Method for evaluating vibration reduction effect of energy-absorbing, vibration-reducing and noise-reducing high-speed railway elevated bridge

Abstract

The invention discloses an energy-absorbing, vibration-reducing and noise-reducing high-speed railway viaduct vibration-reducing effect evaluation method, which comprises the following steps: S1, arranging force sensors and displacement sensors in a restraint layer, a base layer and a damping layer of a high-speed railway viaduct structure, and collecting normal stress of the force sensors and the displacement sensors in three-axis directions, shear stress of x-y, y-z and z-x planes and displacement of the force sensors and the displacement sensors in corresponding directions; s2, performing the following assumptions to calculate a loss factor: (1) the viscoelastic damping material satisfies a linear viscoelastic constitutive relationship; (2) the restraint layer and the base layer meet the plane assumption in the vibration process, namely, the deformation is uniform; (3) the influence of shear deformation and rotational inertia of the structure is neglected; s3, determining the circular frequency of the vibration mode and the first-order mode of the constraint damping structure; s4, calculating strain energy of the constraint layer, the damping layer and the base layer; s5, calculating dissipated energy of the damping layer; and S6, calculating a transverse loss factor and a vertical loss factor in the first-order mode.

Description

Technical Field

[0001] This invention relates to the field of vibration reduction and noise reduction technology for rail transit, specifically to a method for evaluating the vibration reduction effect of high-speed railway viaducts that absorb energy and reduce vibration and noise. Background Technology

[0002] When high-speed trains pass through curved sections of track, superelevation of the outer rail is typically used to facilitate smooth passage. Compared to straight sections, maintaining a constant speed is crucial when navigating curves. When the train's speed on a curve is lower or higher than this constant speed, inward or outward horizontal forces are generated. The combined effect of rail irregularities and these horizontal forces exacerbates horizontal vibrations on curves. This horizontal vibration reduces passenger comfort and, over time, can lead to slippage in simply supported bridge structures. Therefore, controlling horizontal vibrations in bridge structures on curves is of paramount importance.

[0003] Increasing structural damping is a common method for structural vibration reduction and noise reduction. Traditional damping methods mainly include free damping and constrained damping. Constrained damping involves covering the entire or a large area of ​​the damping material on the surface of the base structure, and then adding a constrained layer. This method utilizes the shear deformation of the damping layer to dissipate vibration energy, which can effectively reduce the mid-to-high frequency vibration and noise of the structure.

[0004] like Figure 1 and Figure 2 As shown, existing technologies achieve three-dimensional vibration reduction by installing a three-dimensional spring-damping composite device at the bridge ends. Vibrations in viaducts, such as vertical bending vibrations and horizontal lateral vibrations caused by vehicle loads, primarily propagate through the beam itself, with vibration energy concentrated in the middle of the beam rather than at the ends. End devices can only passively dissipate vibrations transmitted to the ends, while their effect on suppressing vibrations in the middle of the beam (such as mid-span deflection vibrations and local shear vibrations) is weak, leading to an imbalance of "strong vibrations in the middle and inefficient control at the ends." Bridge noise mainly originates from the air radiation of beam vibrations (especially the thin-walled vibrations of box girders). End devices can only reduce the transmission of vibrations to the piers and cannot directly suppress the vibration radiation from the beam itself. Therefore, even if the end vibration reduction effect meets the standards, the strong vibrations in the middle of the beam will still radiate a large amount of noise, making it difficult to meet the synergistic requirements of vibration reduction and noise reduction. Summary of the Invention

[0005] One objective of this invention is to provide a method for evaluating the vibration reduction effect of high-speed railway viaduct structures that absorb energy, reduce vibration, and reduce noise. This method accurately predicts and analyzes the vibration reduction capacity of circumferentially constrained damping structure vibration reduction measures, evaluates their vibration reduction effect, and provides a basis for vibration reduction design.

