WO2023098106A1

WO2023098106A1 - Method for designing pile-column combined periodic fractal topology vibration reduction foundation of depot cover

Info

Publication number: WO2023098106A1
Application number: PCT/CN2022/107757
Authority: WO
Inventors: 姜博龙; 刘冀钊; 胡文林; 王少林; 何宾; 齐春雨
Original assignee: 中国铁路设计集团有限公司
Priority date: 2021-12-01
Filing date: 2022-07-26
Publication date: 2023-06-08
Also published as: CN113868776B; CN113868776A

Abstract

Disclosed in the present invention is a method for designing a pile-column combined periodic fractal topology vibration reduction foundation for vibration control of a depot cover. A periodic fractal structure has the characteristic of tending to generate a complete band gap and a directed band gap. For the vibration of a subway depot cover platform at a significant frequency band, the current building structural column of a subway depot operation library is taken as a foundation, and a pile foundation is arranged around the building structural column to realize the construction of a periodic fractal topology foundation structure; and band gap calculation is performed on a pile-column combined periodic fractal topology foundation, and the number of iterations is increased, and the minimum center-to-center spacing of the last-stage center pile of the current-generation pile-column combined periodic fractal topology foundation and the pile diameters of other stages of center piles of the current-generation pile-column combined periodic fractal topology foundation other than the first-stage center pile are adjusted, so as to improve the band gap property of the pile-column combined periodic fractal topology foundation, such that more complete band gaps and directed band gaps having more bandwidths are present within the significant frequency band of the vibration of the subway depot cover platform, thereby achieving the aim of control over the vibration at a target frequency band.

Description

Design method of periodic fractal topological vibration damping foundation of pile-column structure on the upper cover of the depot

technical field

The invention relates to the technical field of rail transit vibration reduction and noise reduction, in particular to a pile-column-column periodic fractal topological foundation design method for vibration control of a vehicle depot upper cover.

Background technique

The property development on the top of the subway depot can organically integrate the rail transit system and urban layout, respond to the call for intensification of urban land use, feed back the construction of rail transit with development income, help rail transit maintain passenger flow, and increase operating income. However, the vibration of the superstructure caused by the train entering and leaving the warehouse and the secondary noise of the structure derived from the vibration have become one of the bottleneck factors restricting its development. The complex structure of subway depots and various influencing factors make its vibration and noise difficult to predict and control. At present, the existing vibration and noise control measures in subway depots mainly include track vibration reduction, building vibration isolation, and path vibration isolation. When track vibration reduction and building vibration isolation are used to the extreme and still cannot solve the problem of vibration and noise on the upper cover of the depot, path vibration isolation is irreplaceable as a supplementary means. Foundation isolation is a typical path isolation.

The Polish scholar Waclaw Sierpinski first proposed the fractal structure, which has been applied to the study of the bandgap characteristics of photonic crystals, and some studies have found that a higher algebraic periodic fractal structure is conducive to the generation of directional bandgap and complete bandgap. Inspired by the periodic structure band gap theory and fractal structure theory, to solve the vibration control problem of the depot, the pile foundation of the depot and the structural column of the building can be combined with periodic fractal topology design, so as to comprehensively improve its band gap characteristics, increase the directional band gap and complete The number and bandwidth of the band gap can further reduce the pile diameter, comprehensively improve the vibration reduction effect and reduce the construction cost.

Contents of the invention

The purpose of the present invention is to provide a method for designing a periodic fractal topological vibration-damping foundation of a pile-column structure on a depot roof, aiming at the technical defect that the vibration noise of the depot superstructure restricts the urban layout in the prior art.

