Size Mobile Unit Cell for the Protection of Buildings and Facilities from Low-Frequency Earthquake Surface Vibration

Abstract

The present invention discloses a size mobrick unit cell for the protection of buildings and installations from low-frequency seismic surface vibrations. A size mobrick (200) capable of reducing surface vibrations comprises a layer of clamping beds (202) and one or more resonators (204) clamped to the clamping beds (202) to maximize wave attenuation. The length of the one or more resonators (204) is configured based on the wavelength of the surface waves propagating within the layer of clamping beds (202) of the one or more size mobricks (200). Further, the size mobrick (200) comprises base material layers (206) at the top and bottom of the clamping beds (202), and one or more resonators (204) are provided to effectively shield civil structures from surface vibrations by creating a bandgap in the frequency range of the surface waves that cause damage to civil structures.

Description

Technical Field

[0001] The field of the invention generally relates to protecting infrastructure assets susceptible to seismic vibrations, and more particularly to the use of a Seismobrick unit cell for protecting buildings and installations from low-frequency seismic surface vibrations.

Background Art

[0002] Earthquakes can cause devastating malfunctions and damage to the environment. Almost every year, more than 60% of disasters are caused by earthquakes that occur at a frequency of twice per minute. In addition to this, low-amplitude ground waves of seismic vibrations caused by substantial human activities (such as trains and heavy machinery such as pile drivers) also affect the ideal operation of very sensitive machinery in the industry and research institutes. The seismic waves and vibrations induced by ground waves caused by seismic vibrations typically fall within a frequency range of 1 Hz to several tens of Hz and can cause huge destruction related to death. Based on geographical conditions, such waves can cover a relatively long distance on the surface and can match the fundamental resonance frequency of the structure. Rayleigh waves propagate at a slower speed than body waves, but Rayleigh waves transmit relatively more energy to a relatively far distance, so they typically cause most of the damage during seismic vibrations. Therefore, the suppression of Rayleigh waves is important for improving the seismic behavior of the target area.

[0003] Currently, existing systems have not been successful in appropriately suppressing seismic vibrations, especially Rayleigh waves, by reliable and efficient methods. These systems face problems in providing effective attenuation at relatively low frequencies and in terms of limitations such as complex system design, disassemblability of mechanical dampers, long response times, narrow band gaps, large geometric parameters, the need for a large geographical area for implementation, limited adaptability to different geological conditions, and high installation costs.

[0004] Other existing systems have attempted to solve this problem. However, the scope of other existing systems has been limited to using prior art such as, for example, active, passive, and hybrid control methods to attenuate seismic vibrations. These methods have shown some effectiveness in extending the lifespan of large-scale structures by isolating them from earthquakes, but these methods are not effective in suppressing seismic vibrations at relatively low frequencies. For example, conventional damping methods such as, for example, vertical rubber bearings have limited bearing performance and cause significant displacements due to low horizontal stiffness. Furthermore, existing methods often ignore or calculate separately the interaction between soil and foundation within a structure, and existing methods have not sufficiently studied the response of superstructures subjected to angled seismic waves.

[0005] Other existing systems have attempted to solve this problem. However, the scope of other existing systems has been limited to the use of seismic metamaterials that show the potential to attenuate seismic vibrations by mechanisms such as, for example, local resonance, Bragg scattering, inertial amplification, and zero-frequency bandgap (ZFB). However, these existing seismic metamaterials have several drawbacks, including a very narrow bandgap, large geometric parameters of resonators, the need for a large geographical area for implementation, limited adaptability to different geological conditions, and high installation costs. Furthermore, achieving effective suppression of seismic vibrations using ZFB and local resonance mechanisms is practically impossible due to the need for very large-sized resonators fixed to bedrock that is very deep in most inhabited areas. Existing systems result in complex designs, the disassemblability of mechanical dampers, long response times, narrow bandgaps, large geometric parameters, extensive geographical requirements, limited adaptability, and high installation costs. SUMMARY OF THE INVENTION PROBLEMS TO BE SOLVED BY THE INVENTION

[0006] Therefore, considering the above description, it is implied that there is a need for a highly reliable and efficient method and system for suppressing seismic vibrations, particularly Rayleigh waves. As a result, it is adaptable to various geological conditions, provides effective attenuation at relatively low frequencies, ensures the safety and stability of structures subjected to seismic vibrations, and is not affected by the above problems.

Means for Solving the Problems

[0007] A main object of the present invention is to provide one or more size - modular unit cells in the form of a confinement zone around a target structure to protect the target structure from ultra - low - frequency seismic vibrations, particularly in the frequency range of 0 Hz to 33 Hz.

[0008] A further object of the present invention is to provide isolation and protection of civil structures from low - frequency seismic vibrations using a novel damping structure that can be adapted to various geological conditions.

[0009] Another object of the present invention is to develop a damping structure (a series of unit cells) that provides a very wide surface bandgap in the ultra - low - frequency range.

[0010] Another object of the present invention is to provide a brick assembly (size - modular) made from a clamping bed layer, where resonators are pinned / clamped to the clamping bed layer, and another layer of parent material at the top and bottom of the clamping bed. These size - modular bricks can reduce surface vibrations such as seismic surface waves and vibrations caused by human activities such as perforation, passing trains, atomic bomb tests, power plants, etc. When the size - modular bricks are embedded in the parent material, surface waves within this bandgap frequency range cannot propagate through the brick shield.

[0011] Another object of the present invention is to provide "shielding" from surface vibrations by attenuation or by scattering surface waves away from the structure.

[0012] The present invention is shown in the accompanying drawings, in which like reference numerals indicate corresponding parts throughout the several views.

