A method for predicting the vibration response of building structures caused by train operation
By establishing models of trains, tracks and building structures, and considering the coupling relationship, calculating the wheel and rail contact force and building structure vibration acceleration time course curve, the problem of difficulty in accurately predicting the vibration response of building structures caused by train operation in the prior art is solved, and fast and accurate vibration prediction and control are achieved.
Patent Information
- Application Number
- CN202410493088.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-04-23
- Publication Date
- 2025-03-21
- Estimated Expiration
- 2044-04-23
AI Technical Summary
The prior art is difficult to accurately predict and control the vibration response caused by trains operating within building structures, resulting in excessive vibration of buildings and affecting building applicability.
By obtaining the design parameters of trains and building structures, establishing train models, track models and building structure models, and considering the coupling relationship between trains and tracks and tracks and buildings, calculating the wheel and rail contact force and the vibration acceleration time course curve of building structures, and achieving rapid and accurate prediction of the vibration response of building structures.
This method can quickly and accurately predict the vibration response of the building structure when taking into account the direct action of the train vibration source, and provide a design basis to reduce vibration and reduce the risk of vibration control of the overhead building of the subway depot.
Smart Images
Figure CN118194598B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of rail transit environment vibration prediction, and in particular relates to a method for predicting the vibration response of a building structure caused by train operation. Background Art
[0002] Subway depots are places for daily inspection and maintenance of trains, often occupying a large amount of urban land and dividing urban space areas. Therefore, in order to rationally develop urban space, subway roof buildings have been rapidly promoted and developed. Elevated subway depots have been proposed to replace the traditional solution of trains running on the ground or underground, allowing trains to enter the 2nd or 3rd floor of the depot through elevated routes, thereby making more intensive use of land resources. However, due to the lack of soil attenuation on vibration, when trains enter the interior of the building, it will cause excessive vibration of the building floor, leading to environmental vibration problems, which is a major challenge faced by rail transit projects.
[0003] The lack of accurate prediction and effective control of excessive vibration may seriously affect the serviceability of buildings. Therefore, vibration must be evaluated in the design stage to provide a basis for the reasonable design of vibration mitigation measures. Before the design of building vibration control, fast and accurate prediction is indispensable. Most of the existing technical solutions for the prediction of vibration response caused by train operation inside building structures focus on numerical simulation and related analytical algorithms. For numerical simulation research, with the large-scale development of buildings along rail transit lines, the establishment of a large finite element model including strata and structures faces a series of problems such as low computational efficiency and difficulty in quantifying soil parameters and computational boundary conditions, which makes the calculation results inaccurate and the subsequent vibration mitigation measures unreasonable. The relevant analytical methods for predicting the vibration response of building structures include the spectral unit method, the dynamic stiffness matrix analysis method based on the frequency domain, and the impedance model method. The rapid vibration prediction methods established by these analytical methods do not take into account the role of the vibration source, and require additional input of the excitation of the required node position to solve the vibration response of the building structure. Summary of the invention
[0004] The purpose of the present invention is to solve the problem of lack of a method for predicting the vibration response of a building caused by the running of a train on the floor of a building in the field of rail transit environmental vibration, and to provide a method for predicting the vibration response of a building structure caused by the running of a train.
[0005] The analytical method for quickly predicting the vibration response of building structures requires the use of additional methods to obtain excitations and input them into the building structure base to predict the vibration response of the structure, but it cannot directly consider the effect of the vibration source to predict the vibration response of the building structure, and is subject to many restrictions. The establishment of a prediction method for the vibration response of building structures that considers the effect of the vibration source of trains running on the floor fully considers the dynamic effect of trains, which plays a key role in quickly and accurately predicting the vibration characteristics of building structures.
[0006] In view of the above problems, the present invention provides a method for predicting the vibration response of a building structure caused by train operation. The method can quickly and accurately predict the vibration response of a building structure while considering the direct effect of the train vibration source on the building floor. This method helps to provide a design basis for the impact prediction and vibration reduction and mitigation measures selection of such building structures, and is of great significance for the vibration control risk management of buildings above subway depots.
[0007] The purpose of the present invention is achieved through the following technical solutions.
