Low-frequency broadband seismic metamaterial filled with five-mode-dot-lattice core and design method thereof

Abstract

The application discloses a low-frequency broadband seismic metamaterial filled with a five-mode dot array core and a design method thereof. The seismic metamaterial is composed of a five-mode dot array core, a concrete hollow pipe and an outermost soil layer. The five-mode dot array core is composed of a plurality of hexagonal crystal system units arranged periodically. The hexagonal crystal system unit is connected by an axial direction and is obtained by space structure conversion. The hexagonal crystal system unit is arranged periodically to form a three-dimensional dot array core structure composed of a plurality of hexagonal crystal system units. The low-frequency broadband seismic metamaterial filled with the five-mode dot array core can form a low-frequency broadband in a target frequency band. The seismic metamaterial is arranged in a vibration isolation area underground. When a seismic Rayleigh wave propagates to the area, the wave energy is significantly weakened under the action of a forbidden band, so that effective isolation and attenuation of the Rayleigh wave can be realized under the condition of a limited space.

Description

Technical Field

[0001] This invention relates to the field of earthquake engineering and wave control technology, and in particular to a low-frequency broadband seismic metamaterial filled with a five-mode lattice core and its design method. Background Technology

[0002] Rayleigh wave isolation and vibration reduction technology is an important research direction in civil engineering, disaster prevention and mitigation, and underground engineering, with broad application prospects in foundation seismic resistance, protection of critical facilities, and urban resilience construction. Compared with mid- and high-frequency vibrations, low-frequency Rayleigh waves are characterized by long wavelengths, strong penetration capabilities, and long propagation distances, making it difficult for traditional vibration isolation measures to achieve ideal control effects. Therefore, how to achieve isolation and attenuation of low-frequency Rayleigh waves under limited space conditions has become a key technical problem that urgently needs to be solved in the field of seismic engineering. Although existing technologies have proposed various methods such as foundation reinforcement, vibration isolation trenches, underground barriers, and periodic earthquake metamaterials, foundation reinforcement has a limited range of action and high costs, while vibration isolation trenches and barrier structures usually require large burial dimensions and are significantly constrained by site conditions.

[0003] In contrast, seismic metamaterials, utilizing artificial periodic structures to form bandgap zones, have shown great potential for low-frequency wave control. However, existing technologies still have significant shortcomings: while structures based on local resonance mechanisms can achieve low-frequency control, they generally suffer from narrow bandwidth and parameter sensitivity; structures based on Bragg scattering mechanisms offer better stability, but low-frequency isolation often relies on large lattice scales, which is not conducive to engineering implementation. Furthermore, existing metamaterial unit configurations are relatively simple, making it difficult to simultaneously meet the requirements of broadband attenuation and isolation, and insufficient consideration is given to Rayleigh wave propagation characteristics, energy dissipation, and isolation efficiency in complex sites. Especially in shallow underground and confined space conditions, there is a lack of relevant seismic metamaterials. This invention, through the design of a five-mode lattice core structure, enables a method for isolating and attenuating low-frequency Rayleigh waves. Summary of the Invention

[0004] To address the limitations of existing seismic metamaterials in isolating Rayleigh waves, their narrow bandwidth, and the large scale of engineering implementation, this invention proposes a low-frequency broadband seismic metamaterial filled with a five-mode lattice core and its design method. By filling a hollow concrete tube with a five-mode lattice core and placing a soil layer on the outside, a composite metamaterial structure with a three-dimensional periodic configuration is formed, creating a bandgap within the target frequency band. This achieves effective isolation and attenuation of low-frequency Rayleigh waves under limited spatial conditions, offering advantages such as strong engineering adaptability and convenient construction. It provides a new technical approach for underground Rayleigh wave seismic isolation and protection.

[0005] The technical solution to achieve the purpose of this invention is as follows:

[0006] A low-frequency broadband seismic metamaterial filled with a five-mode lattice core includes a five-mode lattice core, a hollow concrete tube, and an outermost soil layer. The five-mode lattice core is composed of multiple hexagonal crystal units arranged periodically. The five-mode lattice core fills the interior of the hollow concrete tube and together with the hollow concrete tube forms the main structure. The outer soil layer is used to simulate or correspond to the foundation soil environment in actual engineering.