[0013] Embodiments of the present specification will be better understood from the following description with reference to the drawings.

Brief Description of the Drawings

[0014]

Figure 1

Figure 2

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Figure 6(A)

Figure 6(B)

Figure 6(C)

Figure 6(D)

Figure 6(E)

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Figure 8

[0015] The present invention discloses a size mobrick unit cell for the protection of buildings and facilities from low-frequency earthquake surface vibrations. The size mobrick capable of reducing surface vibration comprises a layer of clamping beds.

[0016] Furthermore, the size mobric includes one or more resonators clamped to a clamping bed to maximize wave attenuation. The length of the one or more resonators is configured based on the wavelength of the surface wave propagating within the clamping bed layer of the one or more size mobrics.

[0017] Furthermore, the size mobric includes parent material layers at the top and bottom of the clamping bed, and one or more resonators are provided that create a bandgap in the frequency range of surface waves that cause damage to civil structures, thereby effectively shielding the civil structure from surface vibrations.

[0018] The embodiments of the present specification and their various features and beneficial details are further fully described with reference to the non-limiting embodiments shown in the accompanying drawings and / or detailed in the following description. Descriptions of well-known components and processing techniques are omitted so as not to unnecessarily obscure the embodiments of the present specification. The examples used in this specification are only intended to facilitate the understanding of how the embodiments of the present specification can be implemented and to enable those skilled in the art to implement the embodiments of the present specification. Therefore, the examples should not be construed as limiting the scope of the embodiments of the present specification.

[0019] The present invention discloses a novel metamaterial-based approach for protecting infrastructure assets that are vulnerable to seismic vibrations. Embodiments of the present invention relate to periodic structures called seismic metamaterials (SM) that are convenient for practical realization and provide effective broadband surface wave mitigation in the ultra-low frequency range. The present invention discloses a novel brick element called "sizemobrick" comprising steel resonator columns embedded in soil and fixed to a rigid platform in the form of a concrete base (referred to as a clamping bed) to achieve a very large attenuation zone. The sizemobrick unit, which takes the form of a confinement zone around the target structure, is used to protect the target structure from ultra-low frequency seismic vibrations. In particular, embodiments of the present invention have shown that surface waves are attenuated in the frequency range of 0 Hz to 33 Hz. The present invention is highly scalable for practical realization of the isolation and protection of civil structures from low-frequency seismic vibrations.

[0020] Figure 1 shows a (a) side view and (b) plan view of a metamaterial-based damper located around the entire outer edge of a confinement zone according to an embodiment of the present disclosure. The present invention relates to providing "shielding" from surface vibrations by attenuation or by scattering surface waves away from a structure. One aspect of the invention disclosed herein consists of a collection of bricks made from a layer of a clamping bed, with resonators pinned / clamped to the layer of the clamping bed, as shown in Figure 1(a), and another layer of parent material at the top and bottom of the clamping bed. Such "size bricks" can reduce surface vibrations such as seismic surface waves and vibrations caused by human activities such as drilling, passing trains, atomic bomb tests, power plants, etc. When the size bricks are embedded in the parent material, surface waves within this bandgap frequency range cannot propagate through the brick shield. Compared with the prior art, the relatively large-width bandgap in the proposed invention is due to the contact between the layer of the clamping bed and the resonator firmly fixed to the clamping bed embedded in the uniform parent material.

[0021] Undesirable noise and vibrations have become all too common in our daily lives. As shown in Figures 1(a) and 1(b), undesirable noise and vibrations can be generated by the use, manufacture, transportation, and small-sized earthquakes of machinery. Noise and vibrations are often harmful to human life and animal activities.

[0022] FIG. 2 shows a schematic representation of a seismic block 200 comprising a steel resonator 204 clamped to a clamping bed 202 (concrete) embedded in a base material 206 (soil) according to an embodiment of the present disclosure. The present invention provides a seismic block 200 capable of reducing surface vibrations. The seismic block 200 may also be referred to as one or more seismic blocks. One or more seismic blocks 200 include a layer of clamping bed 202, one or more resonators 204, a base material layer 206, and the like. One or more resonators 204 are clamped to the clamping bed 202 to maximize wave attenuation, and the length of one or more resonators 204 is configured based on the wavelength of surface waves propagating within the clamping bed 202 layer of one or more seismic blocks 200. There are base material layers 206 present at the top and bottom of the clamping bed 202. Further, one or more resonators 204 are provided to create a bandgap in the frequency range of surface waves that cause damage to civil structures, thereby effectively shielding the civil structures from surface vibrations.

[0023] In this specification, the layer of the clamping bed 202 is also referred to as the clamping bed 202. In the present invention, the resonator 204 is clamped to the clamping bed 202, which is the second layer from the top among the bricks 200. The use of the clamping bed 202 is to provide an effective clamp for the resonator 204 such that an upward shift in the dispersion curve can be induced and a ZFB starting from near 0 Hz can be generated. The material properties of the clamping bed 202 must be selected by a method that can provide sufficient rigidity to prevent any displacement or vibration in the brick 200. The material properties of the clamping bed 202 also depend on the material properties of the resonator 204 and the first base material 206 layer in the brick 200. The clamping bed 202 must have a high mass density, but an increase in mass density also raises the material cost. Therefore, when the acoustic impedance ratio of the resonator 204 to the clamping bed 202 is less than 1 / 35 or greater than 35, respectively, the density ratio of the first base material 206 layer to the clamping bed 202 must be less than 0.1 or greater than 1. This narrow range is selected so that a change in density does not result in a significant change in the bandgap, which enables the use of a relatively inexpensive high-density material such as a composite. Similarly, when the first matrix 206 layer has an acoustic impedance ratio of less than <1 / 35> to the resonator 204 and greater than 35, respectively, the ratio of the elastic constant of the first matrix 206 layer to the clamping bed 202 has a substantially same range from 0.05 to 1.5.