The technical scheme adopted for realizing the purpose of the present invention is:

A method for designing a pile-column joint-structure periodic fractal topology vibration-damping foundation for the upper cover of a vehicle depot, comprising the following steps:

Step 1. Obtain the significant frequency bands of the platform vibration of the same type of vehicle depot and the vibration of building structural columns, and use this frequency band as the target frequency band of vibration isolation;

Step 2, extracting the building column network information of the vehicle depot, based on the building column, by arranging pile foundations around it to realize the construction of periodic fractal topology infrastructure;

Step 3, determining the structural form and parameters of the first-generation pile-column-column periodic fractal topological foundation and the second-generation pile-column-column-column periodic fractal topological foundation, and the building columns in step 2 are used as the first-generation pile-column joint structure The first-level central position pile of periodic fractal topological foundation;

Step 4, perform frequency dispersion calculation and band gap analysis on the periodic fractal topological foundation of the second-generation pile joint structure;

Step 5, evaluate the band gap characteristics obtained in step 4, if the band gap distribution meets the requirements, go to step 6; if the band gap distribution does not meet the requirements, go to step 7;

Step 6, determine the second-generation pile joint structure periodic fractal topological infrastructure as the final solution;

Step 7, adjust the structural form and parameters of the second-generation pile joint structure periodic fractal topology foundation in step 3, and repeat steps 4-6;

Alternatively, in step 3, increase the algebra of the periodic fractal topological foundation of the pile-column structure to the Mth generation step by step, M is a natural number greater than or equal to 3, and carry out the dispersion calculation and band Gap analysis until the band gap distribution meets the requirements. Specifically, the iterative algebra of the periodic fractal topological foundation of the pile-column structure is increased to the third generation, and the frequency dispersion calculation and band Gap analysis, if the band gap distribution meets the requirements, the third-generation pile-column periodic fractal topology foundation is used as the final solution, if it does not meet the requirements, continue to increase the iteration algebra. Perform frequency dispersion calculation and bandgap analysis on the periodic fractal topology foundation. When the bandgap distribution meets the requirements, use the current generation pile joint structure periodic fractal topology foundation as the final solution. When the bandgap distribution does not meet the requirements, continue to add an iteration algebra;

Alternatively, the method of increasing the iterative algebra step by step and adjusting the structural form and parameters of the periodic fractal topological foundation of the pile joint structure is adopted until the band gap distribution meets the requirements.

In the above technical scheme, the pile-column periodic fractal topological foundation of the second generation and above of the pile-column periodic fractal topological foundation is a periodic row of piles arranged in a nine-square grid, and the piles in the central grid of the nine-square grid The cross-sectional area of the nine-square grid is greater than the cross-sectional area of the piles of the outer circumference of the nine-square grid. When the iteration algebra is increased each time, the nine-square grid is arranged around the piles around the nine-square grid of the previous level as the center.

In the above technical solution, in the step 1, the vibration acceleration time history of the vehicle depot upper cover platform and the building structure column is obtained, and a one-third octave frequency analysis is performed, thereby obtaining the significant frequency band, preferably , the upper cover platform is the upper cover platform of the depot operation warehouse or maintenance warehouse.

In the above technical solution, in the step 2, the depot building column network information includes the column network plan, building column cross-sectional size, column network arrangement spacing and column buried depth.

In the above technical solution, in the step 3, the first-generation pile-column-column periodic fractal topological foundation is composed of a first-level center pile, and the second-generation pile-column-column periodic fractal topological foundation is composed of a first-level central pile. Composed of position piles and second-level central position piles, the third-generation pile-column joint structure periodic fractal pile arrangement is composed of first-level central position piles, second-level central position piles, and third-level central position piles; the M-generation periodic fractal pile arrangement structure It is composed of first-level center piles to M-level center piles. The side length of the upper-level center pile is N times the side length of the next-level center pile (N≥3, N is an integer); each generation of piles The minimum distance between the centers of the last level central position piles of the structural period fractal topological foundation, that is, the structural period constant is a.

Assuming that the cross-section of the depot building column is a square with side length L, the horizontal and vertical spacing of the building structure column is divided into H1 and W1;

Then the cross-section of the first-level central pile is a square with side length L, and the cross-section of the second-level central pile is a square with side length L/N. When the fractal topological foundation is formed, the minimum distance between the centers of the M-level central position piles, that is, the structural period constant is a (a≥0.5*(L+L/N) and 2a+N/L≤min{H1, W1}), N The initial value is 3.