[0007] Furthermore, the hexagonal crystal unit includes multiple bipyramidal structures, which are connected at their axial tail ends and are uniformly distributed.

[0008] Furthermore, five hexagonal crystal units are arranged in each of the x-axis, y-axis and z-axis directions to form a 5×5×5 three-dimensional array structure.

[0009] Furthermore, each hexagonal crystal unit comprises three pairs of mirror-image bipyramidal structures.

[0010] Furthermore, the five-mode dot matrix core is made of metal, composite material, or concrete; the hollow concrete pipe is made of concrete; and the soil layer is natural foundation soil, backfill soil, or improved soil layer. Different materials and their parameters are selected according to the isolation and attenuation requirements of Rayleigh waves within the target frequency band.

[0011] Furthermore, the equivalent compressed wave phase velocity of the five-mode lattice core Phase velocity of equivalent shear wave They respectively satisfy:

[0012]

[0013] In the formula, The equivalent bulk modulus of the five-mode lattice core. The equivalent shear modulus of the five-mode lattice core. For the equivalent compressive wave mass density, This represents the equivalent shear wave mass density.

[0014] Furthermore, the quasi-five-mode characteristics of the five-mode lattice core are determined by its equivalent bulk modulus. With equivalent shear modulus The ratio is used to characterize the expression, which satisfies:

[0015]

[0016] and with The ratio is used as a criterion for optimizing the core structure parameters of the five-mode lattice.

[0017] A design method for a low-frequency broadband seismic metamaterial filled with a five-mode lattice core includes:

[0018] Step 1: Based on the target vibration isolation frequency band and the parameters of the site medium and foundation structure, design the five-mode lattice core and determine the initial geometric parameters h2, d, D and the unit cell lattice constant a of the biconical structure, where d is the upper diameter of the biconical structure, D is the lower diameter and h2 is the height.

[0019] Step 2: Connect multiple bipyramidal structures along the axial tail ends and distribute them evenly along the center to form the hexagonal crystal unit;

[0020] Step 3: Arrange the hexagonal crystal units periodically along the x-axis, y-axis and z-axis to form a three-dimensional five-mode lattice core structure containing multiple hexagonal crystal units;

[0021] Step 4: Optimize the geometry, material properties, and number of alternating rows of the metamaterial based on concrete parameters and actual site conditions.

[0022] Furthermore, the optimization of the geometric dimensions in step 4 is as follows:

[0023] By adjusting the diameter of the double cone structure (1-2) Lower diameter And height h2, changing the equivalent compressed wave phase velocity of the five-mode lattice core (1) Phase velocity of equivalent shear wave Adjusting the equivalent bulk modulus With equivalent shear modulus ratio To improve the isolation and attenuation of Rayleigh waves by the five-mode dot matrix core (1).

[0024] Furthermore, the material properties, array arrangement, and geometric parameters are determined based on the isolation requirements of Rayleigh waves within the frequency band, so that the five-mode lattice core has a large ratio of equivalent bulk modulus to equivalent shear modulus. It exhibits quasi-zero shear modulus characteristics, thereby reducing shear deformation and promoting Rayleigh wave decoupling, localizing Rayleigh wave energy in the five-mode lattice core, thus blocking Rayleigh wave propagation and achieving low-frequency broadband isolation and attenuation.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] 1. The present invention proposes a low-frequency broadband seismic metamaterial filled with a five-mode lattice core and its design method, which can effectively isolate and attenuate low-frequency Rayleigh waves within a limited spatial scale, thereby forming a more efficient blocking effect within the target frequency band.

[0027] 2. The present invention proposes a low-frequency broadband seismic metamaterial filled with a five-mode lattice core and its design method. By adjusting the size, arrangement and material parameters of the hexagonal crystal unit (1-1), the low-frequency vibration isolation characteristics of the metamaterial can be flexibly adjusted to meet the Rayleigh wave control requirements under different site conditions and different engineering application scenarios.

