Precast concrete local resonance periodic vibration reduction wall and construction method

Abstract

The invention discloses a prefabricated concrete local resonance periodic vibration reduction wall and a construction method. The prefabricated concrete local resonance periodic vibration reduction wall comprises a first leaf wallboard assembly, a local resonance unit array layer and a second leaf wallboard assembly. The local resonance unit array layer is arranged between the first leaf wallboard assembly and the second leaf wallboard assembly, and the local resonance unit array layer, the first leaf wallboard assembly and the second leaf wallboard assembly are integrally poured to form the prefabricated wall. According to the scheme, a sandwich wall structure containing the local resonance unit array layer is designed, and rail transit vibration is controlled and attenuated through the elastic wave band gap filtering effect of a local resonance unit array and the damping synergistic vibration attenuation effect of rubber concrete.

Description

Technical Field

[0001] The invention relates to the technical field of building engineering, and in particular to a precast concrete local resonance periodic vibration reduction wall and a construction method. Background Art

[0002] Urban rail transit plays an important role in alleviating urban traffic congestion due to its large carrying capacity, high efficiency, safety and reliability.

[0003] At the same time, the vibration problem generated during subway operation is becoming more and more serious. Among them, the vibration problem caused by urban transportation has been listed as one of the seven major environmental hazards in the world. The vibration generated by rail transit operation propagates outward in the form of longitudinal waves, transverse waves and surface waves, and is transmitted along the track to fasteners, sleepers, roadbeds, linings and soil. Due to the filtering effect of the soil, the high-frequency waves decay rapidly with the increase of distance, while the low-frequency part continues to propagate due to the slow decay and has strong penetration ability, which will cause vibration of underground and ground buildings near the subway. Since the main frequency of vibration of urban rail transit is generally 40-80Hz, it is highly overlapped with the natural frequency of the main organs of the human body (1-80Hz), which is very easy to resonate and cause great harm to human health. Since urban rail transit generally operates for more than 20 hours a day and is open all year round, the vibration it generates is characterized by low frequency, repetitiveness, universality and long-term nature, which will not only cause fatigue damage to building structures, but also seriously affect the normal life and health of residents.

[0004] At present, the vibration control methods of rail transit are mainly divided into three categories, namely active vibration elimination at the vibration source, vibration reduction in the propagation path, and passive vibration isolation of the vibrated object. Among them, the vibration intensity control at the vibration source mainly relies on track grinding and vehicle characteristics improvement. Track grinding needs to be carried out regularly and maintained in time; while vehicle characteristics improvement involves technical upgrades such as vehicle lightweighting and bogie improvement, and the current technical improvement space is limited. In some special vibration reduction with high vibration reduction requirements, energy-consuming devices can be arranged, but they have problems such as poor structural integrity and difficulty in replacing vibration reduction devices, and the cost is high. Wave barriers are artificial vibration isolation barriers set on the propagation path of elastic waves. They use the reflection, refraction and diffraction of elastic waves to attenuate and isolate the propagation of elastic waves. They have the characteristics of diverse structures, flexible designs and controllable effects. However, there are generally many high-rise buildings around urban subway lines, the underground space is fully utilized, and the pipelines are complicated, which has caused certain difficulties for the construction of wave barriers.

[0005] Prefabricated structures are a common form of construction for modern residential buildings, which have the advantages of fast construction speed, controlled quality, environmental protection and energy saving. However, although traditional building walls have high strength, rigidity and durability, they generally do not consider vibration reduction design. Therefore, the subway cover structure and the normal life of residents along the line are easily affected by subway vibration.

[0006] Therefore, a precast concrete local resonance periodic vibration-damping wall is developed, which can not only meet the needs of efficient residential construction, but also greatly reduce the harm of rail transit vibration to human health and structural safety with a relatively small initial investment. Summary of the invention

[0007] In view of the technical problems existing in the prior art, the purpose of the present invention is to provide a precast concrete local resonance periodic vibration damping wall, which can dissipate the low-frequency vibration energy generated by rail transit on the basis of meeting the strength and construction requirements, reduce the negative impact of vibration propagation on the human body and building structures, and can achieve efficient installation, construction and application. On this basis, a construction method of the precast concrete local resonance periodic vibration damping wall is also provided, which effectively overcomes the problems existing in the prior art.