[0008] A method for predicting the vibration response of a building structure caused by train operation comprises the following steps:
[0009] S1. Obtain train dynamics design parameters and establish a train model;
[0010] S2, obtaining track structure design parameters and establishing a track model;
[0011] S3. Using the train-track contact relationship, establish a train-track structure model;
[0012] S4, obtaining the design parameters of the building structure at the operating location and establishing a building structure model;
[0013] S5. Using the contact conditions between the track structure and the building structure, a train-track structure-building structure coupling model is established;
[0014] S6. Consider the influence of track irregularity to calculate the wheel-rail contact force generated by train operation;
[0015] S7. Calculate the vibration acceleration time history curves of the track structure and building structure.
[0016] According to a method for predicting the vibration response of a building structure caused by train operation disclosed in the present invention, preferably, the train dynamics design parameters in step S1 include the body mass m of the locomotive and trailer. c , bogie mass m t , wheelset mass m w , the moment of inertia of the car body and bogie center of mass J c and J t , stiffness and damping k of primary and secondary suspension Js ,k Jp ,c Js ,c Jp , and the corresponding vehicle length L Jt and vehicle distance L J1 , bogie wheelbase L J2 .
[0017] Preferably, the train model in step S1 is composed of multiple locomotives and trailers, and each vehicle is considered as a multi-rigid spring and damping system. The mass, stiffness, and damping matrix expressions for constructing the train model are:
[0018] M v =diag[M v1 ,M v2 ,M vj ,...,M vNv ]
[0019] K v =diag[K v1 ,K v2 ,K vj ,...,K vNv ]
[0020]
[0021] Where N v Represents the number of vehicles constituting the train model, M vj ,K vj ,C vj They represent the vehicle mass, stiffness, and damping matrix that make up the train model respectively.
[0022] Preferably, the track structure design parameters in step S2 include the rail elastic modulus E r , moment of inertia of rail center of mass I r , rail mass per unit length Rail cross-sectional area A r ; Elastic modulus of track plate E s , track plate density ρ s , track plate center of mass inertia moment I s , track plate width B s and thickness H s ; Fastener stiffness k rs and the damping coefficient c rs .
[0023] Preferably, the track model in step S2 is composed of a track and a track plate, wherein the track is composed of a Bernoulli Euler beam unit, and the track plate is composed of an elastic thin plate unit. The track and track plate structures are connected by fasteners equivalent to springs and dampers, and the stiffness and damping matrix expressions constructed are respectively:
[0024]
[0025]
[0026] Where N rs represents the shape function of the orbital element, n p represents the total number of discrete fasteners, krs and c rs represent the fastener stiffness and damping coefficient respectively.
[0027] Preferably, the train-rail contact relationship in step S3 adopts Hertzian nonlinear contact, and the expression of Hertzian nonlinear wheel-rail vertical contact force is:
[0028]
[0029] where q v and q r They represent the vertical displacement of the contact point between the wheel and the rail, h represents the vertical irregularity amplitude of the rail, and G represents the contact constant between the wheel and the rail.
[0030] Preferably, in step S3, a train-track structure model is established, and its motion equation is expressed as:
[0031]
[0032] Where M, C and K in the equation of motion represent the mass, damping and stiffness matrices of the train or track structure, respectively. and X represent the acceleration, velocity and displacement vector of the train or track structure, respectively, and F v / r is the wheel-rail vertical contact force vector.
[0033] Preferably, the building structure design parameters in step S4 include floor density ρ f , elastic modulus of floor slab E f 、Moment of inertia of floor mass center I f , Floor thickness H f 、Floor width W f and length L f ; Mass per unit length of structural column Elastic modulus of structural column E c 、Moment of inertia of the center of mass of the structural column I c 、Cross-sectional area of structural column A c , Structural column length L c ; Beam mass per unit length Beam elastic modulus E bm , beam center of mass moment of inertia I bm , beam cross-sectional area A bm .
[0034] Preferably, the building structure model in step S4 is composed of concrete floor slabs, structural columns and beams, wherein the structural columns and beams are composed of Bernoulli-Euler beam units, and the floor slabs are composed of elastic thin plate units.
[0035] Preferably, in step S5, the contact condition between the track structure and the building structure is connected by CA mortar, and the CA mortar is simplified into continuously distributed springs and dampers, and the expressions of the unit stiffness and damping matrix are respectively:
[0036]
[0037]
[0038] Where N tf represents the shape function of the track plate element, and denote the spring and damper stiffness and damping coefficient of the continuous distribution under the track plate, a and b denote half of the length and width of the elastic thin plate unit, respectively. s or f Indicates the thickness of the track plate or floor slab.
