Resonance type metamaterial unit cell structure and buried vibration isolation barrier system

Abstract

The invention relates to the field of metamaterials, in particular to a resonance type metamaterial unit cell structure and a buried vibration isolation barrier system.The resonance type metamaterial unit cell structure comprises a closed box with the interior in a sealed state, supporting columns are arranged in the closed box, and rubber rings coaxial with the supporting columns are arranged on the supporting columns at equal intervals in the axial direction; the outer rings of the rubber rings located at the two ends of the supporting column are coaxially and fixedly provided with stabilizing rings, the stabilizing rings are attached to the box wall of the closed box, the outer rings of the rubber rings located between the two stabilizing rings are coaxially and fixedly provided with resonance rings, the outer diameters and the inner diameters of the resonance rings are equal, and the thicknesses of the resonance rings are not equal. According to the invention, the main frequency range of an earthquake can be effectively covered, seismic wave energy transmission can be completely isolated in a wide frequency range, the seismic isolation effect is obvious, and the cost is low.

Description

Technical Field

[0001] This invention relates to the field of metamaterials, specifically a resonant metamaterial unit cell structure and a buried vibration isolation barrier system. Background Technology

[0002] Earthquakes, due to their unpredictability and immense destructive power, have caused incalculable losses worldwide and are considered one of the most catastrophic natural disasters. Earthquakes transmit energy through seismic waves, which can be divided into body waves and surface waves. When body waves reach the Earth's surface, they form Rayleigh waves, which are characterized by large amplitude, slow attenuation, and long propagation distances, and are a major factor causing building damage.

[0003] Due to the unpredictability of earthquake intensity, increasing the load-bearing capacity of structural components to resist seismic forces increases construction costs and incurs significant repair expenses after component damage. To reduce costs, seismic isolation devices (such as rubber bearings and friction pendulum bearings) can be installed in the building foundation or between floors to extend the structure's natural vibration period and reduce the transmission of seismic energy to the upper structure; alternatively, dampers (viscous dampers and metal yield dampers) can be installed inside the building to absorb seismic energy. However, seismic isolation bearings or dampers relying on fixed parameters are only effective for specific frequency bands during the seismic resistance phase and cannot cover the broadband characteristics of seismic waves. If the dominant earthquake frequency exceeds the design range, the seismic isolation effect decreases significantly, thus requiring urgent solutions. Summary of the Invention

[0004] To avoid and overcome the technical problems existing in the prior art, this invention provides a resonant metamaterial unit cell structure and a buried vibration isolation barrier system. This invention can effectively cover the dominant frequency range of earthquakes, completely blocking the transmission of seismic wave energy over a wide frequency range, resulting in significant seismic isolation effects at a low cost.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A resonant metamaterial unit cell structure includes a sealed box with a support column inside. The support column is provided with rubber rings arranged coaxially with the support column at equal intervals along the axial direction. The outer rings of the rubber rings at both ends of the support column are fixed with stabilizing rings. The stabilizing rings are fitted against the box wall. The outer rings of the rubber rings between the two stabilizing rings are fixed with resonant rings. The outer diameter and inner diameter of each resonant ring are equal, and the thickness of each resonant ring is unequal.

[0007] As a further embodiment of the present invention: the stabilizing ring, the support column, and the enclosed box are all made of steel, and the resonant ring is made of lead.

[0008] As a further aspect of the present invention: the thickness of each rubber ring and the corresponding stabilizing ring and resonating ring of its outer ring are equal; the inner diameter and outer diameter of each stabilizing ring and resonating ring are equal.

[0009] As a further aspect of the present invention: the enclosed box has a cubic structure, and the support columns are arranged along the axial center line of the enclosed box.

[0010] As a further embodiment of the present invention: the sealed box has a split structure, including a cylindrical body with openings at both ends, and the openings at both ends of the cylindrical body are closed by cover plates.

[0011] As a further embodiment of the present invention: the support column, rubber ring, resonant ring and stabilizing ring are bonded and fixed together, and the cover plate and stabilizing ring are welded and positioned together.

