Method for calculating vibration response of foundation beam with locally-disengaged bottom under moving load

Abstract

The invention relates to a method for calculating the vibration response of a foundation beam with a locally-disengaged bottom under a moving load, and the method comprises the steps: determining a vibration equation of the foundation beam with the locally-disengaged bottom under the moving load according to the stress balance of the foundation beam; a separation variable method is adopted to determine a vibration modal equation of the foundation beam with the locally-void bottom; determining a vibration mode expression of the foundation beam by adopting an analytical method according to the vibration mode equation of the foundation beam with the locally-void bottom; according to boundary conditions and continuous conditions of the foundation beam, establishing a linear equation set of undetermined parameters in the free vibration frequency and vibration mode expression of the foundation beam with the locally-void bottom; determining a generalized coordinate of the vibration mode of the bottom local void foundation beam according to the vibration mode of the bottom local void foundation beam and the orthogonality of the structural vibration mode; and according to a structural vibration mode superposition principle, a vibration response expression of the foundation beam with the locally-disengaged bottom under the moving load is determined. The method is beneficial to accurately analyzing and predicting the dynamic response influence of the bottom void on the foundation beam under the excitation of the moving load.

Description

Technical Field

[0001] The invention relates to the technical field of building engineering, and in particular to a method for calculating the vibration response of a foundation beam with a local hollow bottom under a moving load. Background Art

[0002] As vehicle speeds increase, the dynamic response of road and railway systems under traffic loads has attracted much attention. However, due to the effects of underground pipeline leakage, plastic deformation of roadbeds, and subway tunnel construction, local voids in concrete pavements frequently occur. In addition, under the coupling effects of train dynamic loads, temperature, and rain, tiny cracks on the connection surface between double-block sleepers and the ballast plate gradually develop into voids. Local voids in the foundation will aggravate the dynamic response of the structure under vehicle loads and shorten the service life of the structure. The dynamic interaction problem between the pavement, track, and foundation under vehicle loads can usually be simplified to the dynamic problem of elastic foundation beams under moving loads.

[0003] At present, some scholars have conducted relevant research on the dynamic response of non-continuous beams under moving loads. Some studies have used the finite element method to solve the dynamic response problem of non-local foundation beams. Some studies have established the free vibration equation of rectangular plates on non-uniform Winkler-Pasternak elastic foundations, and used the differential transformation method to obtain its natural frequency characteristic equation. The theoretical analytical method is highly favored because of its clear concepts, high computational efficiency, simplicity and practicality. Some studies have introduced non-local damping models into the dynamic control equations of Euler beams and Kirchoff plates, and used the Galerkin method to obtain approximate solutions of complex eigenvalues ​​and complex modes. Other studies have used the integral transformation method to derive the modal functions of non-local damping foundation beams.

[0004] At present, there are many analytical calculation methods for the dynamic response of non-continuous beam systems under moving loads, but there are few studies on the influence of bottom voids on the dynamic response of foundation beams and their analytical methods. Summary of the invention

[0005] The object of the present invention is to provide a method for calculating the vibration response of a foundation beam with a partially debonded bottom under a moving load, which method is conducive to accurately analyzing and predicting the influence of the bottom debonding on the dynamic response of the foundation beam under the excitation of the moving load.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is: a method for calculating the vibration response of a foundation beam with a local bottom void under a moving load, comprising the following steps:

[0007] S1. According to the force balance of the foundation beam, determine the vibration equation of the foundation beam with local bottom debonding under moving load;

[0008] S2. According to the vibration equation of the bottom partially hollowed foundation beam under the moving load, the vibration modal equation of the bottom partially hollowed foundation beam is determined by using the separation variable method;

[0009] S3. According to the vibration modal equation of the bottom partially hollow foundation beam, the vibration modal expression is determined by using an analytical method;

[0010] S4. According to the boundary conditions and continuity conditions of the foundation beam, a linear equation group is established regarding the free vibration frequency of the bottom partially deprived foundation beam and the undetermined parameters in the vibration mode expression;

[0011] S5. Determine the generalized coordinates of the vibration mode of the bottom partially hollowed-out foundation beam under the moving load according to the vibration mode of the bottom partially hollowed-out foundation beam and the orthogonality of the structural vibration mode;

[0012] S6. According to the principle of structural vibration modal superposition, determine the vibration response expression of the foundation beam with local debonding at the bottom under moving load.

