Metamaterial concrete beam with local resonance properties

Abstract

The application discloses a metamaterial concrete beam with a local resonance property, which is composed of a plurality of unit cells arranged periodically; the unit cell comprises a concrete pipe and a dynamic vibration absorber arranged in the concrete pipe in a radial direction of the concrete pipe; the dynamic vibration absorber comprises a metal heavy core and a soft coating wrapped on the surface of the metal heavy core and attached to the inner wall of the concrete pipe; and the plurality of unit cells are spliced by the two ends of the concrete pipe. The application is aimed at the fact that a phononic crystal metamaterial is limited by a structure size, is difficult to form a high-frequency band gap in a limited size, and is based on a local resonance mechanism to design a metamaterial concrete beam structure which can form a resonance band gap in an engineering structure of a limited size, so as to attenuate input waves whose wavelengths are not in the same order of magnitude as the size of the beam unit cell, thereby playing a vibration reduction role in actual engineering applications.

Description

TECHNICAL FIELD

[0001] The present application relates to a concrete beam, in particular to a metamaterial concrete beam with local resonance properties. BACKGROUND

[0002] In recent years, metamaterials, as a kind of artificial composite structure material that controls vibration by using its own band gap (a frequency range that can attenuate or block the movement of waves), have been widely used in the fields of electromagnetism, acoustics, etc. The existing metamaterial structure is generally constructed by periodically arranged artificial elastic medium, and is mostly phononic crystal metamaterial based on Bragg scattering mechanism to form band gap. Bragg band gap refers to the fact that when waves propagate in a periodic structure, due to the coherent superposition (destructive interference) of scattered waves, waves of a specific frequency are prevented from propagating, thereby forming a frequency band gap.

[0003] However, it is difficult to form a periodic spatial size of the same order of magnitude as the input wave length in civil engineering, so it is difficult to attenuate the vibration of the building structure by using the Bragg band gap. Unlike the band gap formed by the Bragg scattering mechanism, the band gap formed by the local resonance mechanism depends on the relative motion inside the unit cell, so the metamaterial with local resonance properties can form a resonance band gap in the limited size of the engineering structure to attenuate the input wave whose wavelength is not in the same order of magnitude as the size of the unit cell.

[0004] Based on the existing working mechanism of local resonance, it is very meaningful to develop more kinds of concrete metamaterial structures, systematically study their vibration attenuation performance, and then apply them to engineering practice. SUMMARY

[0005] The purpose of the present application is to provide a metamaterial concrete beam with local resonance properties that can form a resonance band gap in a limited size of engineering structure.

[0006] Technical scheme: The metamaterial concrete beam with local resonance properties comprises a plurality of unit cells arranged periodically, wherein the unit cell comprises a concrete pipe and a dynamic vibration absorber arranged in the concrete pipe in the radial direction of the concrete pipe; the dynamic vibration absorber comprises a metal heavy core and a soft coating wrapped around the surface of the metal heavy core and attached to the inner wall of the concrete pipe; and the plurality of unit cells are spliced to form the metamaterial concrete beam through the two ends of the concrete pipe.

[0007] The unit cell has a cuboid shape, the concrete pipe is a hollow cylinder arranged in the cuboid, and the dynamic vibration absorber is embedded in the hollow cylinder.

[0008] The two ends of the hollow cylinders of the plurality of unit cells are aligned to form a circular pipe.

[0009] The metal heavy core is a cylinder, and the soft coating layer is a circular cylinder wrapped outside the cylinder, and the outer side of the soft coating layer is tightly attached to the inner wall of the circular pipeline.

[0010] The cell main body is a concrete material; the soft coating layer material is a material with a smaller elastic modulus, the elastic modulus being 1-100 MPa, preferably at least one of polyurethane, nylon and silicone rubber; the material of the metal heavy core is a material with a larger elastic modulus, the elastic modulus being 6000-20000 kg / m 3 , preferably steel or lead.

[0011] The dynamic vibration absorber is an axisymmetric structure, and each dynamic vibration absorber is arranged at the center position of the cell.

[0012] The length of the cuboid cell is l, the width is b, the height is a, the radius of the circular hole is r1, the radius of the metal heavy core is r2, and the height is h m ; the thickness of the soft coating layer is D r , and the height is h r .