[0028] 3. The present invention proposes a low-frequency broadband seismic metamaterial filled with a five-mode lattice core and its design method. By utilizing the quasi-zero shear modulus characteristics of the five-mode lattice core structure, Rayleigh wave energy can be effectively localized, enhancing the accumulation and dissipation capabilities of Rayleigh waves within the metamaterial region and suppressing their continuous propagation to the vibration isolation target region, thereby further improving the isolation and attenuation effect on low-frequency Rayleigh waves.

[0029] 4. The low-frequency broadband seismic metamaterial and its design method filled with a five-mode lattice core proposed in this invention have a clear structural composition, can be realized using conventional engineering materials and processing and construction methods, are easy to integrate with existing foundation engineering systems, and have the advantages of strong engineering adaptability, convenient construction and good prospects for promotion and application. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the structure of the five-mode lattice core cell of the present invention. Figure 2 This is a schematic diagram of the five-mode lattice core metamaterial structure of the present invention. Figure 3 This is a schematic diagram of the bandgap of the five-mode lattice core metamaterial of the present invention.

[0031] Figure 4 This is a schematic diagram of the fusion of the five-mode lattice core metamaterial of the present invention.

[0032] Figure 5 This is a schematic diagram of the frequency domain response of the five-mode lattice core metamaterial of the present invention. Figure 6 This is a schematic diagram of the transmission of the five-mode dot matrix core of the present invention. Detailed Implementation

[0033] The present invention will now be described in more detail with reference to the accompanying drawings, which illustrate preferred embodiments of the invention. It should be understood that those skilled in the art can modify the invention described herein while still achieving its advantageous effects. Therefore, the following description should be understood as being of general knowledge to those skilled in the art and is not intended to limit the invention.

[0034] The following description, in conjunction with the accompanying drawings, further illustrates an embodiment of the present invention: a low-frequency broadband seismic metamaterial filled with a five-mode lattice core and its design method.

[0035] like Figure 1As shown in the figure, this embodiment presents a low-frequency broadband seismic metamaterial filled with a five-mode lattice core. The seismic metamaterial consists of a five-mode lattice core 1, a hollow concrete tube 2, and an outermost soil layer 3. The five-mode lattice core 1 fills the interior of the hollow concrete tube 2, forming the main structure of the composite metamaterial together with the hollow concrete tube 2. The outer soil layer 3 is used to simulate or correspond to the foundation soil environment in actual engineering projects. This seismic metamaterial can be placed between the foundation soil layer and the superstructure foundation, or buried in the shallow underground target vibration isolation area to achieve effective isolation and attenuation of low-frequency Rayleigh waves within the target frequency band.

[0036] The five-mode lattice core 1 is composed of multiple hexagonal crystal units 1-1 arranged along the x-axis, y-axis, and z-axis. Five hexagonal crystal units 1-1 are arranged in each of the x-axis, y-axis, and z-axis directions, forming a 5×5×5 three-dimensional array structure, comprising a total of 125 hexagonal crystal units 1-1. The array number of the five-mode lattice core 1 can be adjusted according to the target frequency band, the size of the vibration isolation region, and actual engineering requirements.

[0037] The hexagonal crystal unit 1-1 is composed of bipyramidal structures 1-2. The bipyramidal structure 1-2 is the basic geometric unit, with an upper diameter of d, a lower diameter of D, and a height of h2. Furthermore, three pairs of mirror-image bipyramidal structures 1-2 are placed on the XYZ axis plane and connected together to form the hexagonal crystal unit 1-1.

[0038] After obtaining the hexagonal crystal unit 1-1, it is arranged in a regular array along the x-axis, y-axis, and z-axis, with five unit cells preferably arranged in each axis direction, thus forming a three-dimensional five-mode lattice core structure composed of 125 hexagonal crystal units. By changing the geometric dimensions, array number, and spatial distribution of the hexagonal crystal units, the equivalent mechanical parameters of the five-mode lattice core 1 and its isolation performance against low-frequency Rayleigh waves can be adjusted.