In the above technical solution, in the step 4, when performing the dispersion calculation and band gap analysis, the finite element analysis method is adopted, combined with the Bloch theory, so that the infinite degrees of freedom of the periodic structure are condensed between the main control nodes of the research object primitives Above, the periodic structure bandgap can be solved in the basic unit domain, and then the periodic boundary condition U(r+a)=e ^iG·a U(r) is added on the boundary of the basic unit, where a is the structural periodic constant, and r is Position vector, i is a complex number symbol, G is a wave vector, establishes the relationship between the basic unit and the infinite periodic structure, the continuous field in each basic unit is represented by the node displacement and difference function of the unit, so that the continuous problem Discretization: the connection between the basic unit node displacement and the nodal force is established through a single stiffness matrix, and the adjacent basic units are structured through the balance equation of the node to form an overall stiffness matrix. The governing equations for the elements and the ensemble are as follows:

In the formula: m ^e and k ^e represent the mass and stiffness matrix of the unit, u ^e is the node displacement array, M and K represent the overall mass and stiffness matrix respectively, and u is the overall node displacement array;

The dispersion curve ω(G) is obtained by sweeping the irreducible Brillouin region with the Bloch wave vector G, and the blank band in the dispersion curve is the bandgap.

In the above technical scheme, for the evaluation of the bandgap characteristics of the second-generation pile-column periodic fractal topological foundation or the iterated M-generation pile-column periodic fractal topological foundation, if it occurs within the target frequency range in step 1 If the typical complete bandgap or directional bandgap is found, the bandgap distribution is considered to meet the requirements. If the typical complete bandgap or directional bandgap does not appear within the target frequency range, it is considered not to meet the requirements.

In the above technical solution, in the step 6, in the periodic fractal topology foundation structure of the pile-column joint structure, the pile length is the same as the column length of the building column.

In the above technical solution, in the step 7, periodic fractal structures with higher algebra are more likely to produce directional band gaps and complete band gaps, so the third-generation piles with M=3, 4, 5...M can be determined continuously The periodic fractal topology foundation of joint structure, the periodic fractal topology foundation of the fourth generation pile joint structure, the fifth generation pile joint structure periodic fractal topology foundation... The M generation pile joint structure periodic fractal topology foundation, and band gap calculation, Until a typical complete bandgap or directional bandgap appears in the target frequency range determined in step 1, it is deemed to meet the requirements, and the cycle can be ended to determine the final structural scheme;

In the step 7, the method for adjusting the structure and parameters is as follows:

Gradually increase the value of N, take N=4, 5, 6..., gradually reduce the side length of each level of central position pile except the first level of central position pile, and perform band gap calculation until the target determined in step 1 If a typical complete bandgap or directional bandgap appears in the frequency range, it is deemed to meet the requirements, and the cycle can be ended to determine the final structural scheme;

Or, gradually reduce the minimum distance between the centers of the last level of the center piles of the current generation of pile-column-column-column periodical fractal topological foundation, that is, gradually reduce the value of the period constant a, and increase the current-generation pile-column-column-column period in this way The filling rate of the piles of the last stage of the fractal topology foundation, the increase of the filling rate is realized by increasing the area of a single pile or reducing the distance between piles, which promotes the generation of directional band gaps and complete band gaps, and is beneficial to reducing the periodic constant The structure after a is subjected to bandgap calculation until a typical complete bandgap or directional bandgap appears within the target frequency range determined in step 1, which is deemed to meet the requirements, and the cycle can be ended to determine the final structural scheme.

Compared with prior art, the beneficial effect of the present invention is:

1. The present invention cuts in from the periodic structure band gap theory and fractal structure theory, and aims at the significant frequency band vibration of the upper cover platform of the subway car depot (or maintenance warehouse, etc.), and carries out periodic fractal design on the joint of pile foundation and building structure column. Pile foundations are arranged around it to realize the structural period fractal topological foundation structure, and the band gap calculation is performed on the pile-column joint structure periodic fractal topological foundation. , to improve the bandgap characteristics of the periodic fractal topological foundation of the pile-column structure. Through bandgap calculation and parametric analysis, a set of pile fractal topological foundation design methods suitable for the significant frequency band vibration control of the depot superstructure is formed.