[0013] Furthermore, in step S1, the specific form of the vibration equation of the bottom partially deprived foundation beam under the moving load is as follows:

[0014]

[0015] Where: w(x,t) is the vertical vibration displacement of the beam, x is the horizontal coordinate, t is the time; EI is the bending stiffness of the beam, m is the mass per unit length of the beam, k is the foundation coefficient, and c is the foundation damping coefficient; F(x,t) is the moving load, F(x,t) = F0·δ(x-vt), F0 is the load size, δ(x-vt) is the Dirac-delta function, and v is the load moving speed; H(x) is the step function, L1 and L2 are the lengths of the left and right sections of the beam respectively, and s is the half-width of the void area.

[0016] Furthermore, the implementation method of step S2 is:

[0017] According to the vibration equation of the foundation beam with local void at the bottom under moving load, the free vibration equation of the foundation beam with local void at the bottom is:

[0018]

[0019] According to the separation of variables method, assuming that w(x,t) = φ(x)·T(t), φ(x) is the vibration mode of the beam, and T(t) is the generalized coordinate of the beam vibration; substituting it into the free vibration equation of the beam with local void foundation at the bottom, we get:

[0020]

[0021] Arranged:

[0022]

[0023] Then the specific form of the vibration modal equation of the foundation beam with local void at the bottom is obtained as follows:

[0024]

[0025] Where: ω is the vibration frequency.

[0026] Furthermore, the step S3 specifically includes:

[0027] 3.1. The vibration modal equation of the grounded beam is:

[0028]

[0029] The corresponding characteristic equation is:

[0030]

[0031] The roots of the characteristic equation are:

[0032] hour,

[0033] hour, The vibration mode of the grounded beam is obtained as follows:

[0034]

[0035] Where: φ1(x) is the vibration mode of the grounded beam, a1-a8 are unknown coefficients; 3.2. The vibration modal equation of the grounding section beam is:

[0036]

[0037] The corresponding characteristic equation is:

[0038]

[0039] The roots of the characteristic equation are:

[0040]

[0041] The vibration mode of the middle hollow section beam is obtained as follows:

[0042] φ2(x)=b1sin(β3x)+b2cos(β3x)+b3sinh(β3x)+b4cosh(β3x) (4)

[0043] Where: φ2(x) is the vibration mode of the hollow section beam, b1-b4 are unknown coefficients.

[0044] Furthermore, the step S4 specifically includes:

[0045] 4.1. Based on the freedom of both ends of the beam, establish the following boundary conditions:

[0046]

[0047] Where: L1 and L2 are the lengths of the left and right sections of the beam respectively;

[0048] 4.2. According to the continuity of displacement and internal force of the beam at the segment, the following continuity conditions are established:

[0049]

[0050] 4.3. Based on the above boundary conditions and continuity conditions, a linear equation system is established for the free vibration frequency of the bottom partially debonded foundation beam and the undetermined coefficients in the vibration mode expression, which is rewritten into a matrix form as follows:

[0051]

[0052] Where: A 4×1 , B 4×1 and A4′ ×1 are matrices composed of the coefficients of the vibration modal expressions of the left grounded foundation beam, the middle empty section beam, and the right grounded foundation beam; C 2×4 , D 4×4 、E 4×4 、F 4×4 , G 4×4 and H 2×4 are non-zero matrices respectively;

[0053] A 4×1 =[a1 a2 a3 a4] Γ , A4′ ×1 =[a1′a2′a3′a4′] Γ ;

[0054]

[0055]