[0013] The height of the metal heavy core is not less than the height of the soft coating layer, that is, h m ≥ h r , and the distance between the center of the dynamic vibration absorber in the beam end cell and the beam end is l / 2.

[0014] The ratio of the radius r2 of the metal heavy core to the thickness D r of the soft coating layer is 1-4.

[0015] The elastic modulus of the soft coating layer is 1-100 MPa.

[0016] The density of the metal heavy core is 6000-20000 kg / m 3 .

[0017] The number of the cells is at least 6.

[0018] The plurality of cells are not bonded by using a bonding material.

[0019] The material and size of the cells are uniform.

[0020] Advantages: Compared with the prior art, the present application has the following significant effects:

[0021] (1) The present application aims at the technical problem that the phonon crystal metamaterial is limited by the structure size and is difficult to form high-frequency band gap in limited size, and based on the local resonance mechanism, a metamaterial concrete beam structure capable of forming resonance band gap in the limited size of engineering structure is proposed, which attenuates the input wave whose wavelength and beam cell size are not in the same order of magnitude, thereby playing a role in vibration reduction in actual engineering application.(2) When the lattice size is much smaller than the wavelength, high-frequency band gap is generated by the self-vibration of the resonance unit (vibration absorber) composed of the heavy core and soft coating in the metamaterial concrete beam, and the metamaterial concrete beam structure of the present application provides a new idea for the vibration control of civil engineering structures. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 It is a three-dimensional model diagram of the metamaterial concrete beam structure composed of six beam cells and a model diagram of the metamaterial concrete beam cell.

[0023] Figure 2 It is a structural schematic diagram of the metamaterial concrete beam.

[0024] Figure 3 It is a band gap diagram of the metamaterial concrete beam cell and a diagram showing the influence of each structural parameter on the band gap of the metamaterial concrete beam cell.

[0025] Figure 4 It is a first to eighth order modal diagram of the metamaterial concrete beam.

[0026] Figure 5 It is a modal frequency diagram.

[0027] Figure 6 It is a deformation frequency response diagram of the metamaterial concrete beam under given boundary conditions.

[0028] Figure 7 It is a displacement response diagram of the solid concrete beam in the prior art and the metamaterial concrete beam of the present application corresponding to different time points under the action of impact load. DETAILED DESCRIPTION

[0029] The present application will be further described in detail below.

[0030] As Figures 1-3As shown, the present application provides a metamaterial concrete beam with local resonance properties, which is composed of a plurality of unit cells 1 arranged periodically; the unit cell 1 comprises a concrete pipe 2, a dynamic vibration absorber arranged radially in the concrete pipe 2; the dynamic vibration absorber comprises a metal heavy core 3, a soft coating 4 wrapped on the surface of the metal heavy core 3 and adhered to the inner wall of the concrete pipe 2; a plurality of unit cells 1 are spliced to form a metamaterial concrete beam through the two ends of the concrete pipe 2. The overall shape of the unit cell 1 of the embodiment is a cuboid, the concrete pipe 2 is a hollow cylinder arranged in the cuboid, and the dynamic vibration absorber is embedded in the hollow cylinder. The two ends of the hollow cylinders of the plurality of unit cells 1 are aligned to form a circular pipe.

[0031] The metal heavy core 3 of the embodiment is a cylinder, and the soft coating 4 is a torus cylinder wrapped outside the cylinder, and the outside of the soft coating 4 is tightly adhered to the inner wall of the circular pipe.

[0032] The main body of the unit cell 1 is a concrete material; the material of the soft coating 4 is at least one of polyurethane, nylon and silicone rubber; the material of the heavy core is steel or lead. The number of unit cells 1 is at least 6; the plurality of unit cells 1 are not bonded by using bonding materials; the material and size of the unit cells 1 are consistent.

[0033] The dynamic vibration absorber is an axisymmetric structure, and each dynamic vibration absorber is arranged at the center position of the unit cell 1.

[0034] The length of the cuboid unit cell 1 is l, the width is b, the height is a, and the radius of the circular hole is r1; the radius of the metal heavy core 3 is r2, and the height is h m ; the thickness of the soft coating 4 is D r =r1-r2, and the height is h r .