[0039] Preferably, in step S5, a train-track structure-building structure coupling model is established, and its motion equation is expressed as:
[0040]
[0041] Among them, M total , C total , K total Represent the overall mass, damping, and stiffness matrices of the coupled model, respectively. q represents the full-node acceleration, velocity, and displacement vector of the coupled model, and F represents the overall force vector of the coupled model.
[0042] Preferably, in step S6, the impact of track vertical irregularity adopts the American six-level spectrum and considers short-wave irregularity, and its power spectrum density expression is:
[0043]
[0044] Among them A v =3.39×10 -6 m 2 / (rad / m),Ω c =0.8245rad / m, Ω is the cut-off frequency range. According to the power spectrum density, the trigonometric series method is used to calculate the vertical irregularity amplitude of the generated track and calculate the wheel-rail contact force generated by the contact between the train and the track.
[0045] Preferably, the vibration acceleration time history curves of the track structure and the building structure in step S7 are the vibration responses of the track structure and the building structure.
[0046] It can be seen from the above technical solutions that the advantages and positive effects of the present invention are:
[0047] The present invention provides a method for predicting the vibration response of a building structure caused by train operation. The train is simplified into a multi-rigid body vehicle connected by multiple springs and dampers, a train model is constructed, and calculation efficiency is improved. The established building structure model takes into account the influence of structural columns and beams, and considers factors more comprehensively. At the same time, the influence of vertical unevenness of the track, that is, the role of the vibration source, is considered, and the obtained prediction result is more accurate and reasonable. BRIEF DESCRIPTION OF THE DRAWINGS
[0048] Figure 1 A schematic diagram of a block diagram of the steps of a method for predicting vibration response of a building structure caused by train operation according to an embodiment of the present invention is shown;
[0049] Figure 2 A schematic diagram of a train model according to an embodiment of the present invention is shown;
[0050] Figure 3 A schematic diagram of a track structure model according to an embodiment of the present invention is shown;
[0051] Figure 4 A schematic diagram of a train-track structure model according to an embodiment of the present invention is shown;
[0052] Figure 5 A schematic diagram of a building structure model according to an embodiment of the present invention is shown;
[0053] Figure 6 A schematic diagram of a train-track structure-building structure coupling model according to an embodiment of the present invention is shown;
[0054] Figure 7 A schematic diagram of a time history curve of building floor vibration acceleration calculated according to an embodiment of the present invention is shown. DETAILED DESCRIPTION
[0055] In order to make the purpose, features and advantages of the present invention more obvious and understandable, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.
[0056] Obviously, the embodiments described below are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0057] like Figure 1 As shown, the present invention provides a method for predicting the vibration response of a building structure caused by train operation, comprising the following steps:
[0058] S1. Obtain train dynamics design parameters and establish a train model;
[0059] S2, obtaining track structure design parameters and establishing a track model;
[0060] S3. Using the train-track contact relationship, establish a train-track structure model;
[0061] S4, obtaining the design parameters of the building structure at the operating location and establishing a building structure model;
[0062] S5. Using the contact conditions between the track structure and the building structure, a train-track structure-building structure coupling model is established;
[0063] S6. Consider the influence of track irregularity to calculate the wheel-rail contact force generated by train operation;
[0064] S7. Calculate the vibration acceleration time history curves of the track structure and building structure.
[0065] According to the above embodiment, preferably, in step S1, according to the train design data, the train dynamics design parameters include the body mass m of the locomotive and the trailer. c , bogie mass m t , wheelset mass m w , the moment of inertia of the car body and bogie center of mass J c and J t , stiffness and damping k of primary and secondary suspension Js , k Jp 、c Js 、c Jp , and the corresponding vehicle length L Jt and vehicle distance L J1 , bogie wheelbase L J2 .
[0066] like Figure 2 As shown in the figure, the train model consists of multiple locomotives and trailers, and each vehicle is considered as a multi-rigid spring and damping system. The mass, stiffness, and damping matrix expressions for constructing the train model are:
[0067]
[0068]
[0069]
[0070] Where N v Represents the number of vehicles constituting the train model, M vj , K vj , C vj They represent the vehicle mass, stiffness, and damping matrix that make up the train model respectively.