[0006] Therefore, the present invention adopts the following technical solution:

[0007] A method for evaluating the vibration reduction effect of high-speed railway viaducts that absorb energy, reduce vibration, and reduce noise includes the following steps:

[0008] S1. Force and displacement sensors are deployed in the constraint layer, base layer, and damping layer of the high-speed railway viaduct structure to collect the normal stress in the x, y, and z axes. Shear stress in the xy, yz, and zx planes And the corresponding displacements x, y, z;

[0009] S2, make the following assumptions to calculate the loss factor:

[0010] (1) Viscoelastic damping materials satisfy the linear viscoelastic constitutive relation;

[0011] (2) The constraint layer and the base layer satisfy the plane assumption during vibration, that is, the deformation is uniform;

[0012] (3) Ignore the effects of shear deformation and rotational inertia of the structure;

[0013] S3, determine the vibration modes of the constrained damping structure and the first... The angular frequency of the first mode;

[0014] S4, calculate the strain energy of the constraint layer, damping layer, and base layer;

[0015] S5, calculate the energy dissipation of the damping layer;

[0016] S6, calculate the... Transverse loss factor under first mode and vertical loss factor .

[0017] In step S3 above, it is assumed that the ring-constrained damping structure is in the first... Vibration under first mode, its displacement field Represented as:

[0018] ;

[0019] in, It is the first The mode shape function of the first mode. It is the first The angular frequency of the first mode, It is an imaginary unit, and t is time.

[0020] In step S4 above, both the constraint layer and the base layer are elastic materials, and their strain energy density and strain energy calculation formulas are the same, respectively:

[0021] ;

[0022] ;

[0023] in, For the first Strain energy density under first mode, For elastic modulus, Poisson's ratio, Shear modulus For the volume of the constraint layer or base layer, For the first Strain energy under first mode;

[0024] In step S4 above, the damping layer is represented by the relaxation modulus. Under uniaxial stress, if the stress... and strain Given that, then the first Strain energy density of damping layer under first mode Calculated by integration:

[0025] ,

[0026] Considering the deformation time accumulation characteristics of a structure under long-term service conditions, if the relaxation modulus of the linear viscoelastic material is known and the stress-strain relationship satisfies... Substituting this into the above equation, we have:

[0027] ;

[0028]

[0029] in, The time difference is relaxation modulus at time The strain energy is considered to account for the deformation time accumulation characteristics of the structure under long-term service conditions.

[0030] In step S5 above, the dissipated energy is calculated using the Karnopp model, assuming the thickness of the damping layer is... The bending stiffness of the elastic layer is The vibration frequency of the ring-constrained damped structure is The equivalent viscous damping coefficient of the composite damping structure is... The calculation formula is shown as follows:

[0031] ;

[0032] in, It is the shear loss modulus of the damping layer material;

[0033] The energy dissipation of the composite structure within one vibration cycle The calculation formula is:

[0034]

[0035] Where A is the area of ​​the damping layer; the composite damping structure is composed of a constraint layer, a base layer and a damping layer.

[0036] In step S6 above, the lateral loss factor and vertical loss factor In the The calculation formula for the first mode is:

[0037] ;

[0038] ;

[0039] in:

[0040] ;

[0041] ;

[0042] , They represent the first The transverse and vertical dissipation energy of the composite structure under the first mode. , They represent the first Transverse and vertical strain energies of the composite structure under first-mode conditions , These represent the sum of the lateral and vertical strain energies of the constraint layer and the base layer, respectively. , These represent the lateral and vertical strain energies of the damping layer, respectively.

