Metamaterial concrete beam with local resonance property

Abstract

The invention discloses a metamaterial concrete beam with a local resonance property. The metamaterial concrete beam is formed by periodically arranging a plurality of cell elements, each cell element comprises a concrete pipeline and a dynamic vibration absorber arranged in the concrete pipeline in the radial direction of the concrete pipeline. The dynamic vibration absorber comprises a metal heavy core and a soft coating which wraps the surface of the metal heavy core and is attached to the inner wall of the concrete pipeline. The multiple cell elements are spliced through the two ends of the concrete pipeline. The metamaterial concrete beam structure capable of forming a resonance band gap in an engineering structure with a limited size is designed on the basis of a local resonance mechanism in order to solve the problem that a photonic crystal metamaterial is limited by the structure size and cannot form a high-frequency band gap in the limited size easily. And the input wave of which the wavelength and the size of the beam cell element are not in the same order of magnitude is attenuated, so that a damping effect is achieved in actual engineering application.

Description

Technical Field

[0001] The invention relates to a concrete beam, in particular to a metamaterial concrete beam with local resonance properties. Background Art

[0002] In recent years, metamaterials, as an artificial composite structural material that uses its own band gap (frequency range that can attenuate or block the movement of waves) to control vibration, have been widely used in the fields of electromagnetism and acoustics. Existing metamaterial structures are generally constructed of periodically arranged artificial elastic media, and most of them are phononic crystal metamaterials that form band gaps based on the Bragg scattering mechanism. The Bragg band gap refers to the formation of a band gap when waves propagate in a periodic structure due to the coherent superposition (destructive interference) of scattered waves, which prevents waves of a specific frequency from propagating.

[0003] However, it is difficult to form a periodic spatial dimension of the same order of magnitude as the input wave wavelength in civil engineering, so it is difficult to use the Bragg band gap to attenuate the vibration of the building structure. Different from 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 cell. Therefore, metamaterials with local resonance properties can form a resonant band gap in an engineering structure of limited size, and attenuate input waves whose wavelength is not of the same order of magnitude as the cell size.

[0004] Based on the existing working mechanism of local resonance, it is very meaningful to develop more types of concrete metamaterial structures, conduct systematic research on their vibration attenuation performance, and then apply them to engineering practice. Summary of the invention

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

[0006] Technical solution: The metamaterial concrete beam with local resonance properties described in the present invention is composed of a plurality of cells arranged periodically; the cells include a concrete pipe and a dynamic vibration absorber arranged in the concrete pipe along the radial direction of the concrete pipe; the dynamic vibration absorber includes a metal weight core and a soft coating wrapped on the surface of the metal weight core and bonded to the inner wall of the concrete pipe; a plurality of cells are spliced ​​at both ends of the concrete pipe to form a metamaterial concrete beam.

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

[0008] Among them, the hollow cylinders of multiple cells are aligned at both ends to form a circular pipe.

[0009] The metal weight core is a cylinder, the soft coating is a circular ring column wrapped around the outside of the cylinder, and the outside of the soft coating is tightly fitted with the inner wall of the circular pipe.

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

[0011] Wherein, the dynamic vibration absorber is an axisymmetric structure, and each dynamic vibration absorber is placed at the center of the cell.

[0012] The length of the rectangular cell is l, the width is b, the height is a, and the radius of the circular hole is r1; the radius of the metal core is r2, and the height is h m ; Soft coating thickness D r =r1-r2, height is h r .

[0013] Among them, the height of the metal core is not less than the height of the soft coating, that is, h m ≥h r The distance between the center of the dynamic vibration absorber in the cells at both ends of the beam and the end of the beam is l / 2.

[0014] Wherein, the radius of the metal core r2 and the thickness of the soft coating D r The ratio is 1-4.

[0015] Wherein, the elastic modulus of the soft coating is 1-100 MPa.

[0016] Wherein, the density of the metal weight core is 6000-20000kg / m 3 .

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

[0018] Wherein, no adhesive material is used to bond the multiple cells.

[0019] The materials and sizes of the cells are consistent.