2. Combined periodic fractal topology design of the pile foundation of the depot and the building structure column, so as to comprehensively improve its bandgap characteristics, increase the number and bandwidth of directional bandgap and complete bandgap, and achieve multi-band vibration reduction and wide-band vibration reduction And while comprehensively improving the vibration reduction effect, the pile diameter can be further reduced, and the construction cost can be reduced while comprehensively improving the vibration reduction effect.

Description of drawings

Fig. 1 is a flowchart of the present invention;

Fig. 2 is a schematic diagram of the periodic fractal topological foundation structure of the typical pile-column joint structure of the present invention;

Among Fig. 3, (a), (b), (c) are respectively the first, second, third generation pile joint structure periodic fractal topological foundation (M=1,2,3) schematic diagram of the present invention;

Figure 4 shows the typical vibration acceleration time history of the platform and structural columns when the depot trains in a certain depot pass through the test section, where (a) is the time history curve of the vibration acceleration of the column, and (b) is the time history curve of the surface vibration acceleration of the upper cover platform;

Figure 5 shows the one-third octave frequency of the typical vibration acceleration of the platform and structural columns when the depot trains in a certain depot pass through the test section;

Figure 6 is a column network diagram (partial) of a typical depot operation warehouse building;

Fig. 7 is the periodic fractal topological foundation (partial) of the second generation pile joint structure period fractal topology of the depot operation library in embodiment 1;

Fig. 8 is the bandgap distribution of the second-generation pile joint structure periodic fractal topological foundation in the depot application library in embodiment 1;

Fig. 9 is the periodic fractal topological basis of the third generation of pile-column joint structure using the library in embodiment 1;

Fig. 10 is the bandgap distribution of the second-generation pile joint structure periodic fractal topology foundation in the depot application library in embodiment 2;

Fig. 11 is the bandgap distribution of the second-generation pile-column joint structure period fractal topology foundation in the depot application library in embodiment 3.1;

Fig. 12 is the bandgap distribution of the second-generation pile joint structure periodic fractal topology foundation in the depot application library in embodiment 3.2;

Fig. 13 is the bandgap distribution of the second-generation pile joint structure periodic fractal topology foundation in the depot application library in embodiment 3.3;

In the picture: 1-first-level central position pile, 2-second-level central position pile, 3-third-level central position pile.

Detailed ways

The present invention will be described in further detail below in conjunction with specific examples. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

Example 1

A method for designing a periodic fractal topological foundation of a pile-column joint structure based on vibration control of the upper cover of a depot, comprising the following steps:

Step 1: Carry out vibration tests on the same type of subway depots, obtain the time history of vibration acceleration at the structural columns and floor (top platform) of the depot roof platform (Figure 4), and perform one-third octave analysis , the results are shown in Figure 5, the significant frequency band of vibration is 25Hz-50Hz, and this frequency band is used as the target frequency band of vibration isolation;

Step 2, extract the building column network information of the vehicle depot. The plan view of the column network is shown in Figure 6. The cross-section of the building column is a square with side length L=1.2m. The row spacing of the column network H ₁ =12.6m, W ₁ ＝8.4m, the buried depth of the column is 10m;

The building column is used as the first-level central pile 1;

Step 3, take N=3, therefore, the side length of the second-level central position pile 2 is 0.4m, and a=0.8m, then the minimum pile spacing of the second-level central position pile 2 is 0.8m.

Therefore, the first-generation central pile 1 cross-section of the first-generation pile-column joint structure periodic fractal topology foundation is a square with a side length of 1.2m, as shown in Figure 6;

The cross-section of the first-level central pile 1 of the second-generation pile joint structure periodic fractal topology foundation is a square with a side length of 1.2m, the cross-section of the second-level central pile 2 is a square with a side length of 0.4m, and the second-level central pile 2 is a square with a side length of 0.4m. The minimum distance a between the centers of Jiugongge where piles 2 are located is 0.8m (satisfying a≥0.5*(L+L/N) and 2a+N/L≤min{H ₁ , W ₁ }).