[0024] The advantage of clamping is that clamping provides an ultra-low frequency bandgap with a starting value of 0 Hz, which is beneficial for attenuating low-frequency seismic vibrations. The material and thickness of the clamping bed 202 play an important role in bringing about the clamping / pinning effect. The harder the clamping bed 202, the better the clamping effect, which helps to guide waves in the soft material layer. The thickness of the clamping bed 202 must be such that the clamping bed 202 can provide sufficient rigidity and clamping. As the thickness of the clamping bed 202 increases, the ZFB also increases. Generally, the thickness of the clamping bed 202 is in the range from half of the brick unit cell constant to infinity, but there is no infinite thickness. Therefore, the most practical thickness range is 0.5 to 1.5 times the brick unit cell constant. Numerical simulations provided insights into the material properties of the clamping bed 202.

[0025] As described, the depth of the clamping bed 202 from the surface of the brick 200 depends on the length of the resonator 204 and the length of the resonator 204 clamped inside the clamping bed 202. The length of the clamping can be determined based on the pinning provided by the clamping. Furthermore, as the length of the clamping increases, it provides a better clamping / pinning effect but also leads to a higher material cost. Therefore, this length is optimized to be 0.5 to 0.7 times the thickness of the clamping bed 202.

[0026] The depth of the clamping bed 202 is equal to or greater than the difference between the length of the resonator 204 and the length of the clamping bed 202, and the difference is generally in the range of 1 to 3 times the brick unit cell constant. The shape of the clamping is the same as the shape of the base material 206.

[0027] In this specification, one or more resonators 204 are also referred to as resonator 204. Resonator 204 is used to generate a band gap using a local resonance mechanism. The local resonance occurring in resonator 204 associated with the clamping effect generates a wider band gap in the proposed invention. In the case of seismic wave mitigation applications, the present invention can generate a band gap in the frequency range of surface waves that propagate the farthest and cause the greatest damage to civil structures. The acoustic impedance of a material (defined as the product of the density of the material and the wave speed in the material) depends on its mass density and elastic constants such as Young's modulus. The material of resonator 204 must have a large mismatch in acoustic impedance compared to the material of the base material 206 and the material of the clamping bed 202. The range of the ratio of the acoustic impedance of the material of the first base material layer to the acoustic impedance of the material of resonator 204 must be greater than 35 or less than 1 / 35. The range of the ratio of the speed of the material of the first base material 206 layer to the material of resonator 204 must be greater than 0.01 or less than 100.

[0028] Surface waves in the low frequency range (from a few hertz to several tens of hertz) occur during disasters such as earthquakes, mining, and nuclear experiments. A bandgap covering this frequency range is realized using an empty borehole, or an outer shield resonator 204, or an embedded resonator 204, having geometric parameters (diameter, length) of about several tens of meters. More specifically, manufacturing or digging these huge resonators 204 and holes in residential areas is clearly not practical. Therefore, an optimal design for the present invention has been designed that can be easily realized even in areas with higher population density and has a wider adjustable bandgap. The length of the resonator 204 depends entirely on the operating wavelength within the bandgap frequency range. In the present invention, the length of the resonator 204 is in the range from λ / 20 to λ / 10, where λ is the wavelength of the surface wave propagating in the first layer of the brick 200. The length of the resonator 204 can differ by 1 to 2 times the unit cell constant of the brick 200 (defined as the periodicity of the brick 200) and is sufficient to generate a wide bandgap. The length of one or more resonators 204 further affects the ZFB, and a longer length results in a narrower bandgap. The length of one or more resonators 204 further determines the depth at which the clamping bed 202 from the surface is disposed.

[0029] The cross-section of the resonator 204 plays an important role in realizing the required bandgap. As the shape of the cross-section changes, both the total bandgap and the width of the ZFB also change. This occurs because two resonators 204 with the same cross-sectional area but different shapes can have different moments of inertia. Since the moment of inertia is directly related to the resonance frequency, different shapes of the resonator 204 can result in different bandgaps. For example, all possible shapes for the cross-section of the resonator 204 can be considered, such as a circle, rectangle, or square as shown in Fig. 2(c), two rectangles arranged to cross each other (Cross with Extended Bar [CEB]) including long bars arranged to cross each other as shown in Fig. 2(a), two rectangles arranged to cross each other (crossed bars), and polygons. The advantage of a polygonal cross-section over a simple cross-section (such as a circle) is that it provides higher rigidity and, as a result, a much wider bandwidth. On the other hand, the manufacture of such shapes is difficult and troublesome.

[0030] The rigidity value of a polygon depends on its side length and the number of sides and can be calculated using the following formula.

Equation

Equation

[0031] The bandwidth of the size mobric 200 depends on the rigidity of the resonator 204. Therefore, the bandwidth of the size mobric 200 including a polygonal resonator can be calculated by using the following formula. Bandwidth = sqrt(K(polygon) * Bandwidth of circular resonator / K(circle)) Here, K is the rigidity.

[0032] Along with the shape, the number of one or more resonators 204 embedded in the brick 200 also affects the bandgap and the width of the ZFB. Increasing the number of resonators 204 results in increasing the volume fraction hv, and up to a certain level, more resonators 204 result in a wider bandgap. The number and dimensions of the resonators 204 depend on the size, shape, and frequency range of the brick 200 for which the bandgap is required. Further, the cross-sectional area of the resonators 204 is selected by a method such that the resonators 204 do not break under the vertical load applied by anything placed on the resonators 204. Thus, in order to achieve a wider bandgap, the ratio of the total cross-sectional area of the resonators 204 to the total cross-sectional area of the brick 200 must be in the range between 0.4 and 0.6. Resonators 204 with the same or different geometric configurations can be further embedded in the brick 200 and clamped to the clamping bed 202. The desired ratio can be calculated using the volume fraction limit of the composite (matrix 206, resonator 204, and clamping bed 202) to form the bandgap.