[0008] In order to achieve the above-mentioned objectives, the present invention provides a precast concrete local resonance periodic vibration reduction wall, comprising a first leaf wall panel assembly, a local resonance unit array layer and a second leaf wall panel assembly, wherein the local resonance unit array layer is arranged between the first leaf wall panel assembly and the second leaf wall panel assembly and is integrally cast with the first leaf wall panel assembly and the second leaf wall panel assembly to form a precast wall.

[0009] Furthermore, the local resonance unit array layer includes a mounting plate and a local resonance component, and the local resonance component is embedded in the mounting plate.

[0010] Furthermore, the end surface of the mounting plate is provided with a plurality of independent mounting grooves, which are distributed on the end surface of the mounting plate in a matrix form, and the size of the mounting grooves is the same as that of the local resonance component.

[0011] Furthermore, the local resonance component is composed of a plurality of local resonance parts, which are respectively composed of a steel scatterer, a rubber wrapping layer, and a concrete base. The concrete base is provided with a mounting groove. After the rubber wrapping layer is wrapped on the steel scatterer, it is embedded in the mounting groove of the concrete base to form an integrated structure and is installed in the corresponding mounting groove on the mounting plate.

[0012] Furthermore, the first leaf wall panel assembly includes a first leaf wall panel, a first steel mesh and tie steel bars, and the first leaf wall panel, the first steel mesh and the tie steel bars are stacked in sequence.

[0013] Furthermore, the second leaf wall panel assembly includes a second leaf wall panel, a second steel mesh, and the second steel mesh and the second leaf wall panel are arranged in coordination.

[0014] In order to achieve the above object, the present invention provides a construction method of a precast concrete local resonance periodic vibration reduction wall, the construction method comprising the following steps:

[0015] Step 1: First, determine the design objectives based on the main frequency of rail transit environmental vibration and the target vibration reduction level requirements, including the main frequency of vibration and the expected vibration reduction effect;

[0016] Step 2: Select appropriate material parameters and structural parameters of the local resonance unit to construct the local resonance vibration reduction unit;

[0017] Step 3: Perform a dispersion analysis on the local resonance unit to obtain the band structure and determine the band gap range;

[0018] Step 4: Determine whether the band gap can cover the target vibration frequency. If the band gap can cover the target vibration frequency, proceed to the next step of design. If the band gap interval does not match the target frequency, modify the material parameters and structural parameters of the local resonance unit until the band gap meets the target frequency.

[0019] Step 5: Determine the arrangement of the local resonance unit, including the vibrator arrangement spacing, the number of arrangement rows, the number of arrangement, etc., and use theoretical methods such as spectral unit method or finite element method to calculate the transfer function;

[0020] Step 6: Determine whether the vibration reduction effect meets the requirements. If the vibration reduction effect does not meet the expectations, adjust the layout and number of local resonance units until the transfer function meets the design expectations, and the final design is obtained.

[0021] Furthermore, the analysis method in step 3 may adopt theoretical calculation using a plane wave expansion method or finite element simulation calculation.

[0022] Furthermore, according to the local resonance vibration reduction unit determined in steps 1-6, the vibration reduction wall is prefabricated in the factory and then hoisted and installed on site after maintenance is completed.

[0023] The present invention provides a precast concrete local resonance periodic vibration reduction wall and a construction method, which designs a sandwich wall structure containing a local resonance unit array layer, and realizes the control and attenuation of rail transit vibration through the elastic wave band gap filtering effect of the local resonance unit array and the damping synergistic vibration reduction effect of rubber concrete. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0025] Figure 1 This is a schematic diagram of the overall structure of the precast concrete local resonance periodic vibration reduction wall;

[0026] Figure 2 This is the overall structural explosion diagram of the precast concrete local resonance periodic vibration reduction wall;

[0027] Figure 3This is a structural diagram of the local resonance component in the precast concrete local resonance periodic vibration reduction wall;

[0028] Figure 4 It is a schematic diagram of the principle of the local resonance component in the wall panel of the present invention;