[0071] Further, in step S2, according to the track structure design data, the track structure design parameters include the rail elastic modulus E r , moment of inertia of rail center of mass I r , rail mass per unit length m r , rail cross-sectional area A r ; Elastic modulus of track plate E s , track plate density ρ s , track plate center of mass inertia moment I s , track plate width B s and thickness H s ; Fastener stiffness k rs and the damping coefficient c rs .
[0072] like Figure 3 As shown in Figure 1, the track model consists of a track and a track plate, where the track is composed of Bernoulli Euler beam elements and the track plate is composed of elastic thin plate elements. The track and track plate structures are connected by fasteners equivalent to springs and dampers, and the stiffness and damping matrix expressions are constructed as follows:
[0073]
[0074]
[0075] Where N rs represents the shape function of the orbital element, n p represents the total number of discrete fasteners, k rs and c rs represent the fastener stiffness and damping coefficient respectively.
[0076] Furthermore, in step S3, the train-rail contact relationship adopts Hertzian nonlinear contact, and the Hertzian nonlinear wheel-rail vertical contact force expression is:
[0077]
[0078] where q v and q r They represent the vertical displacement of the contact point between the wheel and the rail, h represents the vertical irregularity amplitude of the rail, and G represents the contact constant between the wheel and the rail.
[0079] like Figure 4 As shown, a train-track structure model is established, and its motion equation is expressed as:
[0080]
[0081] The M, C, and K in the motion equation represent the mass, damping, and stiffness matrices of the train or track structure, respectively. X represents the acceleration, velocity, and displacement vector of the train or track structure, respectively, and F v / r is the wheel-rail vertical contact force vector.
[0082] Further, in step S4, according to the building design data, the building structure design parameters include the floor density ρ f , elastic modulus of floor slab E f , the moment of inertia of the floor mass center I f , floor thickness H f , floor width W f and length L f ; Mass per unit length of structural column Elastic modulus of structural column E c , the moment of inertia of the center of mass of the structural column I c , cross-sectional area of structural column A c , length of structural column L c ; Beam mass per unit length Beam elastic modulus E bm , beam center of mass moment of inertia I bm , beam cross-sectional area A bm .
[0083] like Figure 5 As shown, the building structure model consists of concrete floor slabs, structural columns and beams, wherein the structural columns and beams are constructed using Bernoulli-Euler beam elements, and the floor slabs are constructed using elastic thin plate elements.
[0084] Furthermore, in step S5, the contact condition between the track structure and the building structure is connected by CA mortar, which is simplified into continuously distributed springs and dampers. The expressions of its unit stiffness and damping matrix are respectively:
[0085]
[0086] Where N tf represents the shape function of the track plate element, and denote the spring and damper stiffness and damping coefficient of the continuous distribution under the track plate, a and b denote half of the length and width of the elastic thin plate unit, respectively. s or f Indicates the thickness of the track plate or floor slab.
[0087] like Figure 6 As shown in the figure, a train-track structure-building structure coupling model is established, and its motion equation is expressed as:
[0088]
[0089] Among them, M total , C total , Ktotal Represent the overall mass, damping, and stiffness matrices of the coupled model, respectively. q represents the full-node acceleration, velocity, and displacement vector of the coupled model, and F represents the overall force vector of the coupled model.
[0090] Furthermore, in step S6, the influence of vertical track unevenness is taken into account to calculate the wheel-rail contact force generated by the contact between the train and the track.
[0091] Finally, if Figure 7 As shown, in the embodiment, the vertical vibration acceleration time history curves of all nodes in the building structure model are calculated by gradually integrating and solving the motion equation of the overall system, which is the prediction result of the vibration response of the building structure caused by the train operation.
[0092] Therefore, the prediction method of the present application simplifies the train into a multi-rigid body vehicle connected by multiple springs and dampers, constructs a train model, improves calculation efficiency, and establishes a building structure model that takes into account the influence of structural columns and beams, taking into account factors more comprehensively. At the same time, the influence of vertical unevenness of the track, that is, the role of the vibration source, is considered, and the prediction results obtained are more accurate and reasonable.