Step 4. Perform dispersion calculation and band gap analysis on the typical second-generation pile joint structure periodic fractal topological foundation. Finite element analysis method can be used, combined with Bloch theory, so that the infinite degrees of freedom of the periodic structure can be condensed into the research object foundation. above the main control node of the element, so that the band gap of the periodic structure can be solved in the basic unit domain, and then add the periodic boundary condition U(r+a)=e ^ik·a U(r) on the boundary of the basic unit, where a is Structural periodic constant, r is the position vector, i is the complex number symbol, k is the wave vector, and the relationship between the basic unit and the infinite periodic structure is established. The continuous field in each basic unit is represented by the node displacement and difference function of the monomer, thereby discretizing the continuous problem; the connection between the node displacement and the nodal force of the basic unit is established through a single rigid matrix, and The space is framed by the equilibrium equations of the nodes to form the overall stiffness matrix. The governing equations for the elements and the ensemble are as follows:

In the formula: m ^e and k ^e represent the mass and stiffness matrix of the unit, u ^e is the node displacement array, M and K represent the overall mass and stiffness matrix, respectively, and u is the overall node displacement array.

The dispersion curve ω(K) is obtained by sweeping the irreducible Brillouin region with Bloch wave vector k. The blank band in the dispersion curve is the bandgap.

The bandgap distribution can be calculated by using the specific parameters of this embodiment, and the bandgap distribution is shown in FIG. 8 .

Step 5, for the evaluation of the bandgap characteristics of the typical second-generation pile-column periodic fractal topology foundation, there are more than 3 typical complete bandgap or directional bands within the target frequency range (25-50Hz) determined in step 1 It is deemed to meet the requirements, and you can go to step 6. It is worth noting that there are 7 directional band gaps in the vibration frequency range of 0-80 Hz, which is more ideal. The number of band gaps and the bandwidth are relatively high. ideal.

Step 6, determine the second-generation co-structured periodic fractal topology infrastructure as the final solution. The technical parameters are as follows:

The cross-section of the building column is a square with side length L=1.2m, the column spacing H1=12.6m, the column spacing W1=8.4m, and the column burial depth is 10m;

The cross-section of the first-level central pile 1 of the second-generation pile joint structure periodic fractal topology foundation is a square with a side length of 1.2m, the cross-section of the second-level central pile 2 is a square with a side length of 0.4m, and the second-level central pile 2 is a square with a side length of 0.4m. The minimum distance a between the centers of Jiugonggege where piles 2 are located is 0.8m.

Example 2

The result of embodiment 1 is relatively ideal, and the second-generation co-structured periodical fractal topology infrastructure can be used as the final solution. In some cases, the band gap result in step 5 may not meet the requirements (the target determined in step 1 There is no typical directional bandgap or complete bandgap in the frequency range (25-50Hz).

For example, when the cross-section of the building column is a square with side length L=0.9m, the column spacing H1=12.6m, the column spacing W1=8.4m, and the column burial depth is 10m;

The cross-section of the first-level central pile 1 of the second-generation pile joint structure periodic fractal topology foundation is a square with a side length of 0.9m, the cross-section of the second-level central pile 2 is a square with a side length of 0.3m, and the cross-section of the second-level central pile 2 is a square with a side length of 0.3m. The minimum distance a between the center of Jiugongge where the position pile 2 is located is 0.9m, and the obtained band gap distribution is shown in Figure 10:

It can be seen from the figure that there is a directional band gap in the 25-50 Hz frequency band only in the X-M direction. In many cases, in order to isolate vibrations from different directions, it is necessary to generate a 25-50 Hz directional band in the Γ-X or M-Γ direction. Gap. At this time, you need to enter step 7, and there are three different adjustment methods in the following embodiment 3:

Example 3

Example 3.1

Adjust the structural form and parameters of the second-generation pile-column joint structure periodic fractal topological foundation. The specific adjustment method is as follows:

Periodic fractal structures with higher algebra are more likely to produce directional band gaps and complete band gaps, so we can continue to determine the periodic fractal topology foundation of the third-generation pile joint structure with M=3, as shown in Figure 9, and perform band gap calculations. The results As shown in Figure 11. Directional band gaps are generated in the Γ-X, M-Γ and X-M directions in the 25-50 Hz frequency band. The periodic fractal topological foundation of the third-generation pile joint structure with M=3 can be determined as the final structure, and the design and band gap analysis of the periodic fractal topological foundation of the fourth-generation pile joint structure with M=4 are no longer carried out.