[0029] Figure 5 It is a structural schematic diagram of the irreducible Brillouin zone in the wallboard of the present invention;

[0030] Figure 6 Schematic diagram of the energy band structure in the wallboard of the present invention;

[0031] Figure 7 It is a structural schematic diagram of a vibrating mold platform in a wall panel of the present invention;

[0032] Figure 8 This is the assembly diagram of the precast concrete local resonance periodic vibration reduction wall;

[0033] Fig. 9 This is a schematic diagram of the process of the construction method of the precast concrete local resonance periodic vibration reduction wall;

[0034] Fig.10 This is a schematic diagram of the process of calculating the band structure using the finite element method in this scheme;

[0035] Fig.11 This is a schematic diagram of the process of calculating the transfer function using the spectral unit method in this scheme;

[0036] Fig.12 Schematic diagram of the spectral unit node numbering of the local resonant Euler beam. DETAILED DESCRIPTION

[0037] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the present invention is further described below with reference to specific diagrams.

[0038] In view of the technical problems existing in the prior art, the present invention provides a precast concrete local resonance periodic vibration reduction wall, see Figure 1 It includes a first leaf wall panel assembly 100, a local resonance unit array layer 200 and a second leaf wall panel assembly 300. The first leaf wall panel assembly 100, the local resonance unit array layer 200 and the second leaf wall panel assembly 300 are stacked in sequence and cast as a whole to form a prefabricated wall. The wall can meet the strength requirements of the wall panel, and through the elastic wave band gap filtering effect of the local resonance unit array layer and the damping synergistic vibration reduction effect of the rubber concrete, the vibration of rail transit can be controlled and attenuated.

[0039] See also Figure 2The first leaf wall panel assembly 100 includes a first leaf wall panel 110, a first steel mesh sheet 120 and a tie steel bar 130. The first leaf wall panel 110, the first steel mesh sheet 120 and the tie steel bar 130 are stacked in sequence.

[0040] The first steel mesh in the present embodiment is preferably a steel mesh in which longitudinal steel bars and transverse steel bars are arranged at a certain interval and the intersections are tied together.

[0041] The tie steel bars are truss steel bars, which are formed by resistance welding of an upper chord steel bar, two lower chord steel bars and web bars on both sides into a steel bar welded skeleton with an inverted "V" shaped cross section.

[0042] The first steel mesh is inserted inside the truss reinforcement and tied to the truss reinforcement. After the reinforcement arrangement is completed, concrete is poured to form a tie structure to ensure the overall stress of the concrete wall panel.

[0043] The second leaf wall panel assembly 300 includes a second leaf wall panel 310 and a second steel mesh sheet 320 . The second steel mesh sheet 320 and the second leaf wall panel 310 are arranged in coordination.

[0044] The second steel mesh is the skeleton of the second leaf wall panel 310, and is arranged in cooperation with the second leaf wall panel 310 to ensure the integrity and coordinated force of the concrete. The second steel mesh has the same structure as the first steel mesh, and will not be described in detail here.

[0045] The local resonance unit array layer 200 is arranged between the tie steel bars 130 and the second steel mesh 320, and is coordinated with the first leaf wall panel assembly 100 and the second leaf wall panel assembly 300. The local resonance unit array layer 200 includes a mounting plate 210 and a local resonance assembly 220. The local resonance assembly 220 is embedded in the mounting plate 210. The control and attenuation of rail transit vibration are achieved through the elastic wave band gap filtering effect of the local resonance unit array layer 200 and the damping synergistic vibration reduction effect of the rubber concrete.

[0046] The mounting plate 210 is a mounting body for the local resonance component 220 , and a plurality of independent mounting grooves 211 are provided on its end surface. The plurality of mounting grooves 211 are distributed in a matrix form on the end surface of the mounting plate 210 . The size of the mounting groove 211 is the same as that of the local resonance component 220 , so that the local resonance component 220 can be embedded in the mounting groove 211 .

[0047] The local resonance component 220 is composed of a plurality of Figure 3 The local resonance components are composed of the local resonance components, and the local resonance components are arranged corresponding to the plurality of mounting grooves 211 on the mounting plate 210, see Figure 3 The local resonance components are respectively composed of a steel scatterer 223, a rubber wrapping layer 222, and a concrete matrix 221.