[0056] When B 4×1 =[b1b2 b3 b4] Γ ,

[0057]

[0058] When B 4×1 =[b5b6 b7 b8] Γ,

[0059]

[0060]

[0061] Furthermore, the step S5 specifically includes:

[0062] 5.1. According to the vibration mode of the foundation beam with partial hollowing at the bottom and the orthogonality of the structural vibration mode, the generalized coordinate equation of the vibration mode of the foundation beam with partial hollowing at the bottom under the moving load is determined; the generalized coordinate equation of any n-th order vibration mode is:

[0063]

[0064] Where:

[0065]

[0066] 5.2. According to the Duhamel integration method, the generalized coordinates of each vibration mode of the bottom partially debonded foundation beam under moving load are determined; the generalized coordinates of any n-th vibration mode are:

[0067]

[0068] Where:

[0069] Furthermore, in step S6, the expression for the vibration response of the bottom partially debonded foundation beam under the moving load is:

[0070]

[0071] Compared with the prior art, the present invention has the following beneficial effects: the present invention provides a method for calculating the vibration response of a foundation beam with a partial bottom debonding under a moving load. The method proposes a modal expression for the vibration of a foundation beam with a partial bottom debonding, and then uses the vibration mode superposition method to calculate the steady-state response solution of the foundation beam with a partial bottom debonding under the action of the moving load. The calculation expression of this method has clear physical meaning, higher calculation efficiency, and more accurate calculation results, thereby accurately analyzing and predicting the influence of the partial bottom debonding on the dynamic response of the foundation beam under the moving load. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 It is a dynamic response calculation model of a foundation beam with a local bottom void in an embodiment of the present invention;

[0073] Figure 2 is a flow chart of a method implementation of an embodiment of the present invention;

[0074] Figure 3 It is the vibration displacement time history curve of the beam midpoint in the embodiment of the present invention. DETAILED DESCRIPTION

[0075] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0076] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0077] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0078] This embodiment provides a method for calculating the vibration response of a foundation beam with a partial bottom void under a moving load. The corresponding dynamic response calculation model of the foundation beam with a partial bottom void is as follows: Figure 1 In this embodiment, it is assumed that the beam thickness h = 400 mm and the beam elastic modulus E b =25Gpa, foundation elastic coefficient k=7.7Mpa, foundation damping coefficient c=100kN·m -1 ·s, total length of beam 2L=40m, width of hollow area 2s=0.5m, load moving speed v=30m / s, load F=50kN.

[0079] like Figure 2 As shown, the specific implementation steps of this method are as follows.

[0080] S1. According to the force balance of the foundation beam, determine the vibration equation of the foundation beam with local bottom debonding under moving load. The specific form is as follows:

[0081]

[0082] Where: w(x,t) is the vertical vibration displacement of the beam, x is the horizontal coordinate, t is the time; EI is the bending stiffness of the beam, m is the mass per unit length of the beam, k is the foundation coefficient, and c is the foundation damping coefficient; F(x,t) is the moving load, F(x,t) = F0·δ(x-vt), F0 is the load size, δ(x-vt) is the Dirac-delta function, and v is the load moving speed; H(x) is the step function, L1 and L2 are the lengths of the left and right sections of the beam respectively, and s is the half-width of the void area.

[0083] S2. Based on the vibration equation of the foundation beam with partial hollowing out at the bottom under moving load, the vibration modal equation of the foundation beam with partial hollowing out at the bottom is determined by using the separation of variables method.

[0084] The implementation method of step S2 is:

[0085] According to the vibration equation of the foundation beam with local void at the bottom, the free vibration equation of the foundation beam with local void at the bottom is:

[0086]

[0087] According to the separation of variables method, assuming that w(x,t) = φ(x)·T(t), φ(x) is the vibration mode of the beam, and T(t) is the generalized coordinate of the beam vibration; substituting it into the free vibration equation of the beam with local void foundation at the bottom, we get:

[0088]

[0089] Arranged:

[0090]

[0091] Then the specific form of the vibration modal equation of the foundation beam with local void at the bottom is obtained as follows:

[0092]

[0093] Where: ω is the vibration frequency.