[0012] As a further embodiment of the present invention: two sets of resonant rings are arranged, and the resonant metamaterial unit cell structure includes two sets of band gaps with independent frequency ranges, which are defined as the first band gap and the second band gap respectively; the enclosed box and the support column together form the matrix, and the frequency ranges of the first band gap and the second band gap are calculated using the mass of the matrix, the mass of the resonant ring and the effective stiffness of the rubber ring as design variables.

[0013] The starting frequencies of the first and second band gaps are:

[0014] |K1-ω1 2 M1|=0

[0015]

[0016] Where: ω1 is the starting frequency of the first bandgap and the second bandgap;

[0017] M1 is the first structural mass matrix;

[0018] K1 is the first structural stiffness matrix;

[0019] m1 and m2 are the masses of the two sets of resonant rings, respectively;

[0020] k1 and k2 are the effective stiffnesses of the rubber rings corresponding to the outer rings of the two sets of resonant rings, respectively.

[0021] The solution yields two sets of values ​​for ω1, with the smaller value being the starting frequency of the first bandgap and the larger value being the starting frequency of the second bandgap.

[0022] The cutoff frequencies of the first and second band gaps are:

[0023] |K2-ω2 2 M2|=0

[0024]

[0025] ω2 is the cutoff frequency of the first bandgap and the second bandgap;

[0026] M2 is the second structural mass matrix;

[0027] K2 is the second structural stiffness matrix;

[0028] m3 is the mass of the matrix;

[0029] The solution yields two sets of values ​​for ω2, with the smaller value being the cutoff frequency of the first bandgap and the larger value being the cutoff frequency of the second bandgap.

[0030] As a further embodiment of the present invention: m1 = ρ3π(r3 2 -r2 2 )t2;

[0031] m2=ρ3π(r3 2 -r2 2 )t3;

[0032] m3=ρ1[2.3a 2 -h(a-2t1) 2 +πr1 2 h+2πt2(r3 2 -r2 2 )]+2πρ2(r2 2 -r1 2 )t2;

[0033] Where: ρ3 is the material density of the resonant ring;

[0034] r2 is the outer diameter of the resonant ring;

[0035] r3 is the inner diameter of the resonant ring;

[0036] t2 and t3 are the thicknesses of the two sets of resonant rings, respectively;

[0037] ρ1 is the density of the steel material;

[0038] ρ2 is the material density of the rubber ring;

[0039] a is the lattice constant, with a value of 1.5m ≤ a ≤ 2.5m;

[0040] h is the height of the supporting column;

[0041] t1 is the thickness of the cover plate;

[0042] r1 is the radius of the support column.

[0043] As a further aspect of the present invention: the effective stiffness of the rubber ring is:

[0044]

[0045] Where: E is the Young's modulus of the rubber ring;

[0046] λ and μ are both Lamé constants.

[0047] ν is the Poisson's ratio of the rubber ring.

[0048] A buried vibration isolation barrier system, wherein a resonant metamaterial unit cell structure is uniformly arranged around the periphery of the building to be isolated, and each resonant metamaterial unit cell structure is pre-buried underground and arranged flush with the ground surface.

[0049] Compared with the prior art, the beneficial effects of the present invention are:

[0050] 1. This invention utilizes a stiffness gradient design of a rubber ring, a resonant ring, and a stabilizing ring, with varying thicknesses in the resonant ring, to create two independent frequency band gaps: 1.31–9.19 Hz and 9.68–18.21 Hz. These band gaps essentially cover Rayleigh waves within a 20 Hz frequency range, providing a wide vibration suppression frequency band coverage. This effectively protects existing buildings behind wave barriers or buildings highly sensitive to earthquakes. When Rayleigh waves interact with the metamaterial structure, some are prevented from advancing further due to strong coupling between the resonant units, while others are converted into body wave modes that propagate deep underground. This effectively covers the main frequency range of earthquakes, completely blocking seismic wave energy transmission over a wide frequency range, resulting in significant seismic isolation effects at a low cost.