[0048] The size of the concrete base 221 matches the mounting groove 211 on the mounting plate 210, and the concrete base 221 can be embedded in the mounting groove 211. At the same time, the concrete base 221 is also provided with a mounting groove 2211. The rubber wrapping layer 1222 is wrapped on the steel scatterer 1221 and then embedded in the mounting groove of the concrete base 1223 to form an integrated structure. Several local resonance components composed of the steel scatterer 1221, the rubber wrapping layer 1222, and the concrete base 1223 are respectively embedded in the corresponding mounting grooves 1211 on the mounting plate 121, and form a local resonance component 122 with the mounting plate 121, which can form an elastic wave band gap within a certain frequency range. The vibration wave of the target frequency passes through the local resonance unit array, generates energy localization phenomenon and is dissipated, thereby achieving a band gap filtering and vibration reduction effect.

[0049] For details, see Figure 4-Figure 5 According to the phononic crystal theory, periodically arranged local resonance units can produce local resonance band gaps. The figure is a schematic diagram of the local resonance unit and the corresponding irreducible Brillouin zone. By traversing the wave vector along the irreducible Brillouin zone, we can get the following: Figure 6 The band structure of the band structure, the horizontal axis is the wave vector, and the vertical axis is the frequency. The colored shaded area has no band curve passing through, which is the local resonance band gap.

[0050] Extract the vibration modes of the band gap starting point A and the band gap cutoff point B from the energy band curve, such as Figure 7 As shown, the color indicates the relative size of the amplitude, and the arrow indicates the direction of vibration. At the starting frequency of the band gap, the displacement amplitude of the steel scatterer 223 is dominant, while the concrete matrix 221 is almost stationary. The translational vibration of the steel scatterer 223 produces a resultant force and strongly couples with the long-wave traveling waves in the concrete matrix 221, opening the local resonance band gap. At the cutoff frequency, the distribution characteristics of the displacement vector field show that the steel scatterer 223 and the concrete matrix 221 show significant relative motion, while the concrete matrix 221 maintains a relatively large displacement amplitude. Compared with the starting frequency, the movement of the steel scatterer 223 and the concrete matrix 221 is in opposite directions, and the two show opposite motion. The coupling between the steel scatterer 223 and the concrete matrix 221 is weakened, resulting in the closure of the local resonance band gap.

[0051] Therefore, during the entire vibration process, when the excitation frequency is in the band gap range and the elastic wave passes through the local resonance structure, the incident wave is reflected and scattered after propagating to the steel scatterer 223, triggering the local resonance of the steel scatterer 223, and a part of the wave is transmitted back to the rubber wrapping layer 222 to be reflected and scattered again. This process is repeated many times, so that the energy is confined in each resonance unit and continuously converted between kinetic energy and strain energy, resulting in energy superposition in the rubber wrapping layer 222, forming an energy barrier to prevent the elastic wave from continuing to propagate, resulting in the generation of a local resonance band gap, thereby achieving the attenuation of the elastic wave.

[0052] Secondly, several local resonance components in this scheme are preferably distributed in an array because the application of irreducible Brillouin zone and band structure analysis methods must be based on the fact that a single unit cell can characterize the entire local resonance structure. According to the Bragg theorem, only a periodic structure with a specific arrangement can use the analysis results of a single unit cell to characterize the vibration reduction characteristics of the entire structure.

[0053] Furthermore, the vibration attenuation effect of the local resonance unit array layer 200 can be adjusted by adjusting the material parameters, structural dimensions and arrangement of the local resonance component 220 to meet different engineering requirements. Figure 8 .

[0054] Among them, the customizable material parameters include the mass density, elastic modulus and Poisson's ratio of the scatterer 223, the wrapping layer 222 and the substrate 221; the customizable structural parameters include the radius of the scatterer 223, the inner diameter of the wrapping layer 222, the thickness of the wrapping layer 222, the lattice constant of the local resonance component 220, the thickness of the local resonance component 220, etc.; the customizable arrangement method includes the unit spacing, number of unit rows, arrangement method, etc. of the local resonance component 220.