[0033] The resonator 204 behaves as a Helmholtz resonator 204, and the resulting local resonance brings about a bandgap, so the position where the resonator 204 is placed has little effect on the bandgap. Even when the bricks 200 are arranged periodically, the resonators 204 are aperiodic in the damping structure. The resonators 204 can be coupled to each other using thin plates or rod-like structures to provide higher rigidity. In both cases, all the bricks 200 can be tightly connected, resulting in one large brick 200.

[0034] In this specification, the base material layer 206 is also referred to as the base material 206. As shown in FIGS. 2(a) and 2(b), the brick 200 may include a single-layer or multi-layer base material 206 with different material properties. The base material 206 layered using various brick 200 materials provides a much wider ZFB compared to a single base material 206 material. This is because the presence of a hard or very high-density layer leads to the wave energy being directed to the soft layer and the presence of the clamping bed 202 leads to it being redirected again. Thus, the wave energy is confined and attenuated, which results in a wider ZFB in the brick with a layered base material of different materials. By controlling the composition, arrangement, and shape of the base material 206, a desired bandgap can be obtained. In the proposed brick 200 structure, the width of the bandgap mainly depends on the material of the base material 206 with a low acoustic impedance. The base material 206 layer below the clamping bed 202 may have an acoustic impedance higher than that of the first base material 206 layer, but it must not be more than 35 times and not less than 1 / 35 times that of the material of the resonator 204.

[0035] The height (Hm2 + Hm3 + Hm4) of the base material 206 layer below the clamping bed 202 must be an integer multiple of the reciprocal of the wavelength corresponding to the center frequency of the bandgap. This does not depend on the order in which the materials are arranged when the acoustic impedance criterion is satisfied. The material of the base material 206 can be the same as or different from the surrounding materials. In an optimized design, the height of the layered soil is a multiple of the unit cell constant of the brick 200. The sum of all the heights is approximately equal to 20*a or λ, where λ is the wavelength of the surface wave propagating in the first layer of the brick 200. The cross-sectional shape and length of the base material 206 provide the overall geometric configuration of the brick 200, which is described in detail in the section of the unit cell of the size mobrick 200.

[0036] The cross-sectional shape of the size mobrick 200 unit cell plays an important role in further determining the factor of bandgap nucleation. Since these bricks 200 are periodically arranged, these bricks 200 function as a bravais lattice, and the symmetry of these bricks 200 can be used to efficiently calculate the dispersion plot for the bricks 200. The unit cell of the brick 200 can have square, rectangular, honeycomb, or hexagonal lattice symmetry (as shown in FIGS. 2(a) to 2(e)). Among all lattice symmetries, the brick 200 with square or rectangular lattice symmetry and the brick 200 with hexagonal lattice symmetry exhibit a wider bandgap and ZFB. However, the brick 200 with honeycomb lattice symmetry is associated with a lower material cost.

[0037] Furthermore, the most important and optimized one in the present invention is the brick unit cell constant. In the present invention, for the brick 200 with square or rectangular lattice symmetry, the dimensions of the cross-section of the brick 200 (the length and width of the brick 200 with square symmetry are the same) are about λ / 25, where λ is the wavelength of the surface wave propagating in the first layer of the brick 200. In another brick 200 model, the length and width can be different, and the ratio of the length to the width must be within 0.75 to 1.2 in order to achieve a wider bandwidth. Similarly, for the brick 200 with hexagonal lattice symmetry, the dimensions of the cross-section of the brick 200 (unit cell constant) must be about λ / 25, where λ is the wavelength of the surface wave propagating in the first layer of the brick 200. The minimum dimension of the cross-section of the brick 200 for seismic applications is in the range of 1.5 m to 2 m for the bandgap of 0 Hz to 33 Hz, which is a great advantage over the prior art. This is the best possible optimized design of the brick 200 structure for any surface vibration attenuation.

[0038] The height (Hm1 + Hc + Hm2 + Hm3 + Hm4) of the brick 200 must be equal to the wavelength or sub - wavelength (λ / 2) of the surface wave propagating within the first base material 206 layer of the brick 200 in order to completely remove the surface wave. In an optimized design of the brick 200, the height can be 20 times the brick unit cell constant. Further, the height of the first base material 206 layer is the same as the depth of the clamping bed 202.

[0039] The number of bricks 200 to be arranged depends on the level of attenuation required. In theory, an infinite number of bricks 200 are required to achieve 100% isolation. However, in a practical scenario, we can only embed a limited number of bricks 200. Numerical analysis has shown that using more than 4 unit cells is sufficient to reduce the surface amplitude by 80%. Increasing the number of unit cells up to 10 has achieved a sufficient maximum attenuation of the surface wave.

[0040] As described above, the number of bricks 200 required is between 4 and 10, and they are more than a sufficient number to reduce surface vibrations. Therefore, the surrounding thickness is in the range of 8m to 20m, which is very small compared to the prior art.

[0041] The optimized unit cell of the SM can be designed by selecting appropriate geometric parameters and material properties of the brick 200. The brick 200 embedded on the surface can function as a shield and is located around the site to be protected. In another example, the brick 200 can be located below the site and inside the lateral outer edge of the site, but it is not located as the base of the site. In this aspect, the resonator 204 is not attached to the site and is not in direct contact with the site.