[0035] The height of the metal heavy core 3 is not less than the height of the soft coating 4, that is, h m ≥h r , and the distance between the center of the dynamic vibration absorber in the unit cell 1 at the two ends of the beam and the end of the beam is l / 2.

[0036] In order to better show the structure of the metamaterial concrete beam in the present application, the embodiment gives a metamaterial concrete beam composed of 6 beam unit cells 1, the three-dimensional model diagram is shown in Figure 1 (a), Figure 1 (b) is a three-dimensional model diagram of the beam unit cell 1, Figure 2 is a schematic diagram of the structure of the metamaterial concrete beam, and the corresponding structure size is shown in Figure 2 .

[0037] The beam cell 1 of the metamaterial concrete beam is composed of a concrete cuboid and a dynamic vibration absorber embedded in the interior of the cuboid. The interior of the cuboid is hollowed out into a cylinder, and the hollowed-out part is embedded into the dynamic vibration absorber composed of the metal heavy core 3 wrapped by the soft coating 4. However, the structural shape of the metamaterial concrete beam cell 1 of the present application is not limited to this, and the cell 1 main body can also be a cylinder or other geometric shapes, and the shape of the dynamic vibration absorber can also be various shapes, which can be embedded in the interior of the main body.

[0038] In the present embodiment, the material of the main body of the metamaterial concrete beam, i.e., the concrete pipeline 2, is C30 concrete, the vibration absorber selects polyurethane material as the soft coating 4 and lead as the metal heavy core 3, and the material parameters thereof include density p, young's modulus E and Poisson's ratio v. The three materials of concrete, polyurethane and lead are numbered as 1-3, and specifically, p1=2400 kg·m-3, E1=35000 MPa, v1=0.200; p2=900 kg·m-3, E2=42 MPa, v2=0.477, p3=11600 kg·m-3, E3=17000 MPa, v3=0.440. Considering the complexity of actual application, the person skilled in the art can select the structural material as needed, but needs to ensure that there is a certain order of magnitude difference between the elastic modulus of the soft coating 4 and the metal heavy core 3. -3 -3 -3

[0039] In the present embodiment, the length of the cuboid cell 1 is l=0.3 m, the width is b=0.2 m, the height is a=0.3 m, and the circular hole diameter is r1=0.07 m; the radius of the metal heavy core 3 is r2=0.05 m, the height is h m =0.07 m; the thickness of the soft coating 4 is D r =0.02 m, and the height is h r =0.03 m. The structural size of the metamaterial concrete beam in the present application is not limited to this, but the soft coating 4 is tried to ensure that it supports the metal heavy core 3, i.e., h m ≥h r , and the person skilled in the art can select as needed in combination with actual needs.

[0040] The vibration reduction principle of the metamaterial concrete beam in the present application is based on the local resonance mechanism. When excited at a frequency close to the natural frequency of the metamaterial concrete beam, the metal heavy core 3 wrapped by the soft coating 4 locally vibrates, and there is a phase difference between the motion of the concrete pipeline 2 and the metal heavy core 3. A band gap is generated within a certain frequency range, thereby attenuating the dynamic input of the frequency within the band gap and playing a role in vibration reduction.

[0041] ​​​The band gap diagram of cell element 1 of the metamaterial concrete beam was calculated using the finite element simulation software COMSOL Multiphysics. Based on the given structural dimensions and material parameters, the geometry was drawn sequentially, material parameters were set, Floquet periodic conditions were applied to the cross-sectional boundaries, the geometry was divided using a triangular mesh, and the sweep path was set according to Brillouin zone theory. The final calculation results are shown below. Figure 3 As shown in (a), the band gap ranges from 842.83 to 1132.4 Hz, and the band gap width is 289.57 Hz. The system's built-in size specifications can be used when dividing the triangular mesh into shapes.