[0055] By designing the geometric dimensions and material parameters of the local resonance component 220, the frequency band of the local resonance band gap, i.e., the frequency range that produces the vibration reduction effect, can be adjusted;

[0056] By modifying the number and arrangement of the local resonance components 220, the vibration reduction effect within the frequency band can be adjusted. As the number of local resonance units increases, the vibration reduction effect gradually increases.

[0057] The vibration reduction effect of the precast concrete local resonance periodic vibration reduction wall is evaluated by the transmission function. The interval less than 0 on the transmission function curve represents the attenuation range of the wall to the vibration wave. The smaller the transmission function value is, the stronger the attenuation effect of the wall on the vibration wave of the frequency is. Therefore, the frequency response functions of different local resonance units have similar development trends, and with the increase in the number of local resonance components 220, the transmission loss in the attenuation area is strengthened and the attenuation effect is more uniform.

[0058] Since the attenuation of vibration waves by the wall panel is generated through local resonance, that is, the frequency within the band gap range will cause the resonance of the local resonance component 220 when it is transmitted into the structure, thereby causing the localization of energy and the exponential decrease of the vibration displacement. This localization phenomenon gradually becomes significant as the propagation path increases, that is, increasing the number of local resonance components 220 will enhance the vibration reduction effect of the structure.

[0059] In addition, the area of ​​the local resonance unit array layer 200 except the local resonance component 220 is preferably cast with rubber concrete, which can give play to the synergistic effect of local resonance elastic wave band gap filtering and rubber concrete damping and vibration reduction.

[0060] Rubber concrete is obtained from rubber particle concrete obtained by crushing waste tires. It has the characteristics of high toughness, impact resistance, high damping, good crack resistance, low carbon and environmental protection. The damping ratio of rubber concrete is greater than that of ordinary concrete, and the elastic modulus and fundamental frequency decrease with the amount of rubber particles added, which has good vibration reduction ability.

[0061] The precast concrete local resonance periodic vibration damping wall constructed by the above scheme can achieve the attenuation effect of rail transit vibration on the basis of meeting the wall panel strength requirements by setting a sandwich structure of the first leaf wall panel assembly 100, the local resonance periodic vibration damping layer 200, and the second leaf wall panel assembly 300.

[0062] At the same time, the synergistic effect of local resonant elastic wave bandgap filtering and rubber concrete damping vibration reduction is fully utilized to further enhance the vibration reduction performance of the wall panels and reduce the negative impact of low-frequency vibration on human health and structural safety.

[0063] Secondly, by utilizing the local resonance phononic crystal vibration reduction bandgap filtering technology, active control of specific frequency vibrations of rail transit can be achieved by adjusting the material parameters, structural parameters and layout of the local resonance unit, and active customization can be performed according to the vibration environment.

[0064] Based on the precast concrete local resonance periodic vibration reduction wall formed by the above scheme, this scheme also provides a construction method of the precast concrete local resonance periodic vibration reduction wall, see Fig. 9 , the specific construction method includes the following steps:

[0065] Step 1: First, determine the design objectives based on the main frequency of rail transit environmental vibration and the target vibration reduction level requirements, including the main frequency of vibration and the expected vibration reduction effect.

[0066] Step 2: Select appropriate material parameters and structural parameters of the local resonance component 220 to construct the local resonance unit array layer 200.

[0067] Among them, the customizable material parameters include the mass density, elastic modulus and Poisson's ratio of the scatterer 223 and the wrapping layer 222, and the customizable structural parameters include the radius of the scatterer 223, the inner diameter of the wrapping layer 222, the thickness of the wrapping layer 222, the lattice constant of the local resonance component 220, the thickness of the local resonance component 220, etc. By designing the geometric dimensions and material parameters of the local resonance unit, the frequency band of the local resonance band gap, that is, the frequency range that produces the vibration reduction effect, can be adjusted.

[0068] Step 3: Perform dispersion analysis on the local resonance unit to obtain the band structure and determine the band gap range.