[0042] The potential capabilities of the present invention are investigated through numerical simulations and experiments. The phononic dispersion characteristics of the proposed sub - wavelength brick 200 are investigated to identify the elastic wave propagation and non - propagation vibration modes. Dynamic response and time - transient analysis are performed to identify the wave attenuation within the band - gap frequency range.

[0043] By periodically embedding and clamping the steel resonator 204 together with the concrete bed (clamping bed 202) in the soil (base material 206), a new type of brick 200 structure with square, triangular, and hexagonal lattices is realized. The geometric configuration of the proposed SM unit cell and the first Brillouin zone of the minimum unit are shown in Figs. 2(a) to 2(e), and the respective geometric parameters and material properties are listed in Tables 1 and 2. To generate layered soil, the half-space soil domain is divided into three different multilayers. The height (Hm2:Hm3:Hm4) ratio of the layered soil is 2:3:5, and the stiffness ratio of the soil between the soil layers is 5:20:400. Using the Floquet-Bloch condition at the side boundary of the unit cell, the dispersion relation is calculated. Since the proposed system is periodic, the investigation is carried out in the first Brillouin zone of the minimum unit of the unit cell, and the highest symmetry points in the first Brillouin zone for the square, honeycomb, and hexagonal shapes are [Γ(0,0), X(π / a,0), M(π / a,π / a)], [Γ(0,0), X(4π / (3√3)a,0), M(π / (√3)a,π / 3a)], and [Γ(0,0), X(4π / 3a,0), M(π / a,π / (√3)a)], respectively, where "a" is the minimum distance between two consecutive resonators 204. The unit cell constants for the square, honeycomb, and hexagonal lattices are given as "a", "(√3)a", and "a / √3", respectively. The direction and amplitude of the wave vector give the direction and mode of the wave within the Brillouin zone. As shown in Figs. 2(f) to 2(h) for the square, honeycomb, and hexagonal lattices, the dispersion eigenmodes are evaluated along the Γ-X-M-Γ direction that gives the highest symmetry within the first Brillouin zone of the minimum unit. The stress zero condition is considered at the free surface. To mimic the actual scenario of surface waves in the half-space, the bottom wall of the soil is given a fixed boundary condition. It should be noted that applying a fixed boundary or a perfectly matched layer (PML) to avoid reflection from the bottom surface can lead to non-physical wave modes.Therefore, the authors conducted a detailed sound cone investigation to classify the actual propagating surface waves and bulk modes. The numerical model was discretized by 4-node Lagrangian tetrahedral linear elements with a minimum size of λ / 20 and a maximum size of λ / 10, where λ is the minimum wavelength of the Rayleigh wave. An eigenvalue analysis was performed in COMSOL Multiphysics to plot the dispersion curves for the proposed unit cell. In all of these numerical studies, the material of the base member 206 is considered soil, and the material of the base member 206 is modeled as a linear elastic isotropic material. Further, the resonator 204 has steel properties, and the clamping bed 202 has given concrete properties. The material properties of the base member 206, the resonator 204, and the clamping bed 202 are selected according to the above design criteria. The results obtained through the dispersion curves can be generalized by expanding and shrinking the bandgap frequencies with the help of the unit cell dimensions and the wave speed in the unit cell.

[0044] FIG. 3 shows a phononic dispersion diagram for modes at various lattices and cutoff frequencies according to an embodiment of the present disclosure.

[0045] From the numerical simulation of the phononic dispersion analysis, it is observed from the dispersion results that the hexagonal lattice including the circular resonator 204 gives a better cut-off frequency (1.15 Hz) than the square lattice (0.73 Hz) and the honeycomb lattice (0.75 Hz) including the circular resonator 204. As is clear from the absence of the dispersion curve in the white region of the dispersion plots shown in FIGS. 3(a) to 3(f), the existence of the surface wave mode propagation in the present invention for all lattice symmetries does not exist. This is clear from the result that the upper limit of the band gap for the circular pile resonator 204 with honeycomb lattice symmetry (12.3 Hz) is much lower than those of the square lattice symmetry (22.6 Hz) and the hexagonal lattice symmetry (21.4 Hz). The long bar intersection resonator 204 clamped to the concrete bed has a cut-off frequency of 2.72 Hz, and the upper limit of the band gap is 32.36 Hz. As shown in FIGS. 3(e) and 3(f), the cut-off frequencies of the circular pile resonator 204 and the clamped CEB-shaped resonator 204 clamped to the layered soil are 2.41 Hz and 10 Hz, respectively. Since local modes are generated at the interface of the multi-layered structure, the coupling of the surface wave with the structure hinders the wave propagation. Furthermore, the long bar intersection resonator 204 and the circular pile resonator 204 clamped to the concrete bed including the base material 206 of different layered materials have upper limits of the band gap of 22.6 Hz and 32.36 Hz, respectively, similar to the base material 206 of one material. This is because both have the same geometric parameters. It is shown from the global vibration modes of the present invention for all lattice symmetries that there is no surface vibration in the unit cell at the highest symmetry point Γ and the cut-off frequency. The bulk wave propagates below the concrete bed. Instead of reflecting the surface wave in the deep layer of the earth's interior, the present invention traps or reflects the surface vibration so as to return it, thereby reducing the transmission of the surface wave. Furthermore, it is observed from the phononic dispersion investigation that there is an increase in the cut-off frequency of the ZFB.

Table 1

Table 2

[0046] Figure 4 shows a schematic diagram of the finite-length model used for dynamic response and time transient investigation according to an embodiment of the present disclosure ((a) plan view (b) side view).

