A method and system for predicting three-dimensional vibration response of a building
By calculating the dynamic stiffness matrix of the frame-shear wall structure and installing vibration damping supports, the problem of micro-vibration of buildings caused by urban rail transit was solved, achieving accurate prediction of the three-dimensional vibration response of buildings and vibration reduction effect.
Patent Information
- Application Number
- CN202211611839.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-12-14
- Publication Date
- 2026-02-13
- Estimated Expiration
- 2042-12-14
AI Technical Summary
Existing technologies are insufficient to effectively predict and mitigate the impact of micro-vibrations in buildings caused by urban rail transit on precision instruments and residents' rest, and there is a lack of effective vibration reduction measures.
By obtaining the dynamic stiffness matrix of each component in the frame-shear wall structure, the displacement response of the building is calculated, and vibration damping supports are installed at the bottom of the building to reduce vibration. The stiffness design of the vibration damping supports is used to meet specific frequency conditions for vibration reduction.
It enables accurate prediction and effective vibration reduction of the three-dimensional vibration response of buildings, reducing the impact of micro-vibrations on precision instruments and residents' lives.
Smart Images
Figure CN115982812B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of construction, specifically to a method and system for predicting the three-dimensional vibration response of buildings. Background Technology
[0002] Frame-shear wall structures are currently a mainstream building structural form. Vibrations generated by urban rail transit vehicles (such as subways, light rail, and intercity railways) during operation are transmitted to buildings through the track structure, tunnels, and soil, causing micro-vibrations. These micro-vibrations do not damage the building structure, but they may affect the normal use of precision instruments and residents' rest. Therefore, predicting the vehicle-induced vibration response of buildings before the construction of transportation lines or buildings, and taking corresponding vibration reduction measures based on the prediction results, is particularly important. Summary of the Invention
[0003] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for predicting the three-dimensional vibration response of a building, comprising the following steps:
[0004] Step 1: Obtain the dynamic stiffness matrix of the four components—columns, beams, floor slabs, and shear walls—in the frame-shear wall structure of the building. Assemble them according to the spatial geometric coordinate relationships to obtain the dynamic stiffness matrix of the building [D]. G ;
[0005] Step two, based on the external force load vector [F] G And the dynamic stiffness matrix of the building [D] G The displacement response vector [X] of the building is obtained. G ;
[0006] Step 3: Based on the obtained displacement response vector [X] of the building. G The building displacement response is obtained, and based on the building displacement response, a strategy of installing vibration damping supports at the bottom of the building is adopted for vibration reduction.
[0007] Furthermore, the dynamic stiffness matrices of the four components—columns, beams, floor slabs, and shear walls—in the frame-shear wall structure of the building are obtained, and then assembled according to the spatial geometric coordinate relationships to obtain the dynamic stiffness matrix [D] of the building. G ,include:
[0008] For columns and beams in a building subjected to axial forces, the longitudinal vibration dynamic stiffness matrix of the rod element is obtained based on the longitudinal frequency domain vibration equation of the rod element:
[0009]
[0010] In the formula, L b A b, These are the length, cross-sectional area, and complex modulus of elasticity of the rod element, respectively; k l Indicates the longitudinal wave number of the rod element;
[0011] For columns and beams in a building subjected to torsion, the torsional dynamic stiffness matrix of the bar element is obtained based on the torsional frequency domain vibration equation:
[0012]
[0013] In the formula, I p , These are the polar moment of inertia and complex shear modulus of the rod element section, respectively; k t Indicates the torsional wavenumber of the rod element;
[0014] For columns and beams in a building subjected to bending forces, the bending vibration dynamic stiffness matrix of the bar element can be obtained based on the bending frequency domain vibration equation:
[0015]
[0016] The elements in the matrix are represented as follows:
[0017]
[0018] In the formula, I b k b These are the moment of inertia and bending wave number of the bar element section, respectively.
[0019] For floor slabs and shear walls subjected to out-of-plane bending in buildings, the out-of-plane dynamic compliance matrix of the thin plate element is obtained based on the out-of-plane frequency domain vibration equation:
[0020]
[0021] Elements in the matrix
[0022]
[0023] This represents the out-of-plane displacement at point l of the thin plate when an out-of-plane unit force is applied at point k. The inverse matrix of the out-of-plane vibration dynamic compliance matrix is taken to obtain the out-of-plane vibration dynamic stiffness matrix of the plate element.