[0051] 2. The stabilizing ring of the present invention is in close contact with the inner wall of the sealed box, and the rubber ring is constrained by the resonant ring and the stabilizing ring to prevent the rubber ring from undergoing radial deformation, thereby avoiding structural instability during resonance. At the same time, it ensures that the vibration energy is efficiently transferred to the resonant ring. The closed arrangement of the sealed box avoids the influence of the external environment on the formation of internal elastic elements, thus extending the service life of the structure. The split arrangement of the sealed box facilitates mass production and assembly, making it suitable for engineering applications.

[0052] 3. The support columns of this invention are arranged along the center line to ensure symmetrical vibration transmission path and improve the accuracy of bandgap frequency; the combination of bonding and welding takes into account both structural strength and vibration energy transmission efficiency; the combination of steel-lead-rubber optimizes the mass-stiffness distribution and enhances the bandgap control capability.

[0053] 4. This invention can directly calculate the start / cutoff frequencies of the bandgap through explicit formulas for the mass matrix and stiffness matrix, facilitating the customization of unit cell parameters for the target frequency band and ensuring precise matching of the bandgap frequency. By changing the materials of the resonant ring and rubber ring as needed, and by altering the relevant material or geometric properties of the resonant ring and rubber ring, the generated bandgap can be flexibly adjusted. The elastic Rayleigh wave is attenuated by the arrangement of buried metamaterial wave barriers, almost completely blocking the propagation of Rayleigh waves within a specific frequency range.

[0054] 5. The vibration isolation barrier system of this invention has the characteristic of being completely buried underground, and can be arranged in the soil without affecting the use of the surface space. It can be periodically arranged around existing buildings or buildings with high seismic sensitivity to form a periodic wave barrier. It utilizes the resonance characteristics of the unit cell structure itself to interact with the seismic Rayleigh wave to generate a band gap. Elastic waves within the band gap range are effectively attenuated after passing through the wave barrier. Attached Figure Description

[0055] Figure 1 This is an exploded view of the structure of the present invention.

[0056] Figure 2 This is a schematic diagram of the structure of the present invention.

[0057] Figure 3 This is a schematic diagram of the dispersion curve of the present invention.

[0058] Figure 4 This is a schematic diagram of the displacement distribution in the Z direction at f = 4.5 Hz according to the present invention.

[0059] Figure 5 This is a schematic diagram of the Z-direction acceleration response of the present invention under Chi-Chi seismic wave excitation.

[0060] In the picture:

[0061] 1. Support column; 11. Rubber ring; 12. Resonant ring; 13. Stabilizing ring;

[0062] 2. Enclosed box; 21. Cover plate. Detailed Implementation

[0063] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] Please see Figures 1-5In this embodiment of the invention, a resonant metamaterial unit cell structure and a buried vibration isolation barrier system include a cubic enclosed box 2, with both ends of the enclosed box 2 sealed by cover plates 21. A set of support columns 1 are arranged inside the enclosed box 2 along the central axis, the length of which is equal to the distance between the two cover plates 21. The cover plates have geometric dimensions of 2.2m × 2.2m × 0.1m, the enclosed box 2 has geometric dimensions of 2.2m × 2.2m × 2.3m, and the wall thickness of the enclosed box 2 is 0.1m.

[0065] The support column 1 is made of the same material as the enclosed box 2, which is steel, and its outer diameter is 0.06m. The outer diameter of the rubber ring 11 is 0.12m. The outer diameters of the resonant ring 12 and the stabilizing ring 13 are both 0.4m, and the thickness of the two sets of stabilizing rings 13 is 0.15m. The thicknesses of the two sets of resonant rings 12 are preferably 0.1m and 0.2m, respectively.