[0047] The dynamic response of the present invention was performed by conducting a frequency domain analysis to verify the results realized by the analysis of variance. The authors modeled an array of 105 unit cells in a uniform matrix (soil) block. Further, 5 unit cells were considered in the direction orthogonal to the wave propagation to understand the effect of the number of unit cells on the attenuation of waves coming from the inclined direction. For comparison, the dynamic response of the "brick-free" case was evaluated by modeling a uniform soil of a special width. The geometric configuration of the 3D model considered is shown in FIGS. 4(a) and 4(b). To avoid reflections due to scattering of waves from the soil region boundaries, PML was applied to all boundaries. The length, width, height, and thickness of the PML are "L + 10a", "W + 10a", "H + 5a", and "5a", respectively. Soil properties were assigned to all regions of the PML and the uniform matrix 206, steel properties were assigned to the resonator 204, and the clamping bed 202 was modeled using concrete properties.

[0048] To model the propagation of elastic surface waves in the present invention, a low amplitude harmonic excitation was applied near the edge between the PML and the uniform part at the left boundary. The excitation edge was maintained at a distance of "5a" from the array of brick unit cells, which ensures that only the surface wave hits the unit cell and the bulk wave propagates deeper in the substrate. The frequency response of the present invention is recorded in the form of the total displacement over the frequency range of 0 Hz to 40 Hz at positions A1 and A2. Data acquisition for the dynamic response investigation was performed at points A1 and A2 near the opposite side of the edge wave excitation, and points A1 and A2 are equidistant from the wave excitation edge. Furthermore, A1 and A2 are positioned sufficiently far apart ("7.5a") from each other so that the wave interaction in the barrier of the present invention does not affect the results at A2.

[0049] To further understand the dispersion behavior, a dynamic response analysis was performed. The data obtained from A1 represents the case "including the brick barrier", and thus the data obtained from A2 represents the case "not including the brick 200 barrier". The frequency response function (FRF) is calculated as follows.

Equation

[0050] Figure 5 shows the results obtained from the time transient analysis according to an embodiment of the present disclosure. To further verify the efficiency of wave attenuation and to observe the behavior of waves in the array of unit cells of the present invention, the authors performed time transient analysis by simulation. The authors modeled a finite volume containing homogeneous soil including an array of 10×5 unit cells, similar to the model used in the dynamic response survey. The dimensions of the homogeneous soil are also considered to be the same as those of the model used in the dynamic response survey. In this model, wave attenuation due to soil is not considered, and thus it helps to estimate the actual wave attenuation due to the brick 200. To investigate the wave behavior, the excitation frequency is conveniently selected as 19 Hz (from the frequency range of the bandgap), and the excitation wave profile considered is a Hannin tone burst containing 20 cycles to ensure a narrowband excitation at approximately 19 Hz. Time transient explicit simulations were performed for the CEB resonator 204 and the circular pile resonator 204 using durations of 1.6 s and 1.8 s, respectively, and the time step is considered to be 1 / (20fmax), where fmax is the highest frequency of interest.

[0051] As shown in FIGS. 5(a) and 5(b), as the excitation frequency (19 Hz) decreases within the frequency range of the bandgap, the surface vibration is significantly reduced. The absolute amplitude is calculated by taking the ratio of the displacement at the receiving point to the maximum amplitude of the displacement without using the proposed SM. It is understood that more than 80% of the wave is attenuated for both cases. The brick 200 made from the long bar cross resonator 204 is more effective in reducing the wave amplitude than the barrier of the circular pile resonator 204 for an array of the same size. This is because the propagating frequency is within the omnidirectional (Γ-X) bandgap for the CEB-shaped resonator 204, while for the circular pile resonator 204, the propagating frequency is outside. The results obtained from this investigation further verify the results from the dynamic response analysis and show that the unit cell containing the CEB-shaped resonator 204 is more effective in the relaxation of the propagating wave. Snapshots of the total displacement at 0.92 s for both cases are shown in FIGS. 5(c) and 5(d), and it is observed that there is no wave transmission at the barrier across several unit cells. In addition, as shown in FIGS. 5(e) and 5(f), the induction of the wave from the clamping bed 202 to the low-density (soft material) base material 206 can be confirmed.

[0052] Figure 6(a) shows a photograph of the laboratory-scale experimental setup. (b) is a numerically calculated dispersion plot for the proposed SM scaled at 1:40. The total AZ (0 Hz to 640 Hz) is indicated by the gray-shaded area, and the ZFB (0 Hz to 55 Hz) is indicated by the red-shaded area. The vertical line represents the natural frequency of the container box. (d) is a schematic diagram of the numerical model of the container box used for the natural frequency analysis. (e) is the modal shape of the container box at different natural frequencies according to an embodiment of the present disclosure. To verify the numerical calculation results obtained for the proposed SM design, a small-scale laboratory experiment was conducted using the SM scaled at 1:40. As shown in Figure 5(a), wave transmission was investigated for a sample specimen made from a 5×3 array of unit cells. The unit cell comprises a 25 mm diameter steel rod 62.5 mm long fixed to a clamping bed 202 made of concrete with a thickness of 12.5 mm. The experimental setup is 0.6×0.3×0.3 m 3It was constructed by filling a container of