[0043] In the above method, the energy-absorbing, vibration-reducing, and noise-reducing high-speed railway viaduct includes a top plate, a web plate, and a U-shaped bottom plate. The web plate is a hollow columnar structure lying down. Serrated grooves are respectively provided on the bottom surface of the top plate, the upper and lower surfaces of the web plate, and the inner bottom surface of the U-shaped bottom plate. Rectangular grooves are provided on the inner side wall of the U-shaped bottom plate and the outer side wall of the web plate. The web plate is located below the top plate and inside the U-shaped bottom plate. The serrated grooves on the upper surface of the web plate engage with the serrated grooves on the bottom surface of the top plate, and the serrated grooves on the lower surface of the web plate engage with the serrated grooves on the inner bottom surface of the U-shaped bottom plate. The rectangular grooves on the inner side wall of the U-shaped bottom plate engage with the rectangular grooves on the outer side wall of the web plate. A layer of damping material is formed on the contact surfaces of the top plate, web plate, and U-shaped bottom plate. The top plate, web plate, U-shaped bottom plate, and damping material layer constitute a circumferentially constrained damping structure.

[0044] Preferably, the damping material has a density ρ of 1200–1400 kg / m³, an elastic modulus E of 12–14 MPa, and a Poisson's ratio of 12–14 MPa. for The damping layer thickness is 1-2 cm.

[0045] The method of the present invention is particularly applicable to the vertical and horizontal vibration control of viaducts on curved sections.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] 1. The vibration reduction effect evaluation method of the present invention takes into account the time accumulation characteristics of viscoelastic structural deformation under long-term action, and can more scientifically and accurately predict and analyze the vibration reduction capacity of circumferentially constrained damping structure vibration reduction measures, accurately evaluate the vibration reduction effect of the complex vibration reduction structure, and provide a strong basis for vibration reduction design.

[0048] 2. The energy-absorbing, vibration-reducing, and noise-reducing high-speed railway viaduct of this invention adopts a circumferentially constrained damping structure. This structure dissipates vibration energy by converting mechanical energy into heat energy, while simultaneously reducing vertical and lateral vibrations. This effectively reduces vibration and structural noise in the high-speed railway station structure and waiting hall, providing passengers with a more comfortable waiting environment. This structure can be prefabricated, allowing for rapid construction, high precision, and convenient maintenance.

[0049] 3. The high-speed railway viaduct in this invention features an integrated vibration reduction design, upgrading from traditional distributed integrated vibration control to full-domain vibration control. When a box girder bridge vibrates, the strain is greatest in the central region. The damping layer can directly dissipate energy through shear deformation, suppressing the vibration of the box girder itself (especially high-frequency vibration of thin walls). This reduces airborne noise from the source, achieving vibration suppression as soon as it occurs, and providing vibration control covering the entire beam, solving the problem of uncontrolled vibration in the central region in existing technologies. This structure achieves synergistic vibration reduction and noise reduction, meeting combined requirements. Existing technologies can only reduce vibration transmission but cannot directly reduce beam-radiated noise.

[0050] 4. The constraint damping structure in this invention has a wide-band control capability, and its energy dissipation efficiency increases with the increase of vibration frequency. It can cover the entire frequency band of vibration from low frequency (1-10Hz, vertical bending) to high frequency (100-1000Hz, thin-wall vibration). In particular, it has a prominent effect on suppressing high-frequency vibrations that are directly related to noise, and solves the problem of high-frequency control failure in the prior art. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of an existing bridge damping structure;

[0052] Figure 2 for Figure 1A partially enlarged schematic diagram of the damping structure of a medium-sized bridge;

[0053] Figure 3 This is a perspective view of the energy-absorbing, vibration-reducing, and noise-reducing high-speed railway viaduct structure of the present invention;

[0054] Figure 4 for Figure 3 A three-dimensional structural diagram of the central top slab;

[0055] Figure 5 for Figure 3 A three-dimensional structural diagram of the mid-web;

[0056] Figure 6 for Figure 3 A three-dimensional structural diagram of the U-shaped base plate;

[0057] Figure 7 This is a schematic diagram showing the location of the damping layer in this invention.

[0058] In the picture:

[0059] 1. Top plate 2. Web plate 3. U-shaped bottom plate 4. Serrated groove 5. Damping material 6. Rectangular groove Detailed Implementation

[0060] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and embodiments. Obviously, the following embodiments are only some embodiments of the present invention. Based on the following embodiments, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0061] Example 1

[0062] This embodiment improves the box girder bridge structure as a whole, utilizing a circumferentially constrained damping structure to control vertical and horizontal vibrations in curved viaduct sections. Specifically, the box girder bridge structure is divided into three components, and damping layers are applied to the surfaces of these three components. These three components are then combined to form a constrained damping structure.