[0042] Figure 3 Figures (b)-(d) show the effects of the width-to-thickness ratio, the elastic modulus of the soft coating, and the density of the metal core on the band gap width and upper and lower limits of the band gap frequency in metamaterial concrete beams, respectively. The width-to-thickness ratio is defined as the ratio of the radius r² of the metal core 3 to the thickness D of the soft coating 4. r The ratio is As can be seen from the figure, the band gap width and upper and lower limits of the band gap frequency of the metamaterial concrete beam are directly proportional to the width-to-thickness ratio and the elastic modulus of the soft coating 4; the band gap width of the metamaterial concrete beam is directly proportional to the density of the metal core 3, while the upper and lower limits of the band gap frequency are inversely proportional to the density of the metal core 3.

[0043] Figure 4 The diagram shows longitudinal cross-sectional views of the metamaterial concrete beam from modes one to eight. The natural frequencies corresponding to each mode are as follows: Figure 5 As shown, this embodiment only analyzes the first eight modes of the metamaterial concrete beam. From Figure 4 As can be seen from (c)-(h), the deformations corresponding to the third to eighth modes are concentrated in the local area of ​​the metamaterial concrete beam, that is, mainly on the vibration absorber, and the natural frequencies are close. This indicates that the generation of the band gap is due to the resonance of the local area within the structure. Consequently, the wave in the band gap frequency region will be confined within the metamaterial concrete beam structure and cannot propagate.

[0044] In the finite element simulation software ANSYS Workbench, one end of the metamaterial concrete beam is fixed, and the other end is subjected to an application of magnitude 1×10 along the y-axis and z-axis respectively. 7 The deformation frequency response diagram of the beam structure is calculated based on the force N, as shown below. Figure 6 As shown. The structural dimensions and material parameters are set according to the given values ​​above; the specific operating steps will not be repeated here. Figure 6 In the figure, (a)-(b) represent the real and imaginary parts of the deformation of the beam along the Y-axis, respectively. Figure 6 In the equation (c)-(d), the real and imaginary parts of the deformation of the beam along the Z-axis are respectively.

[0045] Combination Figure 4 (b) andFigure 6 As shown in (a), the frequency corresponding to the response amplitude of the bending deformation of the metamaterial concrete beam, i.e., the deformation along the Y-axis, is the natural frequency of the second-order mode, which is the resonance frequency of the bending deformation of the metamaterial concrete beam. Furthermore, the bending deformation of the metamaterial concrete beam has only one resonance peak. Beyond the second-order natural frequency, the bending deformation response of the beam continuously decreases. Therefore, those skilled in the art can design corresponding dynamic vibration absorbers for this natural frequency based on actual conditions to achieve vibration control of the bending deformation of the metamaterial concrete beam.

[0046] Combination Figure 4 (d)-(h) and Figure 6 (c) shows that the axial deformation of the metamaterial concrete beam, i.e., the frequency corresponding to the response amplitude of deformation along the Z-axis, is the natural frequency of the fourth to eighth modes. The structural deformation is mainly concentrated on the dynamic vibration absorbers, and the displacement response of the metamaterial concrete beam structure itself is at a low level. This indicates that the periodically arranged dynamic vibration absorbers suppress the vibration caused by the axial input wave, and there is only one resonance peak for the axial deformation of the metamaterial concrete beam. Vibration frequencies outside the resonance frequency range have little impact on the axial deformation of the beam. According to the local resonance mechanism, due to the phase difference between the motion of the concrete pipe 2 and the metal weight core 3, a band gap will be generated within a certain frequency range, thereby attenuating the dynamic input at frequencies within the band gap. That is, the vibration of the metal weight core 3 cancels out the large amplitude vibration of the metamaterial concrete beam, and the displacement response of the main body of the beam is very small at this time. This shows that the metamaterial concrete beam can suppress the axial deformation at specific frequencies, and due to the suppression effect of the vibration absorbers, the deformation of the main body of the metamaterial concrete beam hardly changes significantly with the increase of the vibration frequency for other frequency ranges of dynamic input, indicating that it has a good vibration control effect on axial deformation.

[0047] Figure 7 To analyze the structural displacement response diagrams of solid concrete beams in existing technologies and metamaterial concrete beams of this invention under impact loads in COMSOL Multiphysics transient studies, the following points are discussed: Figure 7 In Figures (a)-(e), the left side shows the displacement response of a solid concrete beam, and the right side shows the displacement response of a metamaterial concrete beam. The beam boundary conditions are set as follows: one end is fixed, and an impact load is applied to the other end. The calculation time is 2 seconds, with a step size of 0.05 seconds. Note: Geometric, material, and mesh generation procedures are not described in detail here. This embodiment only selects a few key time points for structural displacement response for comparative analysis; therefore, the displacement responses at all time points are not included. Figure 1 List them.