[0066] Rubber rings 11 are coaxially and equally spaced on the support column 1. The outer and inner diameters of each rubber ring 11 are equal, and the thickness of each rubber ring 11 is equal to the thickness of the outer resonant ring 12 and the stabilizing ring 13. Stabilizing rings 13, made of steel and the same material as the enclosed box 2, are coaxially fixed to the outer rings of the rubber rings 11 located at the top and bottom of the support column 1. Resonant rings 12 are coaxially fixed to the outer rings of each rubber ring 11 located between two stabilizing rings 13. The resonant rings 12, rubber rings 11, and support column 1 are bonded together using cold vulcanizing agent SK313; the steel components are fixed together by welding.

[0067] The resonant ring 12 is preferably made of lead. The support column 1 and the enclosed box 2 are made of steel, and the rubber ring 11 is made of rubber. The density ρ1 of the steel is 7850 kg / m³. 3 The Young's modulus E1 is 210 GPa, and the Poisson's ratio v1 is 0.3; the density ρ2 of the rubber is 1300 kg / m³. 3 The Young's modulus E2 is 1.2 MPa, and the Poisson's ratio v2 is 0.47; the density ρ3 of lead is 11600 kg / m³. 3 The Young's modulus E3 is 40.8 GPa, and the Poisson's ratio v3 is 0.369.

[0068] In this embodiment, only one set of support columns 1 is set inside the enclosed box 2. A set of stabilizing rings 13 is set at each end of the support column 1. Two sets of resonant rings 12 are set between the two stabilizing rings 13. The spacing between adjacent rubber rings 11 is kept equal.

[0069] When two sets of resonant rings 12 are set, the resonant metamaterial unit cell structure forms two independent frequency range band gaps, which are defined as the first band gap and the second band gap, respectively. The enclosed box 2 and the support column 1 together form the matrix. The frequency ranges of the first band gap and the second band gap are calculated using the mass of the matrix, the mass of the resonant ring 12 and the effective stiffness of the rubber ring 11 as design variables.

[0070] The starting frequencies of the first and second band gaps are:

[0071] |K1-ω1 2 M1|=0

[0072]

[0073] Where: ω1 is the starting frequency of the first bandgap and the second bandgap;

[0074] M1 is the first structural mass matrix;

[0075] K1 is the first structural stiffness matrix;

[0076] m1 and m2 are the masses of the two sets of resonant rings 12, respectively;

[0077] k1 and k2 are the effective stiffnesses of the rubber rings 11 corresponding to the outer rings of the two sets of resonant rings 12, respectively.

[0078] The solution yields two sets of values ​​for ω1, with the smaller value being the starting frequency of the first bandgap and the larger value being the starting frequency of the second bandgap.

[0079] The cutoff frequencies of the first and second band gaps are:

[0080] |K2-ω2 2 M2|=0

[0081]

[0082] ω2 is the cutoff frequency of the first bandgap and the second bandgap;

[0083] M2 is the second structural mass matrix;

[0084] K2 is the second structural stiffness matrix;

[0085] m3 is the mass of the matrix;

[0086] The solution yields two sets of values ​​for ω2, with the smaller value being the cutoff frequency of the first bandgap and the larger value being the cutoff frequency of the second bandgap.

[0087] m1=ρ3π(r3 2 -r2 2 )t2;

[0088] m2=ρ3π(r32 -r2 2 )t3;

[0089] m3=ρ1[2.3a 2 -h(a-2t1) 2 +πr1 2 h+2πt2(r3 2 -r2 2 )]+2πρ2(r2 2 -r1 2 )t2;

[0090] Where: ρ3 is the material density of the resonant ring 12;

[0091] r2 is the outer diameter of the resonant ring 12;

[0092] r3 is the inner diameter of the resonant ring 12;

[0093] t2 and t3 are the thicknesses of the two sets of resonant rings 12, respectively;

[0094] ρ1 is the density of the steel material;

[0095] ρ2 is the material density of rubber ring 11;

[0096] a is the lattice constant, with a value of 1.5m ≤ a ≤ 2.5m;

[0097] h is the height of support column 1;

[0098] t1 is the thickness of cover plate 21;

[0099] r1 is the radius of support column 1.