[0039] The five-mode lattice core 1 is encased inside the hollow concrete tube 2, which serves as the external constraint and load-bearing structure and can be made of ordinary concrete. The soil layer 3 is located outside the hollow concrete tube 2 and can be made of natural foundation soil, backfill soil, or improved soil. The double-cone structure 1-2 can be made of metal, composite materials, or concrete, with different materials selected as needed to meet the isolation and attenuation requirements of low-frequency Rayleigh waves in different frequency ranges.

[0040] In this embodiment, the design method of the seismic metamaterial includes the following steps: First, based on the isolation and attenuation requirements of the target low-frequency Rayleigh wave, the upper diameter d, lower diameter D, and height h2 of the biconical structure 1-2 are determined; second, the biconical structure 1-2 is rotated 180° around the x-axis and y-axis to form a hexagonal crystal unit 1-1; then, multiple hexagonal crystal units 1-1 are arranged in an array along the x-axis, y-axis, and z-axis directions to form a three-dimensional five-mode lattice core 1; finally, a hollow concrete tube 2 is set on the outside of the five-mode lattice core 1, and a soil layer 3 is set on the outside of the hollow concrete tube 2 to obtain a low-frequency broadband seismic metamaterial filled with a five-mode lattice core.

[0041] Furthermore, during the design process, the equivalent compression wave phase velocity and equivalent shear wave phase velocity of the five-mode lattice core 1 can be changed by altering the geometric parameters d, D, and h2 of the biconical structure 1-2, thereby controlling the ratio of its equivalent bulk modulus to its equivalent shear modulus. This enhances the suppression effect of the five-mode lattice core 1 on the propagation of low-frequency Rayleigh waves, especially Rayleigh waves, and achieves low-frequency broadband isolation and attenuation effects.

[0042] Using a seismic metamaterial filled with a five-mode lattice core to achieve Rayleigh wave attenuation and foundation isolation, the design method includes the following steps:

[0043] Step 1: Based on the frequency range of the target low-frequency Rayleigh wave, the scale of the vibration isolation area, and the engineering application requirements, establish a geometric model of the hexagonal crystal unit, determine the upper and lower diameters of the cone, the height of the biconical structure, and the unit cell array form, and establish a periodic unit cell model in the finite element software to analyze its wave propagation characteristics.

[0044] Step 2: By adjusting the geometric parameters of the bipyramidal structure and the hexagonal crystal unit, the ratio of the equivalent bulk modulus and the equivalent shear modulus of the five-mode lattice core is changed, thereby controlling the low-frequency dynamic characteristics of the unit cell and forming a band gap within the target frequency band.

[0045] Step 3: Arrange the optimized hexagonal crystal units in an array along the x, y, and z axes to construct a three-dimensional five-mode lattice core, and fill it inside a hollow concrete tube. Set a soil layer on the outside to form a composite seismic metamaterial structure to enhance the blocking and attenuation effect on the propagation of low-frequency Rayleigh waves.

[0046] Step 4: Further adjust the unit cell size, array quantity, embedment range, and material parameters to expand the effective vibration isolation bandwidth and improve the isolation and attenuation performance for low-frequency Rayleigh waves, especially Rayleigh waves.

[0047] Based on the target vibration isolation frequency band and the parameters of the site medium and foundation structure, the initial geometric parameters h2, d, D and the unit cell lattice constant a of the biconical structural members are determined by designing the basic unit cell of the metamaterial;

[0048] Three pairs of mirrored bipyramidal structures are placed on the XYZ axis plane and connected together to form a hexagonal crystal unit.

[0049] The hexagonal crystal units are periodically arrayed along the x-axis, y-axis and z-axis to form a three-dimensional five-mode lattice core structure containing multiple hexagonal crystal units.

[0050] Based on concrete parameters and actual site conditions, the geometric dimensions, material properties, and number of alternating rows of the five-mode lattice were optimized to improve the isolation performance against Rayleigh waves.