[0069] Among them, the analysis method can adopt the plane wave expansion method theoretical calculation or finite element simulation calculation. The specific analysis method adopted is not limited in this scheme and can be determined according to the actual situation.

[0070] For details, see Figure 4-Figure 6 as well as Fig.10 , when the analysis method adopts finite element simulation calculation, as an example, the specific calculation and analysis steps are as follows:

[0071] Firstly, a single local resonance unit cell is selected for the precast concrete local resonance periodic vibration reduction wall, and then an analysis model is established.

[0072] Then, the material properties of each component are assigned, and then the mesh is divided, and periodic boundary conditions are added around the model.

[0073] Then the wave vector of the model is defined and the wave vector is swept over the irreducible Brillouin zone.

[0074] Then the characteristic frequency is solved, and a plot is made with the wave vector on the horizontal axis and the characteristic frequency on the vertical axis to obtain the band structure. The frequency region where the wave vector curve does not pass through the band structure is the band gap.

[0075] The finite element method is used to calculate the energy band structure, which has strong adaptability and can be used to calculate different structural forms.

[0076] Furthermore, when the analysis method adopts the plane wave expansion method for theoretical calculation, as an example, the specific calculation and analysis steps are as follows:

[0077] Firstly, a single local resonance primitive cell is selected for the precast concrete local resonance periodic vibration damping wall, and the elastic constant, density and other parameters of the primitive cell are expanded according to the Fourier series. Combined with the Bloch theorem, the elastic wave equation is expanded in the form of plane wave superposition in the reciprocal lattice vector space, that is, the wave equation is converted into the eigenvalue solution, thereby obtaining the energy band structure.

[0078] For a homogeneous isotropic medium, the elastic wave equation is as follows:

[0079] -ρ(r)ω 2 u i (r)=[λ(r)u j,j (r)] ,i +{μ(r)[u i,j (r)+u j,i (r)]} ,j ,i,j=x,y

[0080] The material parameters of each component of the primitive cell are Fourier expanded to obtain:

[0081]

[0082] Among them, for the circular three-component primitive cell of this structure, the Fourier coefficient is expressed as:

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] In addition, according to Bloch's theorem, the displacement field can also be expressed as:

[0089] u(r,t)=e i(k·r-ωt) u k (r)

[0090] Substituting the Fourier expressions of material parameters and displacement field into the wave equation, we can obtain the wave eigenvalue equation:

[0091]

[0092]

[0093] The plane wave expansion method is easy to implement in programming for band structure calculation. Only global variables need to be modified to realize band calculation of different structural forms, which is convenient for parameter analysis.

[0094] In addition, compared with the traditional plane wave expansion method, this method can also calculate the band structure of primitive cells of different shapes such as square, circle, ellipse, concentric ring, etc., and only needs to perform Fourier coefficient calculation for primitive cells of different shapes. By changing the structure of the band structure, the corresponding structural form can be obtained, which has strong adaptability.

[0095] Step 4: Determine whether the band gap can cover the target vibration frequency. If the band gap can cover the target vibration frequency, proceed to the next step of design. If the band gap interval does not match the target frequency, modify the material parameters and structural parameters of the local resonance unit until the band gap meets the target frequency.

[0096] Step 5: Determine the arrangement of the local resonance unit, including the vibrator arrangement spacing, the number of arrangement rows, the number of arrangement, etc., and calculate the transfer function.

[0097] Here, the transfer function can be calculated using theoretical methods such as the spectral unit method or the finite element method. This scheme does not limit the choice of calculation method, and the specific method can be determined according to actual conditions.

[0098] See also Fig.11 When the finite element method is used to calculate the transfer function, as an example, the specific calculation and analysis process is as follows:

[0099] Firstly, an analysis model is established for the precast concrete local resonance periodic vibration damping wall, and then the material properties of each component are assigned, and then the mesh is divided. In order to reduce the reflection and diffraction of the wave, a perfect matching layer boundary is established on the outside of the structure. Then, the subway acceleration excitation is applied to the lower side of the structure, and the frequency is swept from 0.1 to 200 Hz with an interval of 0.1 Hz. The acceleration is picked up on the upper part of the structure, and the transfer function is calculated by the following formula. The interval less than 0 on the transfer function curve is the frequency attenuation interval.