[0100] The effective stiffness of rubber ring 11 is:

[0101]

[0102] Where: E is the Young's modulus of rubber ring 11;

[0103] λ and μ are both Lamé constants.

[0104] ν is the Poisson's ratio of rubber ring 11.

[0105] After burying the unit cell structure underground, it is periodically arranged along the wave propagation direction to form a buried vibration isolation barrier system with an arrangement of 5×10. When the elastic wave frequency is within the band gap range, it will not be able to pass through the buried vibration isolation barrier system. The elastic wave within the band gap range is effectively attenuated after passing through the barrier. When the Rayleigh wave interacts with the metamaterial structure, part of it cannot continue to advance due to the strong coupling effect of the resonant unit, and part of it is converted into a volume wave mode and propagates deep underground.

[0106] The dispersion curves of the metamaterial unit cell structure were calculated using finite element method software, and a total of 50 energy bands were identified. The dispersion curves are shown below. Figure 3 As shown, the thick black dotted solid line represents the acoustic cone, the area outside the acoustic cone represents the volume wave mode, and each line inside the acoustic cone represents a surface wave mode. The dispersion curve of the unit cell shows that two omnidirectional wide band gaps are generated within the 0–20 Hz range, with band gap ranges of 1.31–9.19 Hz and 9.68–18.21 Hz, respectively. This indicates that elastic waves within this range cannot pass through the barrier system of this invention. The sum of the widths of the two omnidirectional band gaps reaches 16.41 Hz, which can significantly attenuate low-frequency Rayleigh waves below 20 Hz.

[0107] Figure 4 The Z-direction displacement distribution at f = 4.5 Hz (within the bandgap) is presented. Since the incident wave reaches its maximum amplitude before the first barrier, the modes of some waves change after passing through the first barrier, and the barrier undergoes local resonance, consuming energy. The wave attenuates rapidly in the incident direction, effectively weakening the displacement extracted at the response point. Therefore, after passing through the barrier of this invention, the Z-direction displacement at the response point is significantly attenuated compared to the unbarriered state.

[0108] Figure 5 The time-history acceleration analysis results using Chi-Chi seismic waves as excitation are presented. Since the dominant frequency range of Chi-Chi seismic waves is 0.6–6.2 Hz, which is basically within the band gap range of 1.31–9.19 Hz and 9.68–18.21 Hz, the results in the figure show that when the seismic wave is effectively attenuated after passing through the wave barrier, the extracted Z-direction acceleration amplitude is attenuated by 86%.

[0109] The basic principles of this application have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in this application are merely examples and not limitations, and should not be considered as essential features of each embodiment of this application. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not limit the application to the necessity of employing the aforementioned specific details for implementation.

[0110] The block diagrams of devices, apparatuses, devices, and systems involved in this application are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as “comprising,” “including,” “having,” etc., are open-ended terms meaning “including but not limited to,” and are used interchangeably with them. The terms “or” and “and” as used herein refer to the terms “and / or,” and are used interchangeably with them unless the context clearly indicates otherwise. The term “such as” as used herein refers to the phrase “such as but not limited to,” and is used interchangeably with it.

Claims

1. A resonant metamaterial unit cell structure, characterized in that, The enclosure includes a sealed box (2) with a support column (1) inside. Rubber rings (11) are arranged coaxially with the support column (1) at equal intervals along the axial direction. Stable rings (13) are coaxially fixed to the outer rings of the rubber rings (11) at both ends of the support column (1). The stable rings (13) are arranged in close contact with the box wall of the enclosure (2). Resonant rings (12) are coaxially fixed to the outer rings of each rubber ring (11) between the two stable rings (13). The outer diameter and inner diameter of each resonant ring (12) are equal, and the thickness of each resonant ring (12) is not equal.

2. The resonant metamaterial unit cell structure according to claim 1, characterized in that, The stabilizing ring (13), the support column (1), and the enclosed box (2) are all made of steel, while the resonant ring (12) is made of lead.