[0063] See Figures 3-7This invention discloses an energy-absorbing, vibration-damping, and noise-reducing high-speed railway viaduct structure, comprising three components: a top plate 1, a web plate 2, and a U-shaped bottom plate 3. The web plate 2 is a horizontally lying hollow columnar structure. Serrated grooves 4 are respectively provided on the bottom surface of the top plate 1, the upper and lower surfaces of the web plate 2, and the inner bottom surface of the U-shaped bottom plate 3. The cross-section of the serrations is an isosceles triangle, and the serrated grooves extend along the extension direction of the bridge. The apex angle (i.e., the protruding angle) of the isosceles triangle is 90° to 120°. Additionally, rectangular grooves 6 are provided on the inner wall of the U-shaped bottom plate 3 and the outer wall of the web plate 2, also extending along the extension direction of the bridge, serving to limit the vertical displacement of the web and increase the area of ​​the damping layer. In this embodiment, the length and width of the rectangles are equal.

[0064] The web plate 2 is located below the top plate 1 and within the U-shaped bottom plate 3. The serrated grooves on the upper surface of the web plate 2 engage with the serrated grooves on the bottom surface of the top plate 1, and the serrated grooves on the lower surface of the web plate 2 engage with the serrated grooves on the inner bottom surface of the U-shaped bottom plate 3. The rectangular grooves on the inner wall of the U-shaped bottom plate 3 engage with the rectangular grooves on the outer wall of the web plate 2. The design of the serrated and rectangular grooves not only increases the surface area of ​​the damping material, thereby improving vibration reduction capacity, but also provides good limiting function, preventing misalignment of the three components and ensuring driving safety.

[0065] A layer of damping material 5 is applied to the contact surfaces of the top plate 1, web plate 2, and U-shaped bottom plate 3. The position of the damping material 5 can be on the lower surface of the top plate 1, the upper surface of the web plate 2, the lower surface of the web plate 2, or the upper surface of the U-shaped bottom plate 3. The position can be selected according to the prefabrication site conditions without affecting the vibration reduction effect.

[0066] The damping material has a density ρ of 1200–1400 kg / m³, an elastic modulus E of 12–14 MPa, and a Poisson's ratio. It is advisable to The thickness of the damping layer is 1 to 2 cm, and the specific thickness can be determined by comprehensively considering the bridge stiffness requirements.

[0067] The top plate 1, the damping layer, and the web plate 2 form the upper-level constrained damping structure; the web plate 2, the damping layer, and the bottom of the U-shaped bottom plate form the lower-level constrained damping structure; the side walls of the web plate, the damping layer, and the U-shaped bottom plate form the constrained damping structures on the left and right sides of the box girder. These parts together constitute the circumferential constrained damping structure.

[0068] The aforementioned three components—top slab 1, web slab 2, and U-shaped bottom slab 3—can be made of concrete and prefabricated in a factory. They are then transported to the construction site for assembly. The length of each prefabricated section can be determined based on project requirements and transportation capacity. The implementation process is as follows: Top slab 1, web slab 2, and U-shaped bottom slab 3 are prefabricated in the factory according to precision requirements; damping material 5 is sprayed onto the joint surfaces between the slabs. Afterward, top slab 1, web slab 2, and U-shaped bottom slab 3 are assembled in the prefabrication yard and transported to the construction site for installation.

[0069] In the above structure, the U-shaped bottom plate 3 is the base layer, and the top plate 1 and the web plate 2 are the constraint layers.