[0053] the dimensions with soil and embedding unit cells on the surface of the soil layer. To avoid reflections from the container boundaries, a layer of gravel was placed at the bottom and side walls. To measure the wave transmission for the "brick-free" case, the unit cell array was removed and the resulting gap was filled with soil. The density of the soil was maintained constant during the experiment to ensure a certain porosity of the soil. The soil was selected by a method such that the properties of the soil matched those considered for the simulation. Since the environment can also affect the results of the experiment, it was carried out in a controlled environment. Out-of-plane excitation was generated by an electromechanical shaker (micron MEV0010) labeled "E" in Fig. 6(a) located at the edge of the container, and the wave transmission at the other barrier was measured using an accelerometer (PCB353B03) labeled "R" in Fig. 6(a). Two other accelerometers were positioned in front of the scaled SM and the container to understand the wave propagation and observe the natural frequency of the container, and these were labeled "A" and "B" respectively. The vertical component of the surface acceleration was measured for both the "brick-included" and "brick-free" cases. As shown in Fig. 5(b), since the numerical dispersion investigation of the bricks scaled down by 1:40 shows the total omnidirectional bandgap and ZFB in the ranges of 0 Hz to 630 Hz and 0 Hz to 55 Hz respectively, the frequency of the excitation signal between 0 Hz and 900 Hz was swept using a signal generator (micron MCU100) labeled "G" in Fig. 6(a). The accelerometers were connected to a data acquisition system (NI4432) further mounted on a computer. All accelerometers measure the vertical component of the displacement for both cases with and without the proposed SM included.

[0053] The results of the dynamic response survey indicate that in the case without the barriers of the proposed SM, the reduction in the amplitude of the surface wave is negligible. Therefore, the authors specified the transmittance of the surface wave attenuation for the case "including the barriers of the proposed SM" relative to the case "without the barriers of the proposed SM". The transmittance can be defined as the ratio of the amplitude of the wave measured for the case "including the barriers of the proposed SM" (A i ) to the amplitude of the wave (A f ) for the case "without the barriers of the proposed SM". Since there is no surface propagation mode within the bandgap region, the present invention can suppress surface vibrations in the range of 0 Hz to 640 Hz. Due to the assumptions made in the numerical modeling considering soil and concrete as linear elastic materials (although not in the scenario of the actual case), the omnidirectional band is extended and becomes wider than that observed in Simulation 52. The results of the laboratory-scale experiments verified the results obtained by simulation and demonstrated the ability of the proposed bricks to reduce surface vibrations.

[0054] Furthermore, as shown in Fig. 6(c), a higher transmittance can be observed at specific frequencies, which may be due to the natural frequency of the container itself. To verify this, a natural frequency analysis was performed on a container box with appropriate material properties. To simulate the experimental conditions, a small harmonic excitation was applied to the edge of the plate extending from the container box, and a spring base (spring constant = 5 kN / m) was introduced to the bottom wall of the container box as shown in Fig. 6(d). In Fig. 6(c), the numerical analysis results are represented as vertical lines corresponding to the natural frequencies of the box. As expected, these vertical lines coincide with the high transmittance peaks. Furthermore, as shown in Fig. 6(e), the modal shape of the box shows a larger vertical displacement at the box ends. As a result, even when there is an array of SMs, a higher transmittance was observed. Except for these frequencies, most of the energy is attenuated, and the omnidirectional AZ shows an amplitude reduction of 78%.

[0055] Figure 7 shows a method 700 of manufacturing a size mobrick capable of reducing surface vibrations. The method begins with providing a layer of a clamping bed, as shown in step 702. Thereafter, method 700 discloses clamping one or more resonators 204 to the clamping bed 202 to maximize wave attenuation, as shown in step 704, wherein the length of the one or more resonators 204 is configured based on the wavelength of the surface waves propagating within the layer of the clamping bed 202 of the one or more size mobricks. Thereafter, method 700 discloses placing a base material layer 206 on the top and bottom of the clamping bed 202 in step 706, wherein one or more resonators 204 are provided to create a bandgap in the frequency range of surface waves that cause damage to civil structures, thereby effectively shielding the civil structure from the shown surface vibrations.

[0056] Figure 8 shows a method 800 of using a size mobrick to reduce surface vibrations. The method begins with placing one or more size mobricks 200 around a site that requires protection from surface vibrations, as shown in step 802. Thereafter, method 800 discloses embedding one or more resonators 204 in the one or more size mobricks 200 and clamping the resonators 204 to the clamping bed 202 to maximize wave attenuation, as shown in step 804, wherein the length of the one or more resonators 204 is configured based on the wavelength of the surface waves propagating within the layer of the clamping bed 202 of the one or more size mobricks. Further, method 800 discloses placing a base material layer 206 on the top and bottom of the clamping bed 202, as shown in step 806, wherein one or more resonators 204 are provided to create a bandgap in the frequency range of surface waves that cause damage to civil structures. Thereafter, method 800 discloses placing the one or more size mobricks 200 so that destructive waves are prevented from entering the confinement zone of the site, as shown in step 808, thereby effectively shielding the civil structure from surface vibrations.

[0057] Advantages of the present invention include providing effective mitigation of surface vibrations, such as seismic waves and vibrations due to human activities, by attenuation and scattering of surface waves away from the structure.

[0058] A further advantage is that the use of size mobrics enables the generation of a wider bandgap frequency range and provides better protection from surface vibrations compared to the aforementioned methods.

[0059] A further advantage is that the size mobrics can be embedded in the base material, enabling customizable and versatile applications.

[0060] A further advantage is that the design of the size mobrics can be optimized to suit various scenarios, such as protecting structures from seismic waves, reducing vibrations caused by industrial activities, or shielding areas vulnerable to environmental vibrations.

[0061] Uses of the present invention include providing shielding against surface vibrations in various environments, such as civil structures, industrial facilities, residential areas, and critical infrastructure. The size mobrics can be used to reduce vibrations caused by seismic activity, drilling operations, passing trains, atomic bomb tests, power plants, and other sources of unwanted noise and vibrations. This innovative solution provides a reliable and effective means of protecting human life, safeguarding structures, and maintaining a peaceful environment.