[0051] Equivalent compression wave phase velocity Phase velocity of equivalent shear wave They respectively satisfy:

[0052]

[0053] In the formula, The equivalent bulk modulus of the five-mode lattice core. The equivalent shear modulus of the five-mode lattice core. For the equivalent compressive wave mass density, This represents the equivalent shear wave mass density.

[0054] Through equivalent bulk modulus With equivalent shear modulus The ratio is used to characterize the expression, which satisfies:

[0055]

[0056] and with The ratio is used as a criterion for structural parameter optimization.

[0057] Optimizing the geometry of metamaterials involves adjusting the upper diameter of the bipyramidal structure. Lower diameter And height h2, changing the equivalent compressed wave phase velocity of the five-mode lattice core. Phase velocity of equivalent shear wave Thus, the equivalent bulk modulus can be controlled. With equivalent shear modulus ratio To improve the isolation and attenuation performance of the five-mode dot matrix core for low-frequency Rayleigh waves.

[0058] like Figure 2As shown in the figure, this embodiment provides a schematic diagram of a five-layer arrayed five-mode lattice core metamaterial structure, wherein the density of soil is... =1800kg / m 3 Elastic modulus E = 20 MPa, Poisson's ratio υ = 0.3, thickness t1 = 0.1 m, density of concrete =2500kg / m 3 The elastic modulus E = 40 GPa, Poisson's ratio υ = 0.3, thickness t2 = 0.2 m, and the five-mode lattice core is selected as lead, with an elastic modulus E = 17 GPa and a Poisson's ratio υ = 0.42. =11300kg / m 3 Thickness t3 = 1.4m, side length a = 2m, height h1 The base is 2m high, while the bottom is composed of soil with a height of H=30m.

[0059] like Figure 3 As shown, a dispersion analysis model is established based on the core periodic unit cell of the five-mode lattice, which can obtain the band gap of Rayleigh wave energy in multiple frequency bands from 2 to 20 Hz.

[0060] like Figure 4 As shown, after optimizing the material properties, array arrangement, and geometric parameters, the five-mode lattice core has a large ratio of equivalent bulk modulus to equivalent shear modulus. It exhibits quasi-zero shear modulus characteristics, thereby reducing shear deformation and promoting decoupling of Rayleigh waves, promoting bandgap fusion, and obtaining a 2-20Hz bandgap. This localizes Rayleigh wave energy in the five-mode lattice core, thereby blocking Rayleigh wave propagation and achieving low-frequency broadband isolation and attenuation.

[0061] like Figure 5 As shown, when Rayleigh waves are simulated to be incident on a low-frequency broadband seismic metamaterial filled with a five-mode lattice core under load excitation, the wave field displacement distribution shows that Rayleigh waves are significantly attenuated and disturbed after propagating to the five-mode lattice core region. The wave energy is effectively weakened inside the structure, and only a small portion continues to propagate backward, indicating that the structure can effectively block the propagation of Rayleigh waves.

[0062] like Figure 6 As shown, when Rayleigh waves of different frequencies are incident, the response curves after setting the five-mode lattice core metamaterial structure are significantly lower than those without barrier protection, indicating that the five-mode lattice core structure has a significant attenuation effect on Rayleigh waves in the target frequency band. By adjusting the geometric parameters, array quantity, and material properties of the hexagonal crystal unit 1-1, the effective isolation bandwidth can be further extended, improving the isolation and attenuation performance of low-frequency Rayleigh waves.

[0063] The seismic metamaterial with a five-mode lattice core proposed in this invention can form a low-frequency broadband within the target frequency band; the seismic metamaterial is placed in the underground vibration isolation area; when the seismic Rayleigh wave propagates to the area, its wave energy is significantly weakened under the bandgap effect, thereby achieving effective isolation and attenuation of the Rayleigh wave under limited space conditions.

[0064] Finally, it should be noted that the accompanying drawings are for illustrative purposes only, representing schematic diagrams rather than actual physical objects, and should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some components in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings. The embodiments of the present invention are merely descriptions of preferred implementations and are not intended to limit the concept and scope of the invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the inventive concept should fall within the protection scope of the present invention.