[0020] Beneficial effects: Compared with the prior art, the present invention achieves the following significant effects:

[0021] (1) The present invention aims to solve the technical problem that phononic crystal metamaterials are limited by the size of the structure and it is difficult to form a high-frequency band gap within a limited size. Based on the local resonance mechanism, a metamaterial concrete beam structure is proposed that can form a resonant band gap within an engineering structure of limited size, and attenuate input waves whose wavelengths are not in the same order of magnitude as the beam cell size, thereby playing a vibration reduction role in practical engineering applications. (2) When the lattice size is much smaller than the wavelength, the high-frequency band gap is generated by the self-vibration of the resonant unit (vibration absorber) composed of the internal weight core and soft coating of the metamaterial concrete beam. The metamaterial concrete beam structure of the present invention provides a new idea for vibration reduction control of civil engineering structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 A three-dimensional model diagram of a metamaterial concrete beam structure composed of six beam cells and a model diagram of a metamaterial concrete beam cell;

[0023] Figure 2 This is a schematic diagram of the structure of a metamaterial concrete beam;

[0024] Figure 3 The band gap diagram of the metamaterial concrete beam cell and the influence of various structural parameters on the band gap of the metamaterial concrete beam cell;

[0025] Figure 4 The first to eighth order modal diagrams of the metamaterial concrete beam;

[0026] Figure 5 is the modal frequency diagram;

[0027] Figure 6 The deformation frequency response diagram of the metamaterial concrete beam under given boundary conditions;

[0028] Figure 7 The displacement response diagrams of the solid concrete beam in the prior art and the metamaterial concrete beam of the present invention at different time points under impact load. DETAILED DESCRIPTION

[0029] The present invention is described in further detail below.

[0030] like Figure 1-3As shown, the present invention provides a metamaterial concrete beam with local resonance properties, which is composed of a plurality of cells 1 arranged periodically; the cell 1 includes a concrete pipe 2, and a dynamic vibration absorber arranged in the concrete pipe 2 along the radial direction of the concrete pipe 2; the dynamic vibration absorber includes a metal weight core 3, and a soft coating 4 wrapped on the surface of the metal weight core 3 and attached to the inner wall of the concrete pipe 2; a plurality of cells 1 are spliced ​​at both ends of the concrete pipe 2 to form a metamaterial concrete beam. The overall shape of the cell 1 of this embodiment is a rectangular parallelepiped, the concrete pipe 2 is a hollow cylinder arranged in the rectangular parallelepiped, and the dynamic vibration absorber is embedded in the hollow cylinder. The two ends of the hollow cylinders of the plurality of cells 1 are aligned and arranged to form a circular pipe.

[0031] The metal weight core 3 of this embodiment is a cylinder, and the soft coating 4 is a circular ring column wrapped around the outside of the cylinder. The outside of the soft coating 4 is tightly fitted with the inner wall of the circular pipe.

[0032] The main body of the cell 1 is made of concrete; the material of the soft coating 4 is at least one of polyurethane, nylon, and silicone rubber; the material of the weight core is steel or lead. The number of cells 1 is at least 6; no adhesive material is used to bond the multiple cells 1; the material and size of the cells 1 are consistent.

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

[0034] The length of the rectangular 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 core 3 is r2, and the height is h m ; Soft coating 4 thickness D r =r1-r2, height is h r .

[0035] 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 cell 1 at both ends of the beam and the end of the beam is l / 2.

[0036] In order to better demonstrate the metamaterial concrete beam structure in the present invention, a metamaterial concrete beam composed of six beam cells 1 is provided in this embodiment, and the three-dimensional model is shown in FIG. Figure 1 As shown in (a), Figure 1 (b) is the three-dimensional model diagram of beam cell 1. Figure 2 is a schematic diagram of the metamaterial concrete beam structure. Figure 2 The corresponding structural dimensions are shown in .

[0037] The beam cell 1 constituting the metamaterial concrete beam is composed of a concrete cuboid and a dynamic vibration absorber embedded in the cuboid. The interior of the cuboid is hollowed out as a cylinder, and the hollowed-out part is embedded with a dynamic vibration absorber consisting of a metal weight core 3 wrapped with a soft coating 4, but the structural shape of the metamaterial concrete beam cell 1 of the present invention is not limited thereto, the cell 1 body can also be a cylinder or other geometric shapes, and the shape of the dynamic vibration absorber can also be various other shapes, which can be embedded in the body.

[0038] In this embodiment, the material of the main part of the metamaterial concrete beam, i.e., the concrete pipe 2, is C30 concrete, and the vibration absorber is made of polyurethane material as the soft coating 4 and lead as the metal weight core 3. The material parameters include density ρ, Young's modulus E, and Poisson's ratio v. The three materials of concrete, polyurethane, and lead are numbered 1-3, specifically ρ1=2400kg·m -3 , E1=35000MPa, v1=0.200; ρ2=900kg·m -3 , E2=42MPa, v2=0.477, ρ3=11600kg·m -3 , E3 = 17000 MPa, v3 = 0.440. Considering the complexity of actual application, those skilled in the art can select structural materials according to their needs, but it is necessary to ensure that there is a certain order of magnitude difference between the elastic modulus of the soft coating 4 and the metal weight core 3 .