[0062] The above description of specific embodiments fully discloses the general features of the embodiments herein so that others may, by applying current knowledge, readily modify and / or adapt such specific embodiments for various uses without departing from the overall concept. Accordingly, such adaptations and variations are intended to be within the meaning and scope of the disclosed embodiments and equivalents thereof. It is understood that the terms or terminology used herein are for the purpose of description and not of limitation. Thus, although the embodiments herein are described from the perspective of preferred embodiments, those skilled in the art will recognize that the embodiments herein may be practiced with modifications within the scope of the embodiments described herein.

Claims

1. A size mobrick (200) capable of reducing surface vibration, wherein the size mobrick (200) comprises a layer of a clamping bed (202), one or more resonators (204) clamped to the clamping bed (202) to maximize wave attenuation, wherein the length of the one or more resonators (204) is configured based on the wavelength of the surface wave propagating within the clamping bed (202) layer of one or more size mobricks (200), the one or more resonators (204), layers of base material (206) at the top and bottom of the clamping bed (202), wherein the one or more resonators (204) are provided to effectively shield the civil structure from surface vibration by creating a bandgap in the frequency range of the surface waves that cause damage to the civil structure, the layer of base material (206), A size mobrick (200) comprising.

2. The one or more resonators (204) are located at a certain depth from the surface based on the length of the one or more resonators (204), The one or more resonators (204) are attached to each other to provide one large size mobrick (200), The size mobrick (200) according to claim 1.

3. The cross-sectional shape of the area of the one or more resonators (204) is selected from at least one of a circle, a rectangle, a square, two rectangles including elongated bars arranged to intersect each other, two rectangles arranged to intersect each other, and a polygon. The size mobrick (200) according to claim 1.

4. The one or more resonators (204) have a polygonal cross-section to provide higher rigidity and a wider bandwidth. The size mobrick (200) according to claim 3.

5. The one or more resonators (204) are embedded in the one or more size mobricks (200) and are clamped to the clamping bed (202) using thin plates or rod-like structures to increase rigidity. The size mobrick (200) according to claim 1.

6. The one or more resonators (204) have a range of ratios of total cross-sectional area to the area of the one or more size mobiles (200) between 0.4 and 0.6 to achieve a wider bandgap. The size mobile (200) according to claim 1.

7. The material of the one or more resonators (204) has an acoustic impedance ratio to the material of the base material (206) within a range greater than 35 or less than 1 / 35. The size mobile (200) according to claim 1.

8. A method of manufacturing a size mobile (200) capable of reducing surface vibrations, the method comprising: providing a layer of a clamping bed (202); clamping one or more resonators (204) to the clamping bed (202) to maximize wave attenuation, wherein the length of the one or more resonators (204) is based on the wavelength of surface waves propagating within the layer of the clamping bed (202) of the one or more size mobiles (200), the clamping; placing a layer of base material (206) on the top and bottom of the clamping bed (202), such that the one or more resonators (204) are provided to effectively shield the civil structure from surface vibrations by creating a bandgap in the frequency range of surface waves that cause damage to the civil structure, the placing; A method of manufacturing a size mobile (200) comprising.

9. [[ID=j12]]changing the cross-sectional shape of the one or more resonators (204) to optimize the total bandgap and the width of the zero frequency band (ZFB). The method of manufacturing a size mobile (200) according to claim 8.

10. selecting the cross-sectional shape of the area of the one or more resonators (204) from at least one of a circle, a rectangle, a square, two rectangles arranged to intersect each other, two rectangles arranged to intersect each other, and a polygon. The method of manufacturing a size mobile (200) according to claim 8.

11. selecting the one or more resonators (204) having a polygonal cross-section to provide higher rigidity and a wider bandwidth. The method of manufacturing a size mobile (200) according to claim 10.

12. selecting the number and dimensions of the one or more resonators (204) based on the size, shape, and desired bandgap frequency range of the one or more size mobiles (200), A method of manufacturing a size mobile (200) according to claim 8.

13. A method of using a size mobile (200) for reducing surface vibrations, the method comprising: placing one or more size mobiles (200) around a site that requires protection from surface vibrations; embedding one or more resonators (204) in the one or more size mobiles (200); clamping the resonators (204) to a clamping bed (202) to maximize wave attenuation, wherein the length of the one or more resonators (204) is configured based on the wavelength of surface waves propagating within the clamping bed (202) layer of the one or more size mobiles (200); placing a layer of base material (206) on top of and at the bottom of the clamping bed (202), wherein the one or more resonators (204) are provided to create a bandgap in the frequency range of surface waves that cause damage to civil structures; placing the one or more size mobiles (200) so as to effectively shield the civil structure from surface vibrations by preventing destructive waves from entering the confinement zone of the site; A method of using a size mobile (200), comprising:

14. maximizing the effect of wave attenuation by tightly connecting the one or more size mobiles (200) together to form one large size mobile (200), A method of using a size mobile (200) according to claim 13.

15. placing the one or more size mobiles (200) below and inside the lateral outer edge of the site, rather than as a foundation for the site, to protect the site from destructive waves, A method of using a size mobile (200) according to claim 13.

16. To provide additional rigidity and to enhance the clamping effect, the method includes mounting the one or more resonators (204) in the one or more size-moblics (200) using thin plates or rod-like structures. A method of using the size-moblic (200) according to claim 13.

17. To optimize the attenuation of the wave and to achieve a wider bandgap, the method includes adjusting the length and cross-sectional shape of the one or more resonators (204). A method of using the size-moblic (200) according to claim 13.

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