[0094] S3. According to the vibration modal equation of the foundation beam with local void at the bottom, the vibration modal expression is determined by using analytical method.

[0095] The step S3 specifically includes:

[0096] 3.1. The vibration modal equation of the grounded section (H(x) = 1) beam is:

[0097]

[0098] The corresponding characteristic equation is:

[0099]

[0100] The roots of the characteristic equation are:

[0101] hour,

[0102] hour,

[0103] The vibration mode of the grounded beam is obtained as follows:

[0104]

[0105] Where: φ1(x) is the vibration mode of the grounded beam, a1-a8 are unknown coefficients.

[0106] 3.2. The vibration modal equation of the beam in the grounded section (H(x) = 0) is:

[0107]

[0108] The corresponding characteristic equation is:

[0109]

[0110] The roots of the characteristic equation are:

[0111]

[0112] The vibration mode of the middle hollow section beam is obtained as follows:

[0113] φ2(x)=b1 sin(β3x)+b2 cos(β3x)+b3 sinh(β3x)+b4 cosh(β3x) (4)

[0114] Where: φ2(x) is the vibration mode of the hollow section beam, b1-b4 are unknown coefficients.

[0115] S4. According to the boundary conditions and continuity conditions of the foundation beam, a set of linear equations for the free vibration frequency of the bottom partially deprived foundation beam and the unknown parameters in the vibration mode expression are established.

[0116] The step S4 specifically includes:

[0117] 4.1. Based on the freedom of both ends of the beam, establish the following boundary conditions:

[0118]

[0119] Where: L1 and L2 are the lengths of the left and right sections of the beam respectively.

[0120] 4.2. According to the continuity of displacement and internal force of the beam at the segment, the following continuity conditions are established:

[0121]

[0122] 4.3. Based on the above boundary conditions and continuity conditions, a linear equation system is established for the free vibration frequency of the bottom partially debonded foundation beam and the undetermined coefficients in the vibration mode expression, which is rewritten into a matrix form as follows:

[0123]

[0124] Where: A 4×1 , B 4×1 and A4′ ×1 are matrices composed of the coefficients of the vibration modal expressions of the left grounded foundation beam, the middle empty section beam, and the right grounded foundation beam; C 2×4 , D 4×4 、E 4×4 、F 4×4 , G 4×4 and H 2×4 are non-zero matrices respectively.

[0125] A 4×1 =[a1 a2 a3 a4] Γ , A4′ ×1 =[a1′a2′a3′a4′] Γ ;

[0126]

[0127] When B 4×1 =[b1b2 b3 b4] Γ ,

[0128]

[0129] When B 4×1 =[b5b6 b7 b8] Γ ,

[0130]

[0131]

[0132] Enter the model parameters, and solve the vibration frequency and undetermined parameters of the hollow foundation beam as shown in Table 1:

[0133] Table 1 Calculation results of vibration frequency and vibration mode parameters of foundation beam

[0134] parameter Stage 1 Stage 2 Tier 3 Tier 4 Tier 5 Tier 6 Tier 7 <![CDATA[ω / rad·s -1 ]]> 86.0 89.3 103.4 140.3 202.0 286.0 390.4 <![CDATA[a1]]> 0.63 0.32 0.087 0.031 0.0144 -0.0078 -0.0046 <![CDATA[a2]]> 0.63 -0.76 -0.790 -0.747 -0.725 0.716 0.712 <![CDATA[a3]]> 0 -0.32 -0.087 -0.031 -0.0145 0.0079 0.00479 <![CDATA[a4]]> 0 0.32 0.087 0.031 0.0145 -0.0079 -0.00479 <![CDATA[b1(b5)]]> 0 0 0 0 0 0 0 <![CDATA[b2(b6)]]> 0.38 -0.32 -0.582 -0.660 -0.68 0.69 0.702 <![CDATA[b3(b7)]]> 0 0 0 0 0 0 0 <![CDATA[b4(b8)]]> 0.25 -0.12 -0.12 -0.056 -0.023 0.01 0.00495 <![CDATA[a1′]]> 0.63 0.32 0.087 0.031 0.0144 -0.0078 -0.0046 <![CDATA[a2′]]> 0.63 -0.76 -0.790 -0.747 -0.725 0.716 0.712 <![CDATA[a3′]]> 0 -0.32 -0.087 -0.031 -0.0145 0.0079 0.00479 <![CDATA[a4′]]> 0 0.32 0.087 0.031 0.0145 -0.0079 -0.00479