[0100]

[0101] Where, T is the transmission function, dB; A I and A O are the acceleration amplitudes at the excitation end and the receiving end, respectively.

[0102] Similarly, the finite element method is used to calculate the transfer function. The advantage is that it is highly adaptable and can be calculated for different structural forms.

[0103] When the spectral unit method is used to calculate the transfer function, as an example, the specific calculation and analysis process is as follows:

[0104] First, the precast concrete local resonance periodic vibration reduction wall structure is simplified into a local resonance Euler beam model, in which the concrete matrix 221 is represented as a periodically distributed matrix beam, and the local resonance unit can be represented as an oscillator periodically suspended on the matrix beam. Considering n periods (n is the actual number of local resonance units), the length of each beam segment is a j(The lattice constant a is calculated based on the mass equivalent), the base beam 221 can be represented as a spectral unit, and the spring oscillator can be regarded as a point unit attached to the base beam. The interaction between the oscillator and the base beam is described by an additional stiffness matrix. For details, see Fig.12 .

[0105] Based on the Euler beam theory, the spectral element matrix of the matrix beam element can be written as:

[0106]

[0107] Among them, each sub-matrix is ​​expressed as:

[0108]

[0109]

[0110]

[0111]

[0112] The meanings of the parameters in the matrix are as follows;

[0113] α=[cos(k b a j )sinh(k b a j )+sin(k b a j )cosh(k b a j )](k b a j ) 3 Δ -1

[0114]

[0115] β=[-cos(k b a j )sinh(k b a j )+sin(k b a j )cosh(k b a j )](k b a j )Δ -1

[0116]

[0117] γ=[-cos(k b a j)+cosh(k b a j )](k b a j ) 2 Δ -1

[0118]

[0119] Δ=1-cos(k b a j )cosh(k b a j )

[0120] k b =[ρAω 2 (EI) -1 ] 1 / 4

[0121] Where: k b is the bending wave number of the base beam; ρ is the density of the base beam, unit: kg / m 3 ; E is the Young's modulus of the base beam, unit MPa; A is the cross-sectional area of ​​the base beam, unit m 2 ; I is the cross-sectional inertia moment of the base beam, unit: m 4 .

[0122] Since the oscillator only interacts with the base beam at the contact point and is not affected by other external forces, its motion equation under simple harmonic vibration excitation can be written as:

[0123]

[0124] Where V0 is the displacement of the base beam at the vibrator attachment point, in m; V i is the displacement of the vibrator, in m; F0 is the force exerted by the base beam on the vibrator at the vibrator attachment point, in N.

[0125] Further simplifying the above formula, we can get:

[0126] F0=D r,j V0

[0127] Among them, D r,j is the additional dynamic stiffness of the vibrator on the base beam, and its expression is:

[0128]

[0129] For oscillator j, its natural frequency is Substituting it into the above formula, the additional dynamic stiffness can be written as an expression of the natural frequency of the oscillator.

[0130]

[0131] The interaction between the oscillator and the base beam is expressed as an additional dynamic stiffness matrix, which is expressed as follows:

[0132]

[0133] The total stiffness matrix D of the primitive cell can be obtained by assembling the dynamic stiffness matrix of the spectrum unit and the additional stiffness matrix of the point unit. c , so the dynamic equation of a single unit cell can be expressed as:

[0134] D c u c =f c

[0135] In the formula, u c is the generalized displacement vector, f c is the generalized force vector.

[0136] Substituting the geometric and material parameters of the structure, applying simple harmonic displacement excitation at the input end on the left side of the model, and picking up the displacement amplitude at its output end, the frequency response function can be obtained:

[0137]

[0138] Where T is the transfer function in dB; V O (ω) is the output acceleration, V i (ω) is the acceleration at the input.

[0139] Compared with the traditional spectral unit method, the spectral unit method proposed in this patent for calculating the transmission function has the advantages of small workload, simple programming to calculate the transmission, and by modifying the spectral unit matrix, the transmission functions of local resonance structures of multiple different unit cell structures can be calculated.

