure 4 As shown, the relationship between frequency and wave vector in concentrated resonance seismic materials is described using dispersion curves. Each point on the dispersion curve corresponds to a mode, which is divided into volume wave modes and surface wave modes based on different energy distribution characteristics, and these modes are mixed together. As shown by the thin black diagonal line in the figure, this embodiment separates the volume wave modes and surface wave modes using acoustic ray theory. The modes below the acoustic ray are pure surface wave modes, i.e., the unshaded area in the figure; the modes above the acoustic ray are volume wave modes, i.e., the shaded area in the figure. According to... Figure 4 It can be seen that the frequency range of the integrated mode induced by the first-order integrated resonant seismic metamaterial described in this embodiment is mainly 3.24-3.28Hz.

[0070] Dispersion curves are used to describe wireless periodically repeating systems, but in practical engineering, seismic metamaterial arrays are often finitely repeating. To verify that a finitely repeating seismic metamaterial array can attenuate surface waves of a corresponding frequency, Figure 5 A clustered resonant seismic metamaterial array with nine periodically repeating arrangements was calculated. A perfect-matched layer (PML) was placed on both sides and the bottom of the matrix to absorb and reduce reflected waves that would otherwise interfere with the seismic process. Figure 4 Corresponding to the dispersion curve in, Figure 5 The frequency response function of the finite-repetition first-order clustered resonant seismic metamaterial array exhibits a significant transmission trough in the 3.24–3.48 Hz range, with a trough value reaching -41 dB. Since the frequency domain response value is determined by the logarithmic form of the frequency response function, this means that the peak displacement of the surface wave at the rear end of the array is reduced by two orders of magnitude compared to the front end. The first-order clustered resonant seismic metamaterial can effectively attenuate low-frequency surface waves in the 3.24–3.48 Hz range.

[0071] In practical engineering, layered soil is extremely rare. As a form of interference with seismic metamaterials, layered soil typically leads to narrowing of the surface wave bandgap or an increase in the bandgap frequency. However, the clustered resonant seismic metamaterial described in this embodiment attenuates surface waves through the clustered resonance mechanism of the resonator, which is not significantly related to soil properties. Figure 6 As shown, the frequencies corresponding to the clustered modes of the first-order clustered resonant seismic metamaterial in layered soil are basically consistent with those in homogeneous soil. This means that the first-order clustered resonant seismic metamaterial described in this application is not sensitive to soil properties and can adapt to more general engineering environments.

[0072] like Figure 7 The figure shows the frequency domain response of a first-order clustered resonant seismic metamaterial in layered soil. As shown, a significant transmission valley appears in the 3.34-3.48 Hz range, with a peak value reaching -38 Hz. This indicates that in layered soil, the first-order clustered resonant seismic metamaterial can still strongly attenuate surface waves at the frequencies corresponding to the clustered modes, and changes in soil properties have little effect on the frequency and width of the surface wave bandgap.

[0073] Figure 8 This is the displacement response of a finite-repetition first-order clustered resonant seismic metamaterial array in homogeneous soil to surface waves at frequencies corresponding to the clustered modes. The linear source in the figure is located to the left of the finite-repetition clustered resonant seismic metamaterial array, capable of exciting a single-frequency surface wave on the free surface of a semi-infinite matrix. The single-frequency surface wave stably propagates from the source along the free surface to the metamaterial array. When the surface wave reaches the first first-order clustered resonator, part of the surface wave's wave mode transitions from Rayleigh wave to clustered wave mode, in which the surface wave no longer propagates forward; another part of the surface wave is affected by the body wave mode, transitioning from a surface wave wave mode to a body wave, thus moving away from the free surface. After passing through several first-order clustered resonators, the surface wave amplitude significantly decreases, achieving seismic defense for the protected area behind the clustered resonant seismic metamaterial array.

[0074] In this embodiment, the steel tube material used in the first-order integrated resonator has the following parameters: Young's modulus E = 2.07 × 10⁻⁶. 11 (Pa), Poisson's ratio υ=0.3, density ρ=7784 (Kg / m³) 3 The concrete material parameters are: Young's modulus E = 4 × 10⁻⁶ 10 (Pa), Poisson's ratio υ=0.3, density ρ=2500 (Kg / m³) 3 The rubber material parameters are: Young's modulus E = 7.8 × 10⁻⁶ 6 (Pa), Poisson's ratio υ=0.3, density ρ=1200 (Kg / m³) 3 ).

[0075] Example 2

[0076] Unlike Example 1, the clustered resonant seismic metamaterial in this example is a second-order clustered resonant seismic metamaterial, which is composed of several second-order clustered resonators arranged periodically.

[0077] like Figure 9 and Figure 10 As shown, the second-order integrated resonator includes a double-layer concrete platform, which is divided into an outer concrete platform 5 and an inner concrete platform 8. The outer concrete platform 5 and the inner concrete platform 8 are respectively provided with a steel thin-walled hollow square tube and a rubber wrapping layer.