[0039] In this embodiment, the length of the rectangular cell 1 is l = 0.3m, the width is b = 0.2m, the height is a = 0.3m, and the circular aperture is r1 = 0.07m; the radius of the metal core 3 is r2 = 0.05m, and the height is h m =0.07m; the thickness of soft coating 4 is D r = 0.02m, height is h r =0.03m. The structural dimensions of the metamaterial concrete beam in the present invention are not limited to this, but the soft coating 4 is guaranteed to support the metal weight core 3, i.e., h m ≥h r , personnel in this technical field can select according to actual needs.

[0040] The vibration reduction principle of the metamaterial concrete beam in the present invention is based on the local resonance mechanism. When excited by a frequency close to the natural frequency of the metamaterial concrete beam, the metal weight core 3 wrapped by the soft coating 4 vibrates locally. There is a phase difference between the movement of the concrete pipe 2 and the metal weight core 3, and a band gap is generated within a certain frequency range, thereby attenuating the power input of the frequency within the band gap and playing a vibration reduction role.

[0041] The band gap diagram of metamaterial concrete beam cell 1 is calculated by finite element simulation software COMSOL Multiphysics. According to the given structural dimensions and material parameters, geometric figures are drawn in sequence, material parameters are set, Floquet periodicity conditions are set for the cross-section boundary, the figures are divided by triangular meshes, and the sweep path is set according to the Brillouin zone theory. Finally, the calculation results are as follows: Figure 3 As shown in (a), the band gap range is 842.83~1132.4Hz, and the band gap width is 289.57Hz. When dividing the figure into triangular meshes, the size specifications provided by the system can be used.

[0042] Figure 3 (b)-(d) show the influence 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 the upper and lower limits of the band gap frequency of the metamaterial concrete beam. 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 of It can be seen from the figure that the band gap width and the upper and lower limits of the band gap frequency of the metamaterial concrete beam are 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 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 is the longitudinal cross-section diagram of the first to eighth order modes of the metamaterial concrete beam. The natural frequencies corresponding to each order mode are as follows: Figure 5 As shown in FIG. 1 , only the first eight modes of the metamaterial concrete beam are analyzed in this embodiment. Figure 4 From (c)-(h) in the figure, it can be seen that the deformations corresponding to the third to eighth order 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, indicating that the band gap is caused by the resonance of the local area within the structure, and the waves in the band gap frequency area will be confined in 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 a 1×10 7 N force, the deformation frequency response diagram of the beam structure is calculated as follows Figure 6 Among them, the structural dimensions and material parameters are set according to the above given values, and the specific operation steps are not repeated here. Figure 6 (a)-(b) are the real and imaginary parts of the deformation of the beam along the Y-axis, respectively. Figure 6 (c)-(d) are the real and imaginary parts of the deformation of the beam along the Z-axis.

[0045] Combination Figure 4 (b) and Figure 6 In (a), it can be seen that the frequency corresponding to the response amplitude of the bending deformation of the metamaterial concrete beam, that is, the deformation along the Y-axis direction, is the natural frequency of the second-order mode, that is, this order natural frequency is the resonance frequency of the bending deformation of the metamaterial concrete beam. And there is only one resonance peak of the bending deformation of the metamaterial concrete beam. After the second-order natural frequency, the bending deformation response of the beam continues to decrease. Therefore, according to the actual situation, the technical personnel in this field can design the corresponding dynamic vibration absorber for this order natural frequency to achieve vibration control of the bending deformation of the metamaterial concrete beam.

[0046] Combination Figure 4 (d)-(h) and Figure 6 In (c), it can be seen that the axial deformation of the metamaterial concrete beam, that is, the response amplitude of the deformation along the Z-axis direction corresponds to the natural frequency of the fourth to eighth order modes. The structural deformation is mainly concentrated on the dynamic vibration absorber. The displacement response of the metamaterial concrete beam structure itself is at a low level, indicating that the periodically arranged dynamic vibration absorber has a suppressive effect on the vibration caused by the axial input wave, and there is only one resonance peak of the axial deformation of the metamaterial concrete beam. The vibration frequency outside the resonance frequency range has little effect on the axial deformation of the beam. According to the local resonance mechanism, due to the phase difference between the movement 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 power input of the frequency within the band gap, that is, the vibration of the metal weight core 3 offsets the huge vibration of the metamaterial concrete beam, and the displacement response of the main part of the beam is very small. It shows that the metamaterial concrete beam can suppress the axial deformation of a specific frequency, and the power input in other frequency ranges has almost no obvious change due to the suppressive effect of the vibration absorber. The main deformation of the metamaterial concrete beam has a good vibration control effect on the axial deformation.