Claims

1. A low-frequency broadband seismic metamaterial filled with a five-mode lattice core, characterized in that: It includes a five-mode lattice core (1), a hollow concrete tube (2), and an outermost soil layer (3); the five-mode lattice core (1) is composed of multiple hexagonal crystal units (1-1) arranged in a periodic manner. The five-mode lattice core (1) fills the interior of the hollow concrete tube (2) and together with the hollow concrete tube (2) forms the main structure. The outer soil layer (3) is used to simulate or correspond to the foundation soil environment in actual engineering.

2. The low-frequency broadband seismic metamaterial filled with a five-mode lattice core according to claim 1, characterized in that: The hexagonal crystal unit (1-1) includes multiple bipyramidal structures (1-2), which are connected at their tail ends along the axial direction and are uniformly distributed.

3. The low-frequency broadband seismic metamaterial filled with a five-mode lattice core according to claim 2, characterized in that: The hexagonal crystal unit (1-1) is arranged in five positions along the x-axis, y-axis and z-axis directions, forming a 5×5×5 three-dimensional array structure.

4. The low-frequency broadband seismic metamaterial filled with a five-mode lattice core according to claim 3, characterized in that: Each hexagonal crystal unit (1-1) includes three pairs of mirror-image bipyramidal structures (1-2).

5. The low-frequency broadband seismic metamaterial filled with a five-mode lattice core according to claim 1, characterized in that: The five-mode dot matrix core (1) is made of metal, composite material or concrete; the hollow concrete pipe (2) is made of concrete; the soil layer (3) is natural foundation soil, backfill soil or improved soil layer; different materials and their parameters are selected according to the isolation and attenuation requirements of Rayleigh waves in the target frequency band.

6. The low-frequency broadband seismic metamaterial filled with a five-mode lattice core according to claim 1, characterized in that: The equivalent compressed wave phase velocity of the five-mode lattice core (1) Phase velocity of equivalent shear wave They respectively satisfy: In the formula, The equivalent bulk modulus of the five-mode lattice core (1) is given by The equivalent shear modulus of the five-mode lattice core (1) is given by... For the equivalent compressive wave mass density, This represents the equivalent shear wave mass density.

7. The design method for low-frequency broadband seismic metamaterials filled with a five-mode lattice core according to claim 6, characterized in that: The quasi-pentamodal properties of the five-modulus lattice core (1) are demonstrated by its equivalent bulk modulus. With equivalent shear modulus The ratio is used to characterize the expression, which satisfies: and with The ratio of G is used as the criterion for optimizing the structural parameters of the five-mode lattice core (1).

8. A design method for a low-frequency broadband seismic metamaterial filled with a five-mode lattice core as described in any one of claims 1-7, characterized in that: include: Step 1: Based on the target vibration isolation frequency band and the parameters of the site medium and foundation structure, design the five-mode lattice core (1), and determine the initial geometric parameters h2, d, D and unit cell lattice constant a of the biconical structure, where d is the upper diameter of the biconical structure, D is the lower diameter, and h2 is the height; Step 2: Connect multiple bipyramidal structures (1-2) along the axial tail end and distribute them evenly along the center to form the hexagonal crystal unit (1-1); Step 3: Arrange the hexagonal crystal units (1-1) periodically along the x-axis, y-axis and z-axis to form a three-dimensional five-mode lattice core (1) structure containing multiple hexagonal crystal units; Step 4: Optimize the geometry, material properties, and number of alternating rows of the metamaterial based on concrete parameters and actual site conditions.

9. The design method for a low-frequency broadband seismic metamaterial filled with a five-mode lattice core according to claim 8, characterized in that: The optimization of the geometry in step 4 is as follows: By adjusting the diameter of the double cone structure (1-2) Lower diameter And height h2, changing the equivalent compressed wave phase velocity of the five-mode lattice core (1) Phase velocity of equivalent shear wave Adjusting the equivalent bulk modulus With equivalent shear modulus ratio To improve the isolation and attenuation of Rayleigh waves by the five-mode dot matrix core (1).

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