[0140] Step 6: Determine whether the vibration reduction effect meets the requirements. If the vibration reduction effect (measured in dB) does not meet the expectations, adjust the arrangement and number of local resonance units until the transfer function meets the design expectations, thus obtaining the final design.

[0141] According to the local resonance vibration reduction unit determined in steps 1-6, the vibration reduction wall is prefabricated in the factory, and the on-site hoisting and installation construction is carried out after the maintenance is completed. During the operation of the subway, when the vibration waves generated by the rail transit are transmitted to the prefabricated vibration reduction wall, the local resonance band gap filtering effect of the phononic crystal produces localized vibration energy, which is further effectively attenuated by the rubber concrete.

[0142] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A precast concrete local resonance periodic vibration reduction wall, characterized in that: It includes a first leaf wall panel component, a local resonance unit array layer and a second leaf wall panel component. The local resonance unit array layer is arranged between the first leaf wall panel component and the second leaf wall panel component and is integrally cast with the first leaf wall panel component and the second leaf wall panel component to form a prefabricated wall.

2. The precast concrete local resonance periodic vibration reduction wall according to claim 1 is characterized in that: The local resonance unit array layer comprises a mounting plate and a local resonance component, wherein the local resonance component is embedded in the mounting plate.

3. The precast concrete local resonance periodic vibration reduction wall according to claim 2, characterized in that: The end surface of the mounting plate is provided with a plurality of independent mounting grooves, which are distributed on the end surface of the mounting plate in a matrix form, and the size of the mounting grooves is the same as that of the local resonance component.

4. The precast concrete local resonance periodic vibration reduction wall according to claim 3 is characterized in that: The local resonance component is composed of a plurality of local resonance parts, each of which is composed of a steel scatterer, a rubber wrapping layer, and a concrete base. The concrete base is provided with a mounting groove. The rubber wrapping layer is wrapped on the steel scatterer and then embedded in the mounting groove of the concrete base to form an integrated structure and is installed in the corresponding mounting groove on the mounting plate.

5. The precast concrete local resonance periodic vibration reduction wall according to claim 1, characterized in that: The first leaf wall panel assembly includes a first leaf wall panel, a first steel mesh and tie steel bars, and the first leaf wall panel, the first steel mesh and the tie steel bars are stacked in sequence.

6. The precast concrete local resonance periodic vibration reduction wall according to claim 1, characterized in that: The second leaf wall panel assembly includes a second leaf wall panel, a second steel mesh, and the second steel mesh and the second leaf wall panel are arranged in cooperation.

7. A construction method for a precast concrete local resonance periodic vibration reduction wall, characterized in that: The construction method comprises the following steps: Step 1: First, determine the design objectives based on the main frequency of rail transit environmental vibration and the target vibration reduction level requirements, including the main frequency of vibration and the expected vibration reduction effect; Step 2: Select appropriate material parameters and structural parameters of the local resonance unit to construct the local resonance vibration reduction unit; Step 3: Perform a dispersion analysis on the local resonance unit to obtain the band structure and determine the band gap range; Step 4: Determine whether the band gap can cover the target vibration frequency. If the band gap can cover the target vibration frequency, proceed to the next step of design. If the band gap interval does not match the target frequency, modify the material parameters and structural parameters of the local resonance unit until the band gap meets the target frequency. Step 5: Determine the arrangement of the local resonance unit, including the vibrator arrangement spacing, the number of arrangement rows, the number of arrangement, etc., and use theoretical methods such as spectral unit method or finite element method to calculate the transfer function; Step 6: Determine whether the vibration reduction effect meets the requirements. If the vibration reduction effect does not meet the expectations, adjust the arrangement and number of local resonance units until the transfer function meets the design expectations, and the final design is obtained.

8. The construction method of the precast concrete local resonance periodic vibration reduction wall according to claim 7 is characterized in that: The analysis method in step 3 can adopt theoretical calculation of plane wave expansion method or finite element simulation calculation.

9. The construction method of the precast concrete local resonance periodic vibration reduction wall according to claim 7, characterized in that: According to the local resonance vibration reduction unit determined in steps 1-6, the vibration reduction wall is prefabricated in the factory and then hoisted and installed on site after maintenance is completed.

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