[0024] For in-plane extended floor slabs and shear walls in buildings, the in-plane vibration dynamic compliance matrix of the thin plate element is obtained based on the in-plane frequency domain vibration equation of the thin plate element:
[0025]
[0026] Elements in the matrix
[0027]
[0028] This represents the in-plane displacement at point l of the thin plate when a unit force is applied at point k in the same plane. The in-plane dynamic stiffness matrix of the plate element can be obtained by taking the inverse of the in-plane dynamic compliance matrix.
[0029] The dynamic stiffness matrices of the four components—columns, beams, floor slabs, and shear walls—in the obtained frame-shear wall structure are assembled according to spatial geometric coordinate relationships to obtain the dynamic stiffness matrix of the entire building [D]. G .
[0030] Furthermore, the statement regarding the external force load vector [F]... G And the dynamic stiffness matrix of the building [D] G The displacement response vector [X] of the building is obtained. G The following formula is used:
[0031] {F} G =[D] G {X} G .
[0032] Furthermore, the displacement response vector [X] of the obtained building is used as a basis. G The building displacement response is obtained. Based on the building displacement response, a strategy of installing vibration damping supports at the bottom of the building is adopted for vibration reduction, including:
[0033] [X] G Let be a function vector of frequency ω. If the displacement response of the building at a certain frequency ω0 is greater than a set value, a strategy of installing vibration damping supports at the bottom of the building is adopted for vibration reduction; when the excitation frequency is greater than the natural frequency of the building's rigid body... When the vibration damping bearing is doubled, it can reduce the vibration of the building;
[0034] Let the stiffness of the vibration damping support be k, and the mass of the building be m. Then the natural frequency of the building's rigid body is: That is, it should satisfy:
[0035]
[0036] From the above formula, the stiffness of the vibration damping support can be obtained as follows:
[0037]
[0038] A prediction system for the three-dimensional vibration response of a building, which applies a method for predicting the three-dimensional vibration response of a building, includes a data processing module, a load application module, and a data acquisition device; the load application module and the data acquisition device are respectively connected to the data processing module; the data processing module stores the prediction method for the three-dimensional vibration response of a building as described in claims 1-4.
[0039] The beneficial effects of this invention are: this invention can calculate the vibration response of the shear wall in a frame-shear wall structure building, obtain the building displacement response based on the vibration response, and adopt a strategy of installing vibration damping supports at the bottom of the building to reduce vibration based on the building displacement response. Attached Figure Description
[0040] Figure 1 This is a flowchart illustrating a method for predicting the three-dimensional vibration response of a building.
[0041] Figure 2 This is a schematic diagram of a frame-shear wall structure.
[0042] Figure 3 Flowchart of the analytical method for three-dimensional vibration response of buildings;
[0043] Figure 4 This is a schematic diagram of the displacement response in the X direction;
[0044] Figure 5 This is a schematic diagram of the displacement response in the y-direction;
[0045] Figure 6 This is a schematic diagram of the displacement response in the z-direction. Detailed Implementation
[0046] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the following description.
[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention; that is, the described embodiments are only a part of the embodiments of the invention, and not all of them. The components of the embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.
[0048] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention. It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations.
[0049] Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.
[0050] The features and performance of the present invention will be further described in detail below with reference to embodiments.
[0051] like Figure 1 As shown, a method for predicting the three-dimensional vibration response of a building includes the following steps:
[0052] Step 1: Obtain the dynamic stiffness matrix of the four components—columns, beams, floor slabs, and shear walls—in the frame-shear wall structure of the building. Assemble them according to the spatial geometric coordinate relationships to obtain the dynamic stiffness matrix of the building [D]. G ;
[0053] Step two, based on the external force load vector [F] G And the dynamic stiffness matrix of the building [D] G The displacement response vector [X] of the building is obtained. G ;
[0054] Step 3: Based on the obtained displacement response vector [X] of the building. G The building displacement response is obtained, and based on the building displacement response, a strategy of installing vibration damping supports at the bottom of the building is adopted for vibration reduction.