[0070] When a train passes, the vibration caused by the interaction between the wheel and rail is transmitted to the bridge structure via fasteners. For each constrained damping structure, the deformation of its constrained layer is asynchronous, causing shear stress and strain in the prefabricated damping layer, converting mechanical energy into heat energy, significantly reducing the transmitted vibration energy, thereby achieving vibration reduction. In this invention, the energy-absorbing high-speed railway station viaduct structure has a good vibration reduction effect. Furthermore, due to the complexity of the circumferential constrained damping structure, it dissipates both vertical and lateral vibration energy, thus simultaneously reducing both vertical and lateral vibration.

[0071] Example 2

[0072] A method for evaluating the vibration reduction effect of an energy-absorbing, vibration-reducing, and noise-reducing high-speed railway viaduct with the structure of Example 1 includes the following steps: First, the vibration modes of the structure are obtained through theoretical analysis or numerical simulation. After obtaining the vibration modes, the mode shape function of the corresponding order can be directly obtained. Then, the circular frequency under that mode is obtained by using the relationship between the mode shape function and displacement. Next, the strain energy density of the constraint layer and the base layer is obtained by measuring stress data through embedded sensors. The strain energy is then calculated according to the formula. The strain energy density of the damping layer is calculated according to the stress-strain relationship. However, if the deformation time accumulation characteristics under long-term service conditions are considered, a more complex formula is required to obtain its strain energy density. Finally, the volume is quadrated to obtain the strain energy of the damping layer. The dissipation energy of the damping layer is obtained by substituting the circular frequency under that mode obtained in the first step into the formula to obtain the equivalent viscous damping coefficient, and then substituting it into the formula to obtain the dissipation energy. Finally, the horizontal and vertical strain energies of each layer are added to obtain the total strain energy. The loss factor is then obtained by dividing the dissipation energy in the corresponding direction by the total strain energy.

[0073] This method employs a constrained damping plate model, but unlike traditional constrained damping structures that only have a damping layer in the horizontal direction, this invention considers the influence of lateral vibration of the bridge and innovatively sets a damping layer in the vertical direction, thus forming a circumferentially enclosed damping layer. Therefore, when calculating the vibration reduction effect of the circumferentially constrained damping structure in this invention, both lateral and vertical energy losses must be calculated simultaneously.

[0074] This invention evaluates the vibration reduction effect of a ring-constrained damping structure of a high-speed railway viaduct structure with energy absorption, vibration reduction, and noise reduction as described in Example 1, based on the energy method. The evaluation indexes are the transverse loss factor and vertical loss factor under the nth-order mode. The larger the value of the loss factor, the better the vibration reduction effect. The value of n in the nth-order mode depends on the frequency characteristics of the external excitation. When the excitation frequency is close to the natural frequency of a certain order mode, that mode will be significantly excited and thus generate strong vibrations; therefore, that order mode is used for analysis. Specifically, the evaluation method for the vibration reduction effect of the energy absorption, vibration reduction, and noise reduction high-speed railway viaduct structure in this embodiment includes the following steps:

[0075] S1, force sensors and displacement sensors are installed in the constraint layer, base layer, and damping layer to collect the normal stress in the x-axis, y-axis, and z-axis directions. Shear stress in the xy, yz, and zx planes And the corresponding displacements x, y, and z in the directions.

[0076] S2, to calculate the loss factor, makes the following assumptions:

[0077] (1) Viscoelastic damping materials satisfy the linear viscoelastic constitutive relation;

[0078] (2) The constraint layer and the base layer satisfy the plane assumption during vibration, that is, the deformation is uniform;

[0079] (3) Ignore the effects of shear deformation and rotational inertia of the structure.

[0080] S3, determine the vibration modes of the constrained damping structure and the first... The angular frequency of the first mode:

[0081] For the ring-constrained damping structure in Example 1, its vibration modes first need to be determined through theoretical analysis or numerical calculation methods. Assume the ring-constrained damping structure in the... Vibration under first mode, its displacement field It can be represented as:

[0082] ;

[0083] in, It is the first The mode shape function of the first mode. It is the first The angular frequency of the first mode, t is the imaginary unit, and t is time. Solving the above equation using the given conditions, we obtain... .