[0093] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for predicting the vibration response of a building structure caused by train operation, characterized in that: The following steps are involved: S1. Obtain train dynamics design parameters and establish a train model; S2, obtaining track structure design parameters and establishing a track model; S3. Using the train-track contact relationship, establish a train-track structure model; S4, obtaining the design parameters of the building structure at the operating location and establishing a building structure model; S5. Using the contact conditions between the track structure and the building structure, a train-track structure-building structure coupling model is established; S6. Consider the influence of track irregularity to calculate the wheel-rail contact force generated by train operation; S7. Calculate the vibration acceleration time history curve of the track structure and the building structure; The train dynamics design parameters in step S1 include the body mass m of the locomotive and trailer c , bogie mass m t , wheelset mass m w , the moment of inertia of the car body and bogie center of mass J c and J t , stiffness and damping k of primary and secondary suspension Js ,k Jp ,c Js ,c Jp , and the corresponding vehicle length L Jt and vehicle distance L J1 , bogie wheelbase L J2 ; In step S1, the train model consists of multiple locomotives and trailers. Each vehicle is considered as a multi-rigid spring and damping system. The mass, stiffness, and damping matrix expressions of the train model are: Where N v Represents the number of vehicles constituting the train model, M vj , K vj , C vj They represent the vehicle mass, stiffness, and damping matrix that make up the train model respectively; The track structure design parameters in step S2 include the rail elastic modulus E r , moment of inertia of rail center of mass I r , rail mass per unit length Rail cross-sectional area A r ; Elastic modulus of track plate E s , track plate density ρ s , track plate center of mass inertia moment I s , track plate width B s and thickness H s ; Fastener stiffness k rs and the damping coefficient c rs ; In step S2, the track model consists of a track and a track plate, wherein the track is composed of a Bernoulli Euler beam unit, and the track plate is composed of an elastic thin plate unit. The track and the track plate structure are connected by fasteners equivalent to springs and dampers. The stiffness and damping matrix expressions constructed are respectively: Where N rs represents the shape function of the orbital element, n p represents the total number of discrete fasteners, k rs and c rs represent the fastener stiffness and damping coefficient respectively; In step S3, the train-rail contact relationship adopts Hertz nonlinear contact, and the Hertz nonlinear wheel-rail vertical contact force expression is: where q v and q r They represent the vertical displacement of the contact point between the wheel and the track, h represents the vertical irregularity amplitude of the track, and G represents the contact constant between the wheel and the track; In step S3, a train-track structure model is established, and its motion equation is expressed as: The M, C, and K in the equation of motion represent the mass, damping, and stiffness matrices of the train or track structure, respectively. X represents the acceleration, velocity, and displacement vector of the train or track structure, respectively, and F v / r is the wheel-rail vertical contact force vector; The building structure design parameters in step S4 include floor density ρ f , elastic modulus of floor slab E f , the moment of inertia of the floor mass center I f , floor thickness H f , floor width W f and length L f ; Mass per unit length of structural column Elastic modulus of structural column E c , the moment of inertia of the center of mass of the structural column I c , cross-sectional area of structural column A c , length of structural column L c ; Beam mass per unit length Beam elastic modulus E bm , beam center of mass moment of inertia I bm , beam cross-sectional area A bm ; In step S4, the building structure model is composed of a concrete floor slab, structural columns and beams, wherein the structural columns and beams are composed of Bernoulli Euler beam units, and the floor slab is composed of elastic thin plate units; In step S5, the contact condition between the track structure and the building structure is connected by CA mortar, which is simplified into continuously distributed springs and dampers. The expressions of its unit stiffness and damping matrix are: Where N tf represents the shape function of the track plate element, and are the spring and damper stiffness and damping coefficient of the continuous distribution under the track plate, a and b are half of the length and width of the elastic thin plate unit, respectively. sorf Indicates the thickness of the track plate or floor slab; In step S5, a train-track structure-building structure coupling model is established, and its motion equation is expressed as: Among them, M total , C total , K total Represent the overall mass, damping, and stiffness matrices of the coupled model, respectively. q represents the full-node acceleration, velocity, and displacement vector of the coupled model, respectively, and F represents the overall force vector of the coupled model; In step S6, the impact of track vertical irregularity adopts the American six-level spectrum and considers short-wave irregularity. Its power spectrum density expression is: Among them A v =3.39×10 -6 m 2 / (rad / m),Ω c =0.8245rad / m, Ω is the cut-off frequency range. According to the power spectrum density, the trigonometric series method is used to calculate the vertical irregularity amplitude of the generated track, and the wheel-rail contact force generated by the contact between the train and the track is calculated; The vibration acceleration time history curves of the track structure and the building structure described in step S7 are the vibration responses of the track structure and the building structure.