[0055] The method described above obtains the dynamic stiffness matrix of the four components—columns, beams, floor slabs, and shear walls—in a frame-shear wall structure of a building, and assembles them according to spatial geometric coordinate relationships to obtain the dynamic stiffness matrix [D] of the building. G ,include:
[0056] For columns and beams in a building subjected to axial forces, the longitudinal vibration dynamic stiffness matrix of the rod element is obtained based on the longitudinal frequency domain vibration equation of the rod element:
[0057]
[0058] In the formula, L b A b , These are the length, cross-sectional area, and complex modulus of elasticity of the rod element, respectively; k l Indicates the longitudinal wave number of the rod element;
[0059] For columns and beams in a building subjected to torsion, the torsional dynamic stiffness matrix of the bar element is obtained based on the torsional frequency domain vibration equation:
[0060]
[0061] In the formula, I p , These are the polar moment of inertia and complex shear modulus of the rod element section, respectively; k t Indicates the torsional wavenumber of the rod element;
[0062] For columns and beams in a building subjected to bending forces, the bending vibration dynamic stiffness matrix of the bar element can be obtained based on the bending frequency domain vibration equation:
[0063]
[0064] The elements in the matrix are represented as follows:
[0065]
[0066] In the formula, I b k b These are the moment of inertia and bending wave number of the bar element section, respectively.
[0067] For floor slabs and shear walls subjected to out-of-plane bending in buildings, the out-of-plane dynamic compliance matrix of the thin plate element is obtained based on the out-of-plane frequency domain vibration equation:
[0068]
[0069] Elements in the matrix
[0070]
[0071] This represents the out-of-plane displacement at point l of the thin plate when an out-of-plane unit force is applied at point k. The inverse matrix of the out-of-plane vibration dynamic compliance matrix is taken to obtain the out-of-plane vibration dynamic stiffness matrix of the plate element.
[0072] For in-plane extended floor slabs and shear walls in buildings, the in-plane vibration dynamic compliance matrix of the thin plate element is obtained based on the in-plane frequency domain vibration equation of the thin plate element:
[0073]
[0074] Elements in the matrix
[0075]
[0076] This represents the in-plane displacement at point l of the thin plate when a unit force is applied at point k in the same plane. The in-plane dynamic stiffness matrix of the plate element can be obtained by taking the inverse of the in-plane dynamic compliance matrix.
[0077] The dynamic stiffness matrices of the four components—columns, beams, floor slabs, and shear walls—in the obtained frame-shear wall structure are assembled according to spatial geometric coordinate relationships to obtain the dynamic stiffness matrix of the entire building [D]. G .
[0078] The aforementioned is based on the external force load vector [F]. G And the dynamic stiffness matrix of the building [D] G The displacement response vector [X] of the building is obtained. G The following formula is used:
[0079] {F} G =[D] G {X} G .
[0080] Furthermore, the displacement response vector [X] of the obtained building is used as a basis. G The building displacement response is obtained. Based on the building displacement response, a strategy of installing vibration damping supports at the bottom of the building is adopted for vibration reduction, including:
[0081] [X] G Let be a function vector of frequency ω. If the displacement response of the building at a certain frequency ω0 is greater than a set value, a strategy of installing vibration damping supports at the bottom of the building is adopted for vibration reduction; when the excitation frequency is greater than the natural frequency of the building's rigid body... When the vibration damping bearing is doubled, it can reduce the vibration of the building;
[0082] Let the stiffness of the vibration damping support be k, and the mass of the building be m. Then the natural frequency of the building's rigid body is: That is, it should satisfy:
[0083]
[0084] From the above formula, the stiffness of the vibration damping support can be obtained as follows:
[0085]
[0086] A prediction system for the three-dimensional vibration response of a building, which applies a method for predicting the three-dimensional vibration response of a building, includes a data processing module, a load application module, and a data acquisition device; the load application module and the data acquisition device are respectively connected to the data processing module; the data processing module stores the prediction method for the three-dimensional vibration response of a building as described in claims 1-4.
[0087] Specifically, for columns and beams in a building subjected to axial forces, the longitudinal vibration dynamic stiffness matrix of the rod element is derived based on the longitudinal frequency domain vibration equation of the rod element:
[0088]
[0089] In the formula, L b A b , These are the length, cross-sectional area, and complex modulus of elasticity of the rod element, respectively; k l This indicates the longitudinal wave number of the rod element.
[0090] For columns and beams in a building subjected to torsion, the torsional vibration dynamic stiffness matrix of the rod element is derived based on the torsional frequency domain vibration equation of the rod element:
[0091]
[0092] In the formula, I p , These are the polar moment of inertia and complex shear modulus of the rod element section, respectively; k t This indicates the torsional wave number of the rod element.
[0093] For columns and beams in a building subjected to bending forces, the bending vibration dynamic stiffness matrix of the rod element is derived based on the bending frequency domain vibration equation of the rod element:
[0094]
[0095] The elements in the matrix are represented as follows:
[0096]
[0097] In the formula, I b k b These are the bending wave number of the moment of inertia of the bar element section.