[0084] S4, calculate the strain energy of the constraint layer, damping layer, and base layer:

[0085] (1) Both the constraint layer (top plate 1 and web plate 2) and the base layer (U-shaped bottom plate 3) are elastic materials (elastic layers). Their strain energy density and strain energy calculation formulas are the same. The two calculation formulas are as follows:

[0086] ;

[0087] ;

[0088] in, For the first Strain energy density under first mode, For elastic modulus, Poisson's ratio, Shear modulus For the volume of the constraint layer or base layer, For the first Strain energy under first mode.

[0089] (2) The damping layer is represented by the relaxation modulus. For linear viscoelastic materials, the time-cumulative characteristics of structural deformation need to be considered, and the relaxation modulus can be used. To describe its mechanical properties. Under uniaxial stress, if the stress and strain It is known that the first Strain energy density of damping layer under first mode It can be calculated through integration:

[0090] ,

[0091] Considering the deformation time accumulation characteristics of a structure under long-term service conditions, if the relaxation modulus of the linear viscoelastic material is known and the stress-strain relationship satisfies... Substituting this into the above equation, we get:

[0092] ;

[0093] ;

[0094] in, The time difference is relaxation modulus at time The strain energy is considered to account for the deformation time accumulation characteristics of the structure under long-term service conditions.

[0095] S5, Calculate the energy dissipation of the damping layer:

[0096] In this invention, the structure to be evaluated is a composite damping structure consisting of an elastic layer and a damping layer, so the Karnopp model is used to calculate the dissipated energy.

[0097] Assuming the thickness of the damping layer is The bending stiffness of the elastic layer is The vibration frequency of the ring-constrained damped structure is The equivalent viscous damping coefficient of the composite damping structure is... It can be represented as:

[0098] ;

[0099] in, It is the shear loss modulus of the damping layer material.

[0100] Therefore, within one vibration cycle, the energy dissipated by the composite structure is It can be approximated as:

[0101] ;

[0102] Where A is the area of ​​the damping layer.

[0103] S6, calculate the... Transverse loss factor in first mode and vertical loss factor :

[0104] The loss factors of the ring-constrained damped structure are the transverse loss factors. and vertical loss factor In the The calculation formulas for the first mode are as follows:

[0105] ;

[0106] ;

[0107]

[0108] ;

[0109] in , They represent the first The transverse and vertical dissipation energy of the composite structure under the first mode. , They represent the first Transverse and vertical strain energies of the composite structure under first-mode conditions , These represent the sum of the lateral and vertical strain energies of the constraint layer and the base layer, respectively. , These represent the lateral and vertical strain energies of the damping layer, respectively.

Claims

1. A method for evaluating the vibration reduction effect of high-speed railway viaducts, characterized in that, Includes the following steps: S1. Force and displacement sensors are deployed in the constraint layer, base layer, and damping layer of the high-speed railway viaduct structure to collect the normal stress in the x, y, and z axes. Shear stress in the xy, yz, and zx planes And the corresponding displacements x, y, z; S2, make the following assumptions to calculate the loss factor: (1) Viscoelastic damping materials satisfy the linear viscoelastic constitutive relation; (2) The constraint layer and the base layer satisfy the plane assumption during vibration, that is, the deformation is uniform; (3) Ignore the effects of shear deformation and rotational inertia of the structure; S3, determine the vibration modes of the constrained damping structure and the first... The angular frequency of the first mode; S4, calculate the strain energy of the constraint layer, damping layer, and base layer; S5, calculate the energy dissipation of the damping layer; S6, calculate the... Transverse loss factor under first mode and vertical loss factor .

2. The method for evaluating the vibration reduction effect of high-speed railway viaducts as described in claim 1, characterized in that, In step S3, it is assumed that the ring-constrained damping structure is in the first... Vibration under first mode, its displacement field Represented as: ； in, It is the first The mode shape function of the first mode. It is the first The angular frequency of the first mode, It is an imaginary unit, and t is time.