[0135] S5. According to the vibration mode of the foundation beam with partial hollowing out at the bottom and the orthogonality of the structural vibration mode, the generalized coordinates of the vibration mode of the foundation beam with partial hollowing out at the bottom under the moving load are determined.

[0136] The step S5 specifically includes:

[0137] 5.1. According to the vibration mode of the foundation beam with partial hollowing at the bottom and the orthogonality of the structural vibration mode, the generalized coordinate equation of the vibration mode of the foundation beam with partial hollowing at the bottom under the moving load is determined; the generalized coordinate equation of any n-th order vibration mode is:

[0138]

[0139] Where:

[0140]

[0141] 5.2. According to the Duhamel integration method, the generalized coordinates of each vibration mode of the bottom partially debonded foundation beam under moving load are determined; the generalized coordinates of any n-th vibration mode are:

[0142]

[0143] Where:

[0144] S6. According to the principle of structural vibration mode superposition, determine the vibration response expression of the bottom partially deprived foundation beam under moving load. The specific form is as follows:

[0145]

[0146] The vibration displacement time history curve of the beam midpoint in this embodiment is as follows: Figure 3 According to formula (10) and the above calculation process, the figure can be drawn using the Matlab program.

[0147] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0148] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0149] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0150] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0151] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims

1. A method for calculating the vibration response of a foundation beam with a partially hollow bottom under a moving load, characterized in that: The following steps are involved: S1. According to the force balance of the foundation beam, determine the vibration equation of the foundation beam with local bottom debonding under moving load; S2. According to the vibration equation of the bottom partially hollowed foundation beam under the moving load, the vibration modal equation of the bottom partially hollowed foundation beam is determined by using the separation variable method; S3. According to the vibration modal equation of the bottom partially hollow foundation beam, the vibration modal expression is determined by using an analytical method; S4. According to the boundary conditions and continuity conditions of the foundation beam, a linear equation group is established regarding the free vibration frequency of the bottom partially deprived foundation beam and the undetermined parameters in the vibration mode expression; S5. Determine the generalized coordinates of the vibration mode of the bottom partially hollowed-out foundation beam under the moving load according to the vibration mode of the bottom partially hollowed-out foundation beam and the orthogonality of the structural vibration mode; S6. According to the principle of structural vibration modal superposition, determine the vibration response expression of the foundation beam with local debonding at the bottom under moving load.

2. The method for calculating the vibration response of a foundation beam with a partially debonded bottom under a moving load according to claim 1 is characterized in that: In step S1, the specific form of the vibration equation of the bottom partially deprived foundation beam under the moving load is as follows: Where: w(x,t) is the vertical vibration displacement of the beam, x is the horizontal coordinate, t is the time; EI is the bending stiffness of the beam, m is the mass per unit length of the beam, k is the foundation coefficient, and c is the foundation damping coefficient; F(x,t) is the moving load, F(x,t) = F0·δ(x-vt), F0 is the load size, δ(x-vt) is the Dirac-delta function, and v is the load moving speed; H(x) is the step function, L1 and L2 are the lengths of the left and right sections of the beam respectively, and s is the half-width of the void area.