[0098] For floor slabs and shear walls subjected to out-of-plane bending in buildings, the out-of-plane dynamic compliance matrix of the thin plate element is derived based on the out-of-plane frequency domain vibration equation:
[0099]
[0100] Elements in the matrix
[0101]
[0102] This represents the out-of-plane displacement at point l of the thin plate when a unit out-of-plane force is applied at point k.
[0103] By taking the inverse of the out-of-plane vibration dynamic flexibility matrix, the out-of-plane vibration dynamic stiffness matrix of the plate element can be obtained.
[0104] For in-plane extended floor slabs and shear walls in buildings, the in-plane vibration dynamic compliance matrix of thin plate elements is derived based on the in-plane frequency domain vibration equation of the thin plate element:
[0105]
[0106] Elements in the matrix
[0107]
[0108] This represents the in-plane displacement at point l of the thin plate when a unit force is applied at point k within the same plane.
[0109] By taking the inverse of the in-plane vibration flexibility matrix, the in-plane vibration stiffness matrix of the plate element can be obtained.
[0110] The dynamic stiffness matrices of the four components—columns, beams, floor slabs, and shear walls—obtained in the first four steps of the frame-shear wall structure are assembled according to spatial geometric coordinate relationships using a method similar to the "matching" rule in the finite element method, thus obtaining the dynamic stiffness matrix of the entire building [D]. G .
[0111] Based on the known external force load vector [F] G Then the displacement response vector of the building is [X]. G It can be obtained by solving the following equation:
[0112] {F} G =[D] G {X} G
[0113] This prediction method can calculate the building's frequency domain displacement response [X]. G [X] G It is a function vector with respect to frequency ω. If the building's displacement response is large at a certain frequency ω0, vibration reduction can be achieved by installing vibration damping supports at the bottom of the building. According to the design principle of vibration damping supports, after the building is equipped with vibration damping supports, when the excitation frequency is greater than the natural frequency of the building's rigid body... When the vibration damping bearing is doubled, it has a good vibration damping effect.
[0114] Let the stiffness of the vibration damping support be k, and the mass of the building be m. Then the natural frequency of the building's rigid body is: That is, it should satisfy:
[0115]
[0116] From the above formula, the optimal stiffness of the vibration damping support should be designed as follows:
[0117]
[0118] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.
Claims
1. A method of predicting the three-dimensional vibrational response of a building, characterized by, comprising the steps of: Step one, obtain the dynamic stiffness matrix of the column, beam, floor and shear wall in the frame-shear wall structure of the building, assemble according to the spatial geometric coordinate relationship, and obtain the dynamic stiffness matrix [D] of the building G , comprising: for the column and beam in the building subjected to axial action, obtaining the longitudinal vibration dynamic stiffness matrix of the rod element according to the longitudinal frequency domain vibration equation of the rod element; for the column and beam in the building subjected to torsion, obtaining the torsional vibration dynamic stiffness matrix of the rod element according to the torsional frequency domain vibration equation of the rod element; for the column and beam in the building subjected to bending, obtaining the bending vibration dynamic stiffness matrix of the rod element according to the bending frequency domain vibration equation of the rod element; for the floor and shear wall in the building subjected to out-of-plane bending, obtaining the out-of-plane vibration dynamic flexibility matrix of the thin plate element according to the out-of-plane frequency domain vibration equation of the thin plate element; taking the inverse matrix of the out-of-plane vibration dynamic flexibility matrix to obtain the out-of-plane vibration dynamic stiffness matrix of the plate element; for the floor and shear wall in the building subjected to in-plane stretching, obtaining the in-plane vibration dynamic flexibility matrix of the thin plate element according to the in-plane frequency domain vibration equation of the thin plate element; taking the inverse matrix of the in-plane vibration dynamic flexibility matrix to obtain the in-plane vibration dynamic stiffness matrix of the plate element; Step two, according to the external force load vector [F] G , and the dynamic stiffness matrix [D] of the building G , to obtain the displacement response vector [X] of the building G ; Step three, obtaining the displacement response of the building according to the obtained displacement response vector [X] G of the building, and damping the building by installing damping supports at the bottom of the building according to the displacement response of the building, including: a displacement response vector [X] G of the building, wherein the displacement response vector [X] G is a function vector of the frequency ω, and if the displacement response of the building at a frequency ω0 is greater than a set value, damping the building by installing damping supports at the bottom of the building.
2. The method of claim 1, wherein, The external force load vector [F] G , and the dynamic stiffness matrix [D] of the building G , to obtain the displacement response vector [X] of the building G , using the following formula: [F] G = [D] G [X] G .