3. The method for evaluating the vibration reduction effect of high-speed railway viaducts as described in claim 1, characterized in that: In S4, both the constraint layer and the base layer are elastic materials, and their strain energy density and strain energy calculation formulas are the same, respectively: ； ； in, For the first Strain energy density under first mode, For elastic modulus, Poisson's ratio, Shear modulus For the volume of the constraint layer or base layer, For the first Strain energy under first mode.

4. The method for evaluating the vibration reduction effect of high-speed railway viaducts as described in claim 1, characterized in that: In S4, the damping layer is represented by the relaxation modulus. Under uniaxial stress, if the stress... and strain Given that, then the first Strain energy density of damping layer under first mode Calculated by integration: ， Considering the deformation time accumulation characteristics of a structure under long-term service conditions, if the relaxation modulus of the linear viscoelastic material is known and the stress-strain relationship satisfies... Substituting this into the above equation, we have: ； in, The time difference is relaxation modulus at time The strain energy is considered to account for the deformation time accumulation characteristics of the structure under long-term service conditions.

5. The method for evaluating the vibration reduction effect of high-speed railway viaducts as described in claim 1, characterized in that: In S5, the Karnopp model is used to calculate the dissipated energy, assuming the thickness of the damping layer is... The bending stiffness of the elastic layer is The vibration frequency of the ring-constrained damped structure is The equivalent viscous damping coefficient of the composite damping structure is... The calculation formula is shown as follows: ； in, It is the shear loss modulus of the damping layer material; The energy dissipation of the composite structure within one vibration cycle The calculation formula is: Where A is the area of ​​the damping layer; the composite damping structure is composed of a constraint layer, a base layer and a damping layer.

6. The method for evaluating the vibration reduction effect of high-speed railway viaducts as described in claim 1, characterized in that: In S6, the lateral loss factor and vertical loss factor In the The calculation formula for the first mode is: ； ； in: ； ； , They represent the first The lateral and vertical energy dissipation of the composite damping structure under the first mode are... , They represent the first Transverse and vertical strain energies of a composite damping structure under first-order modal conditions , These represent the sum of the lateral and vertical strain energies of the constraint layer and the base layer, respectively. , These represent the lateral and vertical strain energies of the damping layer, respectively.

7. The method for evaluating the vibration reduction effect of energy-absorbing, vibration-damping, and noise-reducing high-speed railway viaducts according to any one of claims 1-6, characterized in that: The energy-absorbing, vibration-reducing, and noise-reducing high-speed railway viaduct includes a top plate (1), a web plate (2), and a U-shaped bottom plate (3). The web plate (2) is a hollow columnar structure lying down. Serrated grooves (4) are provided on the bottom surface of the top plate (1), the upper and lower surfaces of the web plate (2), and the inner bottom surface of the U-shaped bottom plate (3). Rectangular grooves (6) are provided on the inner wall of the U-shaped bottom plate (3) and the outer wall of the web plate (2). The web plate (2) is located below the top plate (1) and inside the U-shaped bottom plate (3). The serrated groove on the upper surface of the top plate (1) engages with the serrated groove on the bottom surface of the top plate (1), and the serrated groove on the lower surface of the web plate (2) engages with the serrated groove on the inner surface of the bottom of the U-shaped bottom plate (3); the rectangular groove on the inner wall of the U-shaped bottom plate (3) engages with the rectangular groove on the outer wall of the web plate (2); a layer of damping material (5) is formed on the contact surfaces of the top plate (1), web plate (2), and U-shaped bottom plate (3); the top plate (1), web plate (2), U-shaped bottom plate (3) and the damping material layer form a circumferentially constrained damping structure.

8. The method for evaluating the vibration reduction effect of high-speed railway viaducts according to claim 7, characterized in that: The density ρ of the damping material (5) is 1200-1400 kg / m³, the elastic modulus E is 12-14 MPa, and the Poisson's ratio is... for The damping layer thickness is 1-2 cm.

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