3. The method for calculating the vibration response of a foundation beam with a partially hollow bottom under a moving load according to claim 1 is characterized in that: The implementation method of step S2 is: According to the vibration equation of the foundation beam with local void at the bottom under moving load, the free vibration equation of the foundation beam with local void at the bottom is: According to the separation of variables method, assuming that w(x,t) = φ(x)·T(t), φ(x) is the vibration mode of the beam, and T(t) is the generalized coordinate of the beam vibration; substituting it into the free vibration equation of the beam with local void foundation at the bottom, we get: Arranged: Then the specific form of the vibration modal equation of the foundation beam with local void at the bottom is obtained as follows: Where: ω is the vibration frequency.

4. The method for calculating the vibration response of a foundation beam with a partially debonded bottom under a moving load according to claim 1 is characterized in that: The step S3 specifically includes: 3.

1. The vibration modal equation of the grounded beam is: The corresponding characteristic equation is: The roots of the characteristic equation are: hour, hour, The vibration mode of the grounded beam is obtained as follows: Where: φ1(x) is the vibration mode of the grounded beam, a1-a8 are undetermined coefficients; 3.

2. The vibration modal equation of the grounded beam is: The corresponding characteristic equation is: The roots of the characteristic equation are: The vibration mode of the middle hollow section beam is obtained as follows: φ2(x)=b1sin(β3x)+b2cos(β3x)+b3sinh(β3x)+b4cosh(β3x)(4) Where: φ2(x) is the vibration mode of the hollow section beam, b1-b4 are unknown coefficients.

5. The method for calculating the vibration response of a foundation beam with a partially debonded bottom under a moving load according to claim 1 is characterized in that: The step S4 specifically includes: 4.

1. Based on the freedom of both ends of the beam, establish the following boundary conditions: Where: L1 and L2 are the lengths of the left and right sections of the beam respectively; 4.

2. According to the continuity of displacement and internal force of the beam at the segment, the following continuity conditions are established: 4.

3. Based on the above boundary conditions and continuity conditions, a linear equation system is established for the free vibration frequency of the bottom partially debonded foundation beam and the undetermined coefficients in the vibration mode expression, which is rewritten into a matrix form as follows: Where: A 4×1 , B 4×1 and A4′ ×1 are matrices composed of the coefficients of the vibration modal expressions of the left grounded foundation beam, the middle empty section beam, and the right grounded foundation beam; C 2×4 , D 4×4 、E 4×4 、F 4×4 , G 4×4 and H 2×4 are non-zero matrices respectively; <h2 style=";text-align:left;direction:ltr">A<h2 style=";text-align:left;direction:ltr"> 4×1 <h2 style=";text-align:left;direction:ltr"> =[a1a2a3a4]<h2 style=";text-align:left;direction:ltr"> Γ <h2 style=";text-align:left;direction:ltr"> A4′<h2 style=";text-align:left;direction:ltr"> ×1 <h2 style=";text-align:left;direction:ltr"> (a1′a2′a3′a4′)<h2 style=";text-align:left;direction:ltr"> Γ <h2 style=";text-align:left;direction:ltr"> ; When B 4×1 =[b1b2b3b4] Γ , When B 4×1 =[b5b6b7b8] Γ , 6. The method for calculating the vibration response of a foundation beam with a partially debonded bottom under a moving load according to claim 1 is characterized in that: The step S5 specifically includes: 5.

1. According to the vibration mode of the foundation beam with partial hollowing at the bottom and the orthogonality of the structural vibration mode, the generalized coordinate equation of the vibration mode of the foundation beam with partial hollowing at the bottom under the moving load is determined; the generalized coordinate equation of any n-th order vibration mode is: Where: 5.

2. According to the Duhamel integration method, the generalized coordinates of each vibration mode of the bottom partially debonded foundation beam under moving load are determined; the generalized coordinates of any n-th vibration mode are: Where:

7. The method for calculating the vibration response of a foundation beam with a partially debonded bottom under a moving load according to claim 1 is characterized in that: In step S6, the expression of the vibration response of the bottom partially debonded foundation beam under the moving load is:

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