[0047] Figure 7 In order to analyze the structural displacement response diagram of the solid concrete beam in the prior art and the metamaterial concrete beam of the present invention under the impact load in the COMSOL Multiphysics transient study, Figure 7 The left figure in (a)-(e) is the displacement response diagram of the solid concrete beam, and the right figure is the displacement response diagram of the metamaterial concrete beam. The boundary condition of the beam is set to be fixed at one end and an impact load is applied at the other end. The calculation time is 2s, and the step size is 0.05s. Note: The geometry, material, meshing and other operation steps are not introduced in detail. In this embodiment, only the structural displacement response at several key time points is selected for comparative analysis, so the displacement response at all time points is not analyzed. Figure 1 A list.

[0048] from Figure 7Combined with the calculation results, it can be seen that the maximum displacement response of the solid concrete beam end is 0.10379m at 0.2s, while the maximum displacement of the metamaterial concrete beam is 0.034558m due to the buffering effect of the vibration absorber, and the displacement of the beam end is smaller; at 0.4s, the displacement of the solid concrete beam end reaches a maximum value of 0.23834m, at this time, the displacement of the main part of the metamaterial concrete beam is very small, and the deformation is mainly concentrated on the vibration absorber near the left end of the beam; from the end of the impact load to 0.6s, the solid concrete beam vibrates rapidly 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 vibration absorber increases; at 1.4s, the maximum deformation of the solid concrete beam transfers 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 1.8s, the deformation response of the solid concrete beam continues to transfer to the mid-span and decays, the local deformation response of the metamaterial concrete beam reaches a maximum value of 0.17856m, and the displacement of the main part remains basically stable. Through analysis, it can be concluded that after being subjected to impact load in a short period of time, due to the buffering effect of the periodically arranged dynamic vibration absorbers on the metamaterial concrete beam, the displacement response of the main part of the beam will not change much, 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 vibration absorber will continue to increase to a stable state due to hysteresis and then slowly decay. Therefore, personnel in this technical field need to consider the robustness and durability of the vibration absorber during actual application.

Claims

1. A metamaterial concrete beam with local resonance properties, characterized in that: The invention is composed of a plurality of cells (1) arranged periodically; the cell (1) comprises a concrete pipe (2) and a dynamic vibration absorber arranged in the concrete pipe (2) along the radial direction of the concrete pipe (2); the dynamic vibration absorber comprises a metal weight core (3) and a soft coating (4) wrapped on the surface of the metal weight core (3) and in contact with the inner wall of the concrete pipe (2); the plurality of cells (1) are spliced ​​at both ends of the concrete pipe (2) to form a metamaterial concrete beam.

2. The metamaterial concrete beam with local resonance properties according to claim 1, characterized in that: The overall shape of the cell (1) is a rectangular parallelepiped, the concrete pipe (2) is a hollow cylinder arranged in the rectangular parallelepiped, and the dynamic vibration absorber is embedded in the hollow cylinder.

3. The metamaterial concrete beam with local resonance properties according to claim 1, characterized in that: The hollow cylinders of a plurality of cells (1) are aligned at both ends to form a circular pipe.

4. The metamaterial concrete beam with local resonance properties according to claim 1, characterized in that: The metal weight core (3) is a cylinder, the soft coating (4) is a circular ring column wrapped around the outside of the cylinder, and the outside of the soft coating (4) is tightly fitted to the inner wall of the circular pipe.

5. The metamaterial concrete beam with local resonance properties according to claim 2, characterized in that: The cuboid cell (1) has a length of l, a width of b, a height of a, and a circular hole radius of r1; the metal core (3) has a radius of r2 and a height of h. m ; Soft coating (4) thickness D r =r1-r2, height is h r .

6. The metamaterial concrete beam with local resonance properties according to claim 1, characterized in that: The height of the metal weight core (3) is not less than the height of the soft coating (4), i.e., h m ≥h r The distance between the center of the dynamic vibration absorber in the cell (1) at both ends of the beam and the end of the beam is l / 2.

7. The metamaterial concrete beam with local resonance properties according to claim 1, characterized in that: The radius r2 of the metal core (3) and the thickness D of the soft coating r The ratio is 1-4.

8. The metamaterial concrete beam with local resonance properties according to claim 1, characterized in that: The elastic modulus of the soft coating (4) is 1-100 MPa.

9. The metamaterial concrete beam with local resonance properties according to claim 1, characterized in that: The density of the metal weight core (3) is 6000-20000 kg / m 3 .

10. The metamaterial concrete beam with local resonance properties according to claim 1, characterized in that: The main body of the cell (1) is made of concrete; the material of the soft coating (4) is at least one of polyurethane, nylon, and silicone rubber; and the material of the metal weight core (3) is steel or lead.

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