[0078] The outer concrete platform 5 has a length of 3.8m, a width of 3.8m, and a height of 0.3m. The inner concrete platform 8 has a length of 2m, a width of 2m, and a height of 0.3m. The inner concrete platform 8 is fixed to the center of the top surface of the outer concrete platform 5. The length and width of the outer concrete platform 5, ranging from 2.8m to 4.5m, can accommodate the arrangement of the steel thin-walled hollow square tube and the inner concrete platform. The length and width of the inner concrete platform 8, ranging from 2.1m to 1.8m, can accommodate the arrangement of the inner steel thin-walled hollow square tube.

[0079] Four sets of thin-walled hollow steel tubes are fixed at intervals on the outer concrete platform 5. Each set of thin-walled hollow steel tubes is located inside the four top sides of the outer concrete platform. Each set of thin-walled hollow steel tubes includes two spaced-apart thin-walled hollow steel tubes 6, with a center-to-center distance of 0.3m between the two outer steel tubes in the same set. The distance between the center of the outer steel tube and the inner concrete platform is also 0.3m.

[0080] The outer concrete platform has insertion holes, and the bottoms of four sets of outer steel thin-walled hollow square tubes are respectively placed in the insertion holes, with two outer steel thin-walled hollow square tubes in each insertion hole. The gap between the outer steel thin-walled hollow square tubes and the insertion holes is filled with an outer rubber coating layer 7. The outer rubber coating layer achieves a fixed connection between the outer steel thin-walled hollow square tubes and the outer concrete platform.

[0081] The height of the outer steel thin-walled hollow square tube is 3.3m. The outer steel thin-walled hollow square tube is vertically inserted into the outer concrete platform, and the depth of the outer steel thin-walled hollow square tube embedded in the outer concrete platform is 0.25m.

[0082] In this embodiment, with the center of the top surface of the outer concrete platform as the origin, the center coordinates of each outer steel thin-walled hollow square tube column are (-1.3,-0.15), (-1.3,0.15), (-0.15,1.3), (0.15,1.3), (1.3,0.15), (1.3,-0.15), (0.15,-1.3), (-0.15,-1.3).

[0083] The cross-section of the outer-stage steel thin-walled hollow square tube is square. The outer side length of the outer-stage steel thin-walled hollow square tube is 0.15m, and the inner side length is 0.11m. Therefore, the wall thickness of the outer-stage steel thin-walled hollow square tube is 20mm.

[0084] Four inner-step steel thin-walled hollow square tubes 9 are fixedly fixed at intervals on the inner-step concrete platform 8, with each inner-step steel thin-walled hollow square tube located inside one of the four top sides of the inner-step concrete platform. Insertion holes are provided on the inner-step concrete platform, and the bottoms of the four inner-step steel thin-walled hollow square tubes are respectively placed inside these holes. An inner-step rubber coating layer 10 fills the space between the outer wall of the inner-step steel thin-walled hollow square tube and the inner wall of the insertion hole. The inner-step rubber coating layer 10 achieves a fixed connection between the inner-step steel thin-walled hollow square tube and the inner-step concrete platform.

[0085] The height of the inner-step steel thin-walled hollow square tube is 2.8m. The inner-step steel thin-walled hollow square tube is vertically inserted into the inner-step concrete platform, and the depth of the inner-step steel thin-walled hollow square tube embedded in the inner-step concrete platform is 0.25m.

[0086] In this embodiment, with the center of the top surface of the inner-step concrete platform as the origin, the center coordinates of each inner-step steel thin-walled hollow square tube column are (-0.6,0), (0,-0.6), (0.6,0), (0,0.6).

[0087] The cross-section of the inner-step steel thin-walled hollow square tube is square. The outer side length of the inner-step steel thin-walled hollow square tube is 0.25m, the inner side length is 0.21m, and the wall thickness is 20mm.

[0088] like Figure 11 As shown, unlike the first-order clustered resonant seismic metamaterial, the outer-order thin-walled hollow square steel tube increases the clustered mode with a frequency around 2.04 Hz. This means that the second-order clustered resonant seismic metamaterial produces a wider low-frequency bandgap and a lower bandgap frequency, which can more effectively suppress the propagation of low-frequency surface waves.

[0089] like Figure 12 As shown, this embodiment uses the same method as in Embodiment 1. Figure 4Using the same frequency domain calculation model, the finite repeating array of the second-order integrated resonant seismic metamaterial exhibits significant transmission troughs in the 2.04–2.10 Hz and 3.24–3.48 Hz frequency bands, which is consistent with... Figure 11 The dispersion curves shown are consistent. The peak value of the transmission valley reaches -45dB, which means that the peak value of the surface wave displacement at the rear end of the array is reduced by about two orders of magnitude compared with the front end of the array. Therefore, in this embodiment, the second-order clustered resonant seismic metamaterial can significantly suppress seismic waves in the frequency range corresponding to the clustered mode.

[0090] like Figure 13 As shown, the second-order clustered resonant seismic metamaterial in this embodiment forms two clustered modes with different frequencies in the layered soil. The frequencies corresponding to the clustered modes in the layered soil are basically consistent with the frequency ranges of the clustered modes in the homogeneous soil, both being two frequency bands: 2.04-2.10Hz and 3.24-3.48Hz. This means that changes in soil properties have little impact on the bandgap frequency and bandgap width of the surface waves of the second-order clustered resonant seismic metamaterial.