Example 3.2

Taking N=4, the pile side length of the secondary central position of the second-generation pile-column joint-structure periodic fractal topology foundation becomes L/N=0.225m, and the band gap calculation and evaluation are carried out. The results are shown in Figure 12, in which It can be seen that a directional bandgap has been generated in the 25-29Hz frequency band in the M-Γ direction, which can produce a vibration damping effect in this direction, and the process can be ended. If it is necessary to generate a directional bandgap in the Γ-X direction, continue to adjust the parameters to calculate N =5.

Example 3.3

Reduce the value of the period constant a, such as a=0.8m, that is, the distance between the secondary center piles of the second-generation pile-column joint structure periodic fractal topology foundation is 0.8m. By this method, the distance between the piles is reduced and the filling rate of the piles is increased. , to promote the generation of directional bandgap and complete bandgap. As a result, as shown in Figure 13, directional bandgap is generated in the 25-50Hz frequency band in the Γ-X, M-Γ and X-M directions, and the process can be ended.

Claims

The design method for the periodic fractal topological vibration damping foundation of the pile-column joint structure on the upper cover of the depot is characterized in that it includes the following steps:

Step 1. Obtain the significant frequency bands of the platform vibration of the same type of vehicle depot and the vibration of building structural columns, and use this frequency band as the target frequency band of vibration isolation;

Step 2, extracting the building column network information of the vehicle depot, based on the building column, by arranging pile foundations around it to realize the construction of periodic fractal topology infrastructure;

Step 3, determining the structural form and parameters of the first-generation pile-column-column periodic fractal topological foundation and the second-generation pile-column-column-column periodic fractal topological foundation, and the building columns in step 2 are used as the first-generation pile-column joint structure The first-level central position pile of periodic fractal topological foundation;

Step 4, carry out frequency dispersion calculation and band gap analysis on the periodic fractal topological foundation of the second-generation pile joint structure, and obtain the band gap characteristics;

Step 5, evaluating the bandgap characteristics obtained in step 4, if the bandgap distribution meets the requirements, proceed to step 6; if the bandgap distribution does not meet the requirements, proceed to step 7;

Step 6, determine the second-generation pile joint structure periodic fractal topological infrastructure as the final solution;

Step 7, adjust the structural form and parameters of the second-generation pile joint structure periodic fractal topology foundation in step 3, and repeat steps 4-6;

Alternatively, in step 3, increase the iterative algebra of the periodic fractal topological foundation of the pile-column structure to the third generation, and perform frequency dispersion calculation and band gap analysis on the periodic fractal topological foundation of the pile-column structure of the third generation, if the band gap distribution conforms to The requirement is to use the third-generation periodic fractal topological foundation of the pile-column structure as the final solution. If it does not meet the requirements, continue to increase the iteration algebra. For each additional iteration algebra, the dispersion calculation is performed on the current-generation pile-column-column periodic fractal topology foundation. And band gap analysis, when the band gap distribution meets the requirements, the current generation of pile joint structure periodic fractal topology foundation is used as the final solution, when the band gap distribution does not meet the requirements, continue to add an iterative algebra;

Or use a combination of increasing the iterative algebra step by step and adjusting the structural form and parameters of the periodic fractal topology foundation of the pile joint structure until the band gap distribution meets the requirements.
The method for designing the pile-column-column-structured periodic fractal topological vibration-damping foundation of the vehicle depot upper cover according to claim 1, wherein the piles of the second generation and above the second-generation piles of the pile-column-column periodic fractal topological foundation The periodic fractal topological foundation of the column joint structure is the periodic row of piles arranged in the nine-square grid. The cross-sectional area of the piles in the central grid of the nine-square grid is larger than that of the piles on the outer perimeter of the nine-square grid. The surrounding piles are used as the center to arrange the nine-square grid.
The method for designing the periodic fractal topological vibration damping foundation of the pile-column structure of the vehicle depot superstructure according to claim 1, wherein in said step 1, the vibration acceleration time history of the vehicle depot superstructure platform and the building structure column is obtained , and perform one-third octave band analysis, thereby obtaining the significant frequency bands.
The pile-column joint-structure periodical fractal topology foundation design method for vibration control of the vehicle depot upper cover as claimed in claim 1, characterized in that, in the step 2, the building column network information of the vehicle depot includes the column network plan and the building column cross section Dimensions, arrangement spacing of column nets and column burial depth.
The method for designing the periodic fractal topological vibration damping foundation of the pile-column structure on the depot upper cover according to claim 1, wherein the first-generation pile-column structure periodic fractal topological foundation is composed of a first-level central position pile, The second-generation pile-column-column periodic fractal topological foundation consists of a first-level central pile and a second-level central pile, and the M-generation pile-column periodic fractal topological foundation consists of a first-level central pile to an M-level central pile. Together, M is a natural number greater than or equal to 3, and the side length of the upper-level center pile is N times the side length of the lower-level center pile;