3. The resonant metamaterial unit cell structure according to claim 1, characterized in that, Each rubber ring (11) has the same thickness as its corresponding stabilizing ring (13) and resonant ring (12); the inner diameter and outer diameter of each stabilizing ring (13) and resonant ring (12) are equal.

4. The resonant metamaterial unit cell structure according to claim 1, characterized in that, The enclosed box (2) has a cubic structure, and the supporting columns (1) are arranged along the axial center line of the enclosed box (2).

5. The resonant metamaterial unit cell structure according to claim 4, characterized in that, The enclosed box (2) is a split structure, including a cylindrical body with openings at both ends, and the openings at both ends of the cylindrical body are closed by cover plates (21).

6. The resonant metamaterial unit cell structure according to claim 1, characterized in that, The support column (1), rubber ring (11), resonant ring (12) and stabilizing ring (13) are bonded and fixed together, and the cover plate (21) is welded and positioned to the stabilizing ring (13).

7. A resonant metamaterial unit cell structure according to any one of claims 1 to 6, characterized in that, Two sets of resonant rings (12) are arranged. The resonant metamaterial unit cell structure includes two sets of independent frequency range band gaps, which are defined as the first band gap and the second band gap, respectively. The closed box (2) and the support column (1) together form the matrix. The mass of the matrix, the mass of the resonant ring (12) and the effective stiffness of the rubber ring (11) are used as design variables to calculate the frequency range of the first band gap and the second band gap. The starting frequencies of the first and second band gaps are: |K1-ω1 2 M1|=0 Where: ω1 is the starting frequency of the first bandgap and the second bandgap; M1 is the first structural mass matrix; K1 is the first structural stiffness matrix; m1 and m2 are the masses of the two sets of resonant rings (12), respectively; k1 and k2 are the effective stiffnesses of the rubber rings (11) corresponding to the outer rings of the two sets of resonant rings (12), respectively; The solution yields two sets of values ​​for ω1, with the smaller value being the starting frequency of the first bandgap and the larger value being the starting frequency of the second bandgap. The cutoff frequencies of the first and second band gaps are: |K2-ω2 2 M2|=0 ω2 is the cutoff frequency of the first bandgap and the second bandgap; M2 is the second structural mass matrix; K2 is the second structural stiffness matrix; m3 is the mass of the matrix; The solution yields two sets of values ​​for ω2, with the smaller value being the cutoff frequency of the first bandgap and the larger value being the cutoff frequency of the second bandgap.

8. The resonant metamaterial unit cell structure according to claim 7, characterized in that, m1=ρ3π(r3 2 -r2 2 )t2; m2=ρ3π(r3 2 -r2 2 t3; m3=ρ1[2.3a 2 -h(a-2t1) 2 +πr1 2 h+2πt2(r3 2 -r2 2 )]+2πρ2(r2 2 -r1 2 )t2; Where: ρ3 is the material density of the resonant ring (12); r2 is the outer diameter of the resonant ring (12); r3 is the inner diameter of the resonant ring (12); t2 and t3 are the thicknesses of the two sets of resonant rings (12), respectively; ρ1 is the density of the steel material; ρ2 is the material density of the rubber ring (11); a is the lattice constant, with a value of 1.5m ≤ a ≤ 2.5m; h is the height of the supporting column (1); t1 is the thickness of the cover plate (21); r1 is the radius of the support column (1).

9. A resonant metamaterial unit cell structure according to claim 7, characterized in that, The effective stiffness of the rubber ring (11) is: Where: E is the Young's modulus of the rubber ring (11); λ and μ are both Lamé constants. ν is the Poisson's ratio of the rubber ring (11).

10. A buried vibration isolation barrier system according to claim 1, characterized in that, The building to be isolated is uniformly arranged with a resonant metamaterial unit cell structure as described in any one of claims 1 to 6 around its periphery. Each resonant metamaterial unit cell structure is pre-embedded underground and arranged flush with the ground surface.

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