[0048] from Figure 7According to the calculation results, the maximum displacement response of the solid concrete beam end is 0.10379 m at 0.2 s, while the maximum displacement of the whole beam of the metamaterial concrete beam is 0.034558 m due to the buffering effect of the absorber, and the beam end displacement is even smaller. The solid concrete beam end displacement reaches the maximum value of 0.23834 m at 0.4 s, at which time the displacement of the main part of the metamaterial concrete beam is very small, and the deformation is mainly concentrated on the absorber near the left end of the beam. After the impact load ends until 0.6 s, the solid concrete beam rapidly vibrates in the opposite direction due to unloading, while the displacement response of the main part of the metamaterial concrete beam remains at a low level, and the deformation of the absorber increases. At 1.4 s, the maximum deformation of the solid concrete beam shifts to the other end of the beam, but the displacement response gradually decreases, while the local deformation of the metamaterial concrete beam continues to increase. At 1.8 s, the deformation response of the solid concrete beam continues to shift and attenuate towards the midspan, and the local deformation response of the metamaterial concrete beam reaches the maximum value of 0.17856 m, and the displacement of the main part basically remains stable. Through analysis, it can be concluded that after being subjected to impact load for a short time, the displacement response of the main part of the beam will not change much due to the buffering effect of the periodically arranged dynamic absorber on the metamaterial concrete beam, and the maximum value is much smaller than that of the solid concrete beam. However, after the impact load ends, the deformation response of the absorber will continue to increase due to hysteresis, then slowly decay to a stable state, so the robustness and durability of the absorber need to be considered in practical applications.

Claims

1. A metamaterial concrete beam having a local resonance property, characterized by, A plurality of cells (1) are periodically arranged; the cell (1) comprises a concrete pipe (2), a dynamic vibration absorber arranged in the concrete pipe (2) in a radial direction of the concrete pipe (2); the dynamic vibration absorber comprises a metal heavy core (3) and a soft coating (4) wrapped on the surface of the metal heavy core (3) and adhered to the inner wall of the concrete pipe (2); a plurality of cells (1) are spliced to form a metamaterial concrete beam through the two ends of the concrete pipe (2); The cell (1) has a cuboid shape, the concrete pipe (2) is a hollow cylinder arranged in the cuboid, and the dynamic vibration absorber is embedded in the hollow cylinder; the two ends of the hollow cylinders of a plurality of cells (1) are arranged in alignment to form a circular pipe; the metal heavy core (3) is a cylinder, and the soft coating (4) is a torus cylinder wrapped on the outside of the cylinder, and the outside of the soft coating (4) is tightly adhered to the inner wall of the circular pipe.

2. The metamaterial concrete beam with locally resonant properties of claim 1, wherein, The cuboid cell (1) has a length of l, a width of b, a height of a, and a circular hole with a radius of r 1; a metal heavy core (3) with a radius of r 2, and a height of h m ; a soft coating (4) with a thickness of D r = r 1- r 2, and a height of h r .

3. The metamaterial concrete beam with locally resonant properties of claim 2, wherein, The height of the metal core (3) is not less than the height of the soft coating (4), that is h m ≥ h r The distance between the center of the dynamic vibration absorber in the beam end cell (1) and the beam end is l / 2.

4. The metamaterial concrete beam with locally resonant properties of claim 2, wherein, The metal core (3) radius r 2 to the soft coating thickness D r is 1-4.

5. The metamaterial concrete beam with locally resonant properties of claim 1, wherein, The elastic modulus of the soft coating (4) is 1-100 MPa.

6. The metamaterial concrete beam with locally resonant properties of claim 1, wherein, The metal core (3) has a density of 6000-20000 kg / m 3 .

7. The metamaterial concrete beam with locally resonant properties of claim 1, wherein, The main body of the cell (1) is a concrete material; the material of the soft coating (4) is at least one of polyurethane, nylon and silicone rubber; and the material of the metal heavy core (3) is steel or lead.

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