The minimum distance between the centers of the last level of central position piles in each generation of pile-column-column periodic fractal topological foundation, that is, the structural period constant, is a.
The method for designing the periodic fractal topological vibration damping foundation of the pile-column upper cover of the vehicle depot as claimed in claim 5, wherein the cross-section of the building column of the vehicle depot is a square whose side length is L, and the transverse section of the building column is The longitudinal spacing is divided into H1 and W1, then the cross section of the first-level center pile is a square with side length L, and the cross-section of the second-level center pile is a square with side length L/N; N≥3, N is an integer , the initial value of N is 3; a≥0.5*(L+L/N) and 2a+N/L≤min{H1, W1}.
The method for designing the periodic fractal topological vibration damping foundation of the pile-column structure on the depot upper cover as claimed in claim 1, characterized in that, in the step 4, when performing frequency dispersion calculation and band gap analysis, the finite element analysis method is used , combined with the Bloch theory, the infinite degrees of freedom of the periodic structure are condensed on the main control node of the research object, so that the band gap of the periodic structure can be solved in the domain of the basic unit, and then the periodic boundary condition U( r+a)=e iG·a U(r), where a is the periodic constant of the structure, r is the position vector, i is the complex symbol, G is the wave vector, the relationship between the basic unit and the infinite periodic structure is established, each basic The continuous field in the unit is represented by the node displacement and difference function of the unit, thereby discretizing the continuous problem; the connection between the nodal displacement and the nodal force of the basic unit is established through a single rigid matrix, and the connection between adjacent basic units is through the node The balance equations are used to frame the overall stiffness matrix, and the governing equations for the elements and the whole are as follows:

In the formula: m e and k e represent the mass and stiffness matrix of the unit, u e is the node displacement array, M and K represent the overall mass and stiffness matrix respectively, and u is the overall node displacement array;

The dispersion curve ω(G) is obtained by sweeping the irreducible Brillouin region with the Bloch wave vector G, and the blank band in the dispersion curve is the bandgap.
The method for designing the periodic fractal topological vibration damping foundation of the pile-column structure on the depot upper cover as claimed in claim 1, wherein if a typical complete bandgap or directional bandgap occurs within the target frequency range in step 1 , it is considered that the bandgap distribution meets the requirements, and if there is no typical complete bandgap or directional bandgap within the target frequency range, it is considered not to meet the requirements.
The method for designing the pile-column-column-structure periodic fractal topological vibration-damping foundation of the depot upper cover as claimed in claim 1, wherein, in the pile-column-column periodic fractal topological foundation structure, the pile length is the same as the column length of the building column same.
The method for designing the pile-column-structure periodic fractal topological vibration-damping foundation of the depot upper cover as claimed in claim 1, characterized in that, in the step 7, the structural form and parameters of the pile-column-structure periodic fractal topological foundation are carried out The adjustment method is as follows: gradually increase the value of N, get N=4, 5, 6..., reduce the side length of each level of center position pile except the first level center position pile, and the side length of each level of center position pile Decrease step by step;

Or, gradually reduce the value of the period constant a, reduce the minimum distance between the centers of the last stage central position piles of the current generation of pile-column joint structure periodic fractal topological foundation, and increase the current generation of pile-column joint structure periodic fractal topological foundation in this way The filling rate of the piles of the last stage promotes the generation of directional band gaps and complete band gaps.