[0091] like Figure 14 As shown, significant transmission valleys appeared in the 2.04-2.10Hz and 3.24-3.48Hz frequency bands, with peak values ​​reaching -42. This means that in layered soil, the second-order clustered resonant seismic metamaterial in this embodiment can still strongly attenuate surface waves at the frequencies corresponding to the clustered modes.

[0092] Everything else is the same as in Example 1.

[0093] In practical applications, the clustered resonant seismic metamaterials proposed in this application can be selected according to different vibration isolation requirements, with different orders of clustered resonant seismic metamaterials being chosen.

[0094] The foregoing has provided a detailed description of the integrated resonant seismic metamaterial for attenuating low-frequency elastic surface waves provided by this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and core ideas of this invention. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from the principles of this invention, and these improvements and modifications also fall within the protection scope of the claims of this invention. The above description of the disclosed embodiments enables those skilled in the art to implement or use this invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of this invention. Therefore, this invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A clustered resonant seismic metamaterial for attenuating low-frequency elastic surface waves, characterized in that, This includes several periodically arranged collector resonators, which include: The concrete platform is hexahedral in shape, with both its top and bottom surfaces being squares, and its bottom surface being fixedly connected to the ground. Several thin-walled hollow square steel tubes are vertically fixed to the inner side of the middle of each side of the top surface of the concrete platform, with their bottoms set in the insertion holes on the top surface of the concrete platform. A rubber-coated layer is filled inside the insertion hole to achieve a fixed connection between the steel thin-walled hollow square tube and the concrete platform; The collector resonator is a second-order collector resonator, including: An outer concrete platform, whose bottom surface is fixedly connected to the ground, and whose top surface has an inner concrete platform fixed at its center. Several outer-step steel thin-walled hollow square tubes are vertically fixed on the inner side of the middle of each side of the top surface of the outer-step concrete platform, and located on the outer side of each side of the inner-step concrete platform. The outer-step steel thin-walled hollow square tubes are all the same size. The bottom surface of the inner concrete platform is fixedly connected to the top surface of the outer concrete platform. Several inner-step steel thin-walled hollow square tubes are vertically fixed to the inner side of the middle of each side of the top surface of the inner-step concrete platform. The inner-step steel thin-walled hollow square tubes are of the same size. The outer steel thin-walled hollow square tube and the outer concrete platform, as well as the inner steel thin-walled hollow square tube and the inner concrete platform, are fixedly connected by a rubber wrapping layer. The top of the rubber wrapping layer is flush with the top surface of the outer and inner concrete platforms, respectively, and the rubber wrapping layer passes through the insertion holes in the outer and inner concrete platforms.

2. The clustered resonant seismic metamaterial for attenuating low-frequency elastic surface waves according to claim 1, characterized in that, The clustered resonant seismic metamaterial comprises n×n clustered resonators, which are arranged in a square array. The clustered resonant seismic metamaterial consists of n rows of clustered resonators, with each row containing n clustered resonators, and adjacent clustered resonators are spaced equally apart.

3. The clustered resonant seismic metamaterial for attenuating low-frequency elastic surface waves according to claim 2, characterized in that, The spacing between two adjacent collector resonators is 5m.

4. The clustered resonant seismic metamaterial for attenuating low-frequency elastic surface waves according to claim 1, characterized in that, The top surface of the outer concrete platform has four inner sides with insertion holes in the middle of each side. Each insertion hole contains two outer steel thin-walled hollow square tubes, and there is a gap between the two outer steel thin-walled hollow square tubes in each insertion hole.

5. The clustered resonant seismic metamaterial for attenuating low-frequency elastic surface waves according to claim 4, characterized in that, The outer-stage concrete platform has equal length and width, ranging from 2.8 to 4.5 meters, and a height of 0.3 meters. The outer side length of the outer-step steel thin-walled hollow square tube is 0.15m, the inner side length is 0.11m, the height of the outer-step steel thin-walled hollow square tube is 3.5m, and the depth of its bottom embedded in the outer-step concrete platform is 0.25m. The distance between the centers of the two outer-step steel thin-walled hollow square tubes in the same socket is 0.3m, and the distance between the center of the outer-step steel thin-walled hollow square tube and the inner-step concrete platform is 0.3m. The inner concrete platform has equal length and width, ranging from 1.8 to 2.1 meters, and a height of 0.3 meters. The outer side length of the inner-step steel thin-walled hollow square tube is 0.25m, the inner side length is 0.21m, the height of the inner-step steel thin-walled hollow square tube is 2.8m, and the depth of its bottom embedded in the outer-step concrete platform is 0.25m. The height of the rubber wrapping layer is 0.3m.

6. The clustered resonant seismic metamaterial for attenuating low-frequency elastic surface waves according to claim 1, characterized in that, The frequency range of the clustered mode induced by the clustered resonant seismic metamaterial composed of second-order clustered resonators is 2.04-2.10Hz and 3.